I ILLINOIS

Production Note
Digital Rare Book Collections
Rare Book & Manuscript Library
University of Illinois Library at
Urbana-Champaign
2020
 
 
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LIBRARY OF THE
UNIVERSITY OF ILLINOIS
AT URBANA—CHAMPAIGN

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2 § A N ,D _
E i‘ M0fi-‘\V0§£I1i1y Honoured *
jPRIEND
3052’ IS DE. WIE ,
MFRCPANT & CITIZEN f
I O F 3 a
jflMES EJOQDER

L in token of Tme Gratitude for
I, \ ’ _L1nmerittcd Kindnc flag

I HMMBLY DEUICAWHJ

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Marla/ll qf Aiztf’memk

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To the Reader

fining for fitndry year: lqut a
' Writing Schoolin tho; City, and

 

that commendable Art,1!honght

' go'o'd heretofore to pnbhflyflomewhat thereofié

And now for the better completing ofTottth
a: to Clorkjhig anti Tradet, I am zna’aceo! to
pabz’zflo this final! Treatife of Arithmetick,

which then 1h It be dedicated more particularly '

to my mach hononred F reend ,yet being aflared
he can be content that other: fhmla’ partake of
the benefit thereof, I make bola’ thn: to 6'0me-
nioate it.

I neea’ not go about to [peak any thing on
praije of Antwan/{int [hall willingly fabmit
what is here treated of; to the candid eenfare
of the more jadecioa/ly sbilfnl ~

And at I jhall condemn no Man: a'ilo' genee in
what he hath formerly done,fo I think none will
blame my ena’eanoar: at the orgefent for though
I know it impoflible to ple zfi: every Man, and
therefore am not folhcztooa how to do it , yet ac.
cording to the ability which God hathginen me,
I have labonred to ”We a more clear difoonery

thereby gatnea’ fame experience in '

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To the Reader;

of fime Intricncies in” this Art, thntzto my
, knowledge hath hitherto been. Whichperhttp:
may not feem to heft: ant infognllnnt d drefs 44 '
fame ather5,lmt I dare nwrrta be done with»; , ';
much plainefi, facility, and jhortnefi, at: any V ”7"
that I hn'wye: ahft’med. ‘ 7 , ’7 ,

‘T/m: not fearing, Gentle Render, lefl any
EMnn fhattltl [cam my thottrx, hecnnfé I
fleem to undervalue them by letting others ,
have the nfe, profit, and plenfitre thereof
ttt fa fmnll t3 rate, I refirr my filf and
-them to thy canfidemti‘an; and if nfier pe-
rtifnl and trynl made, than kindly accept what
I lovingly afar, it fim/l abundantly fiztitfie him
that is devoted to fame God, and profit
when in his C tailing, and alt/ire to remain,

 

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' Ready to pleafuretheemhether
known or unknown to

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T136 Cort/{8‘02” to the @gader.

 

I Inca this Arithmetick came out, it hath
‘ ‘ Efficientlydemonfitated to the World
its Utiiitv and fatih: IVIrztht'nfl'9 and that:—
fore needs 110. further Commendatien‘than
What the Learner (through'éts cafic lnfi‘tu—
Ctions) may have taufe to give it.

'A’nd yet mtwithflanding theVVorld hath
becn‘fixlly fatisfied Wifh the Mtthofi there- .
of; manyhavehcen laid unietgteat difen—
/ couragements (fortze through Egnarance bias
ming the Author)“ for multitudts of Fauhs
that had crept in by the neg-31655} of the
Prei's gand form: by prs‘tending to a perfcfii-
on in the-fetid Amb'cforc they have attainéd
to it, by a praaicfl‘hahit,

Now (Courteous Reader) thou mayet’c
cheetfuhy go 011,311 its former Esrrors being
purged from it, and fame more‘Light givtn
toith being augmented in {évm‘al piacss'
,w‘hergc occafionifor thy t‘tkc) did require; ‘
and that it may anftm‘ thy Expeétations is

the dcfire ofhim who is aLover of Ingeni-
OUS Arts, / "

 

 

 

 

 

 

 

 

 

 

 

 
  
 
 
 
 
 
  
     
 

L \

HE NR2? MOSE.

  
 
 

§ To my Ingenious Friend Mr.I-1enry Mafia,
“ upon his Amendments to Mtj‘amet,
Hodtler’s Arithmetick.

Til-7’13: C ritz'cleflge exclaa’es thing: Olefelete,
; [Vow izezljiag take: wanting a Dre/5 com—
ii. Beauty tlaoagla aaaa’om’d is Beaaty fltll,(plete.
fr Earle/fa wittb Sievleatlor captivate: each Will.
3' 30 I06 flml‘ Wettltl earejk (bit kzzowisig‘ flge,
i~ .Aml meant to appear in Print upon the Stage,
(E‘v’n in tbitHarwfl time,wbenLearaing,/1rts
' And Witt are ripe, and th-efal'elimefl part:
117‘: new arriv’a at what they can afpt're,
At which Age: to come may well admire,)
Ma/l emalate what hath been a’aae before,
Aadmafler tltofe flcqairemenumhicla in flat:
Lay dormant. 7791}: My Pen loath/”ally done;
Tla’hafl added to his Fame, and to thy own,
For amplzfyt'ng let's elaborate Piete,
Multiples: thy Wort/9, 770! Subtrafliag his,
Imbelltflting the Week, is to create
A la/liqg pygmy in aefpite of F ate.
“The Aatlaart mantle detl) itzvelop tlaee,
flatl when the fataregratefal Agefltallfee,
'2 [eat [7y Acemnpliflmmtt tlaoa a’ofi‘ inherit
7/} doul'tle pattioa of thy Mafiert Spirit;
Poflerityflta/l make account it am:
To L‘Ioddtrrs Memwyfiat mach more to Mofc.

S. HODDER.

 
     

  

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A Table {hewing the Cements “it
of this BOOk._

‘ . Chip. I. ‘ _ ,
H E ’iZD’efiz/itz'orz 0f Dizmzéers Md 1%!»ch
ration, wit/9 an mfi Taézic Manama {ae-
(longing. ‘ ‘

 
          

Chap“ 2- Addition of Money,fl4€flfi!7€f,a
Weights, rjuc.‘ ‘ , ' ~
ha p. 3 . Sul’az‘mfiz‘m of I’Mamy, [flezflwm
VVeighn, m. 1- '
4 Chap. 4.. Zl'fidtiplimtionfiifla £595 54% there-
of, laid down 2'22 a plain and mfié [Merlzzad‘
' for youflg Lemma; new? t’fc‘faw 6302293: I
. -.Chap. 5. Dix/{flan the cczmmw W293 and the
ufi” ibereof‘, fil/bflfifihér IV” 0f 9mm mars: ,
' «17rz'ef, mj’z‘emrd [Marni \
’Chap. 6. 4366115552072 cffl/ifwe’y; film/fires,
M/c‘égr’m, (‘96. With "WW {[5 3375‘)“ ’0 fim‘: 0”” ‘

      
   
     

     
   
   
  
 
 
 
 
   

 
  

~v ‘ j
the 'i’ are and Nut. ‘

Chap. 7. W194! Frrzfiim! are, 120w- MPH/F;
and ricefi-vemljbrf: thereof. \ ‘

Chap; 8. Rw’zzfiign amegfiiam :, mic-2’ why
Rea'pzflm 275 before Addm'm. » ~ ,

Chap. 9.'Aafa{ir'io7z offmffémj the can/Imam
way, 42ml! 93 two orbsr may: more mapédiem.
Qhap.‘ ’3 o. Sas’azmfiian amec‘iLéam.

It‘-

      

  
 
 

. \

 

Chap,

  
   
 

M ’f‘fifiir.‘ maggosv‘ 5*- "w B" "
‘1': ’V'~‘ -.' ".'- Pv' . ., -' ' W" V‘, 'P

The Contents.

5f Chap. x1. Mnlrépliention of F'eec‘l‘imo

Chap. 1 2. Dz’wfien of Freeliom.‘
Chap. 13. The Keefe of Three climb} nnd

indireél, in wloole Nnmbers, wrongbtfonr fewe-

‘w, ”41",.

ml way; with n direflion bow to war/Q any
glee/lion npon tloe Rule of Three, witbono
troubling tbe bend with tbe elzfiinflion of
Direé} nnol Indira/SE. - ;
Chap. 14.. The Rnle of‘Tbree in Fmfiions.
Chap. 13. Profile: with very plain and

‘ enfie Tables.

Chap. 16. Tbe DoubleRnle of Three, eon-
fifling of fi-veNnmbe'rs. ,
Chap. 17, Very brief Rnle: for Interefl,

and Interefl upon [mere/I; nlfo by zbelbelp ofn -

plnz‘n Table to know wbet any S nm of [Money
come: to, [mere/l upon Interefi,fo7’ 21 Tears er

1 ‘ under, at one working by the Rnle of ' ‘Tlobee. '-

flnotber Table to know wbnt any flnnnity
will nmonnt nnto for the fame time, est one,

working by tbefnz'ol Rule.

Chap. 18. The Rule ofFelloij-ip or Com: ,

Pan} Without time, nndfillowlbip with time.
Chap, 19. The Rule oanrter. . l *
Chap” 20. Equation of Timefor Payment

of [M ‘

u Rebate or 13110an
’ ’ 22;, Exchange of Money from one
4, meneermndto kiwi? retwwlontfnze
1:? e

   

 
 
 
  

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The Contents.

the €xcharge i: made either of Mame}! 0e,
’ W437.

Chap. 23. T a know what isgainedor [off :1
per cent. in thefale of any Commodity tit/Itch? '
a price; and what it met]? he bea’ for regain or ‘
lofe fa much per cent. Lilqewzfe hen/inggezihed ,'
or loflfi) much per cent. to know what it cofl.

And having gainedfo much per cent. when
[bid at [Each aprice, what [hall hegained or [a]?
whenfo/d at emolher price. _

Chap. 24. Allegatim M6541 and Alter?
mte.

Chap. 2 5. lee/freeman: fir the mmfmiexg
of anyShperfiez'ee, m Baard,Glef1,Hangiqg:,
Pavemeem, C517. AI ell/b the Meet/bring Sr
lids, ea Timber, Stone, 6'0. ,

    
     
   
   
   
   
    
     
   
     
    

 

A72 Advertg'fiément.

Writing, Arithmetick in Whole Numbers
and Fraétions, Vulgar and Decimal, and
Merchants Accompts, are carefully taught

in Sherham Lane near Lombard/freer,

By £1}:er M0551.

 
 
   

..... 111111

I

1161161111111111111
CH A P1 I.
' The De/firzition pf Number.

Number is a multitude of Units

put togethcr, 11521, 3, 4., 3, 6,62%.

Thcrcfore an Unit is properly

no Number, but the original or '

beginning ofNumber, for It being multipli-

cd or divided by 1t icli is rclo!vcd agam

‘ into it felt, Without any incrcaiemcnt or
decrcafcmcnt.

NU ME 1e AT Io'N.
Numeration is that part of Arithmetick

. whereby one may rightly vaiue, exp cfs,
and write any Numbcr or Sum propoun-

‘: dcd

   

To the attaining whereof obfcrve, that
all Numbers are cxprcfiied by thefc Chara-
ficrs following , whoic fimplc vaJuc Qy
B 1111-1111
'v‘v- ~. V
f ~ 3‘» n.->~*- N

2 é‘aétrafiiozz. Chat-9.111. '7 _

themfelves confidered, youmay‘here take
notice of.

one, two, three, four, fivafixJe'ven, eight, 7211716, Cypbef- f

12. 345678/9CS

The Cypher ferveth to make up the num- '
ber of places, but of it felt: fignifieth no-
thing. ' N f ' ‘ a,

Every figure hath two values, whereof ‘
one is always certain, and hath its own fig-
nification', but the » Other is uncertain, by
reafon of the uncertainty of the place where '
itmay happen tofiani 'V > ' ‘

A7 place we cemmonly call a {pace in
which a figure {tandeth gand look how many
\ figures there are, to many places there

‘ are by which they are valued.

Every figure in the firfi place [imply Be—
tokeneth it fell“, but in the fecond place,
whichis towards the left hand ,it is ten times

f6 much aslitwas in the place before, and

fo inereafeth its value according to its place,
as you may fee in the Table following. '

 
  

 
   
  
  
  
  
 
 
  
   
  
  
  
 
   

Chap. I. Namemtz'efi,

Numeration Table, .

h; .' «4,»;

«£23 Egg .

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pt. hawfi©°§ku

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k 9 87.6 54.3 2 .t l The tfi place.

l3 9 8 7:6 54- 3 2 I ‘ 98‘7mi1-65M2m. 2:: '
f2 9 3:76 5- 43 2 l 98 mil. 76g rh024;74%§z
9. 8 76. 54.3 t 9 mil. 876 than.” 543

 

 

 

 

 

 

9 8 7-‘6 s 4 98713190142272! w» 6S4

3‘ The 98.76:; 98tbmfarzd 76;

E left hand 9. 8 7 5 9 thou/Md ’ 856 ,

f 1 2 987 l "A ”907»

. 9 8 I mm.“ 98
9 wwwwmfi 9

E Which you mufk’t read beginning from
the 121?: place on the left hand, and pr’oceed-
ing to the firfi at the right, on this manner
1 "viz. Nine hundred eighty'fevenmillions
Six hundred fifty four thoufzmd, Three hun— Z;
dr’ed twenty one. V , k k *
' ‘And for the better underl’tanding of
the Table, obferve that the fixfi figure
next the right hand is the place of 11-}
nits, and fignifies but hélsfiqwn fingle‘ '
value ;k as the figure of 1 but"One,""“’2fibut
B 2 time,

. ,-,,rw~r~w~w~f‘ , ,

  

' ‘ f‘wk‘,w-ekv wkaw ~
  
   

' «, 3‘5. . inc r-—.l.’ "Jka ,

  

4, Numeratim. Chap. I.

two, 3 but three 69%. Butwhere two or

. more figures are ioynedtogether,the figure
in the lecond place towards theleft hand
betokeneth his own fingle value ten times ;
and f0 in the third place fignifies his own
value an hundred timesain the fourth place
a thoufand times.

     
   
    
     

Example. 6 in the fourth place is {ix l
thouland, 6 in the third place is {ix hun—
dred, 6 in the ninth place is 6 hundred
millions.

And thus you fee the value of the fi-
gure is- according to the placeitfiandeth
in.

The names of the places therefore you
mull hefure to get by heart.

To help you in the expreffng of great
7 numbers, you may make a Period or Prick
With «your Pen between every three figures
beginn'ng at the right hand; as in this Ex-
ample.

i 123. 456. 789. Here you fee is one
hundred 'l‘wenty three, four hundred fifty
l fix, lie-fen hundred eighty nine. Thus you
muff esprefs all figures, But to know the
‘ll Value of them, you mu-l’t begin at the-right
é hand and reclaon towards thelef‘t, accord.
l : ing to the precedent Table, and you will
1 find
l _

   

l
l

 
  

rChap. II. Numemtion ' 5
. 56nd them to be one hundred twentv three
1-1" millions, four hundred fifty fix thouiand 1e—

  

ven hundred eighty nine.

There are three forts of Numbers:
, 1. A Digit.
L 2. An Article
1 - 3. A Mixt or Compound.

All numbers not exceeding the nine:
Units are called Digits , as I, 2, 3,4, 5,6
73,839

Articies be numbers confifling ofa Digit
and aCyphcr, as 10, 20, 30, 40, 50,60,
6‘0.

A Compound is a number confii’ting of
both.', as 13, 14-, 15,16,17, (five

fl

'1

 

c HAP. 11.
ADDITION,

I
1
1'1
11
1

Withmt the leflér Denominations. 1

0'" I begh to acqnw at you with the I
E wn king 02: anv of Ike Ruie~toII?w- ‘
1 _ i115}, I ‘1 II all a o g in their proper pla-
‘ ce ) 5 ii hew voutneb: nature and meaning
'of he Rules, and fecondly the manner of
theit Working.

 
 
 

 

 

 
 

2.“

3:3 ' ' What

 
K r—

Chap. IL

 

What Additim tem‘hetk.
Addition teacheth you to add two or
more {moms together, to make themone
Et’holfl or total fem, viz. ~"
Example. _

Received at feverel timesthefe partichat

taxis {ottow‘mg .
At one time-~:-———-w-—~—- 3—4 I

 

 

 

At another time 1, “MM 1 58'"

' More Mm“ ““217”
More _..._...,_._,_____. , MM 5‘95
More—m»

 

—---- --~~eI79
I defire to know how . w....m.,
much was receiVed in all 1491
I. For the Working of this, and all others

 

of this kind, you muff begin with the. firfl;

or lowetmofi figure at your right hand,
faying , 9, 6, 7, 8, and 1, makes 31; then
fet down the 1 inaLine’underneath, and
carry the 3 unto the next place, where 7, 9,
I , g4, and 3 that I carried make 29,Which
foé‘t down, and carry thezunto the next
piaee towards your left hand, faying, 1,3, 2.,
1, 3, and 2; that ibrought, make 14, which
fet doWn. So that you fee all the particulars
do t‘i‘tsztke 34,91.
A general Kyle;
For Sumsot‘ one Denomination i‘n-Ad—
dition

 

  
    
 
  
  
  
  
   
   
  
 

 

 

  
   
 
   
    
 
  
  
    
 
 
  
 
 
 
  
  
     
 

5 Chap. II. J ddition. 7
I ition, obferve to fet down ail that is above
Ten or Tens, and under’Ten; and for every
In; Ten carry one to the next place,_*untill you
come to the 13%, which mufi; always be fet‘
dawn, as in the former Examgle and this;

    

”111% following appeareth. ‘

3‘“ 2734

“g ' 3945

f‘ \ 6342

E- 9273

¥”” 1712'

1%. 29974

f A Here I think it not amifs to advife you:
n: to be fine for your clearer working, to fet

d0wn the figures of every rank in afireight
line under one another; as you fee in the ‘
foregoing Summs,‘Units under Units, Tens

' under Tens, 8m. _

~ m ”4'97?” F m-
a

E . ‘ .Addition of Momy ‘ Witbthe lefll’r -
' Denominations. . ‘ ,
_ ‘ II. I need not here to acquaint you that

,four‘ Farthings make a-Peny, twelve Pence .‘ ‘
aShilling, and twenty. Shillings a Pound; , - e
» . _ B 4..) > “ Both,

““7 W” 43,7342, « r ‘wr,
N “‘ ' ’ 'z " “WWWHV H, _, V
 

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.8 ‘ Addz’n’m Cha p. Ill C]

Bot thus tnuch I delire you to mind in
33?: Additionfi and Suhtraétions, the Title
5? your Amount, and how many of the
iii Denomination domake one of the f5:-
eoncl, and how many of the fecend do math
one. of the third, and how many of the
that? do make one of the fourth; and in
in this manner if there are more. The Oh.
i'ei'vation of this will muzh facilitate the
work. and fave both you [and mea great
deal oi labour; therefore I {hall only give
one or two Examples of each cai’t up to
your hands. ' l

1301‘ the efi’eé‘ting of this confider as
before, how many of the firft Denomi‘
nation do make one of the fecond, (which
is here 20 :,) therefore for every zo’Shila
lings carry one \ Pound to the Pounds, as
thus, I, 6, 8, 7, and I Shilling is 23 Shil—
lings; then come down uponthe Tens,
and thy, 23 and [O is 33, and ten i543,
and to is 53, and tois63, and wise/3,
and 10 is 83 Shillings; now 83 Shillings
being 4. Round 3 Shillings, fer down only
the 3 Shillings, and carry 4 to the next;
laying, 9, i, 8, z, 7,and4.thatlcarried
in my mindis go; letdown O, and carry
the 3 to theinext, faying, I, 7, 3,2and
3 [cart-fled, is 16;, fet down 6, and carry

1 t0

 
’ ' ‘ W“ ' ‘sz
-,.~.— (.’>fi'_- w' .’. ~ - "

Chap-IL. i Addition. . i 9,-
3,1 with: next,faying, 3, 4, 1,1,1, 3,:md ‘
1 1 that I carried is 14:, which by rcafon

I t tr: his not any other place to carry it u n—
to, only fct itdown according to this Ex»-

 

 

 

 

/ ample. ,

i . ' I. 5. f

i 327 II
107~——————Io >
IOO-w~—~«17
138 18
471 16'?
313**--~IIJ
1460 3“

 

As before», f0 again confidbr the Title
ofwyour Account, {andlhowj many of’ the
one do make the other; then beginwith
thc firfi figures at your righrhand, 53 79 ' s

"8, and I; which. being added together
; make 22,,and coming down upqn thighsfcns. -
fay,2.2 audio is 32, afld‘102i54lyafi‘d IO _
is . 52‘ (and {0, on if “there were, more.)
Now confidcr how many Shillingsgz-Pc‘ ~
nies make, viz. 4. Shillingstand4Pcncc ;" -
far down the 14 .«Pehce, "and carry the 4
Shillings {no} the Shillings, (laying, 4. that
Icarry and .8 is 42,; and7is 19, and I
'f B 5 L .3» is

Wf“

 
  
    
  
  

“MM
k

rug—a A _-A 43

, Pi? "“25"?

      
      

 

,.

Mme”. Chap.

is :o; andg is 23:59am“ 6- is 29,3nd 1 is 30:, ,4

fihfin' come d0wn upon the Tens, 4o, 50, 60, "

7o, 80, and ‘10 is 90 Shillings, which i541 '
Pounds 10 Shiliings; fe-t down the 10 Shil-
Rings and carry the}; Pounds to the Pounds,
feying 4 and 6 is 10, and 1 is 11, and Sfis ,, ,_
16, and 7 is 23, and, 1 i524, which 4&1: _.
down, and carry the 251mm theg; which

will make I 1, and 4 is 15,» and 6 is 2 I, and q ‘}

4is 25 ,A, and 1 is 26 , and i is 27 , which i'et { ‘
down - and the total amounts to 2741. 10,5“;

7

4, q! (as you may fee in the Example,

1., 5, . iii
II:~———'II——-—-IL
Iq-——-‘16~—~—*08 \
4‘7"" 1'3”” N
65‘:~"“*‘II“,‘"‘“<IE :
41"“17w07
96i--18~i+4———‘-05 _,
‘w

274-4—— IQ... 04.

 

 

   

 
       
   
   
   
   
   
       
     
  

You) may, vinake a Prick with your Pen aft 2
emery 4 in. they"Fatthi-‘ngsyan‘d Lee-Very 12
in the Pence, and-«at ever?"- zqinthe Shilé
hugs... But gthiswa‘y :is fineitheri‘s mm more
commendable; for ifryciu once prick faife,
YQu-mufi prick i; Lallpover, again, which

wiil u

1

109k

 
> yr,-,\-K“_

l
I‘M
X
2:" 7

l
l

l r-IW"‘B'I'T3‘ If}??? "off” "-1 V"’7"W'~r‘>+-vwfl.

Cliapll. Addition; i '1 I
looklike fo many Blots, and make you more
fubieét to mil’take.

Therefore [’recommendtthefe two Tables
following to you to be gotten pcrfeétly by
; cart, before you adventure upon Additi—

on, as I Shilling is 12 Pence, ZShillingsi,
$24 Fence, and fo on. b

,V. ”M

5. ' d. d; 5. d.
F 1—is— 12“) f 2c—is-—— 1—— 8']
l 2—-—is-—— 24. I gc—uis— 2—— 6
3._.is.——— 36 40—iS—~— 3—,— 4.
‘ ‘ 4———i§-—- 48 SO——~i‘S-—-— 4—— 2,
t5! 5.4.is——— 6o, lads—ism 5—— o
'5“ 6--is—— '72. 4 7C——iS-——- 3—10
:34 7.45.. 84.? 8o_is—— 6—— 8
Z_ I ‘8-—is-—-— 96 90—is—-‘~ 7—— 6
. 9———is—-—108 IOC—iS——- 8—- 4
‘ 10—43—120 110—;is—- 9——- 2.
l II—iS—l 32 IZO—iS-——IO—— o]
‘L12*—-iS-——-I44J ‘L . ' J

The Proof of Addition

Add all the forms again (except the up‘
petmol’cg-which is. ‘he,re*3col;;‘2:1 13., 6d.
:2 q.) and then add ‘the‘Tétal thereof un—
to .the faid uppermof’c line,*and if it make
the jail Sum of thenfirfi Tozal, itis true,
otherwifc not. . ' ~

Example

 
N I I 2 The ProofofAdalztzozz. Chap 11

Example. ' l. .53/3 62’.- 72-3.; ,3;
‘ goo—*1 1—-06-—-25§ -

102%15—4—‘t 14...}
106——-—17—-—1_o.._.p
241M38-L-uu—e-l‘
6QI—e~II—-H_—1_
3 14-3-4— I O—--—- I 0......2,
mil—“1,1911“!

TOAILQL 3, W 2279—~19~7-:—oo———-o

- I 9 79~Q7W°§fi2
3—-_-.227§--—.._I93-—-co-’—-o '

tuna—aunt

 

 

 

   
 
 
 
 
 
 
     

Additlafz of Cloth -Mflfiififlm

III. Note that 4 Nails :3 1 metr of a 3
Tard. I Tan! 43 @032”, 1 El! Flemijh 3
._ flmrtm of a Tan-4,1 Ell Englzfla 5 '

You fee the Title of your Account is
Yards, Quarters, and Nails- now obferw:
how many Nails make em Quarter, which3
i5 43-; thtgcforc for: even; 4carry 13 Quay ,

. ter, to 3th: 3Q1anrersgandhkewifeforeve- .
Iy. 43 Qqar’tcxgs, which make a Yaxd,,_.c’ar-
  
      

mp .u '6 ' 292m), i; » V 6‘

ry 1 Yard to the Yards, yard gm. 722;.
nd m the Yards(or lafl 37-: ' I
» ennmination, of any 106 3———-.—--2.,
Addition) for every 10 41c: ’2._.—-'_3__
crrv I to the next place, 716——-.-—3_—.—I.;
utiii you mm: to the 151*), g f;
lafi rank; which Tbtal 17I——————I__._.—2 *
fet down,as m thcfc Ex— 412 I I
‘amglgsu 601 _———-9, ,1; ,
912s~—-—-I-——-.—-.-:-3

   
     
 
    
 
   
 
 
 
  

 

 

  

 

 

 

 

 

 

 

       

"yard qr m: H Engwqr m. ElFl'e.qrm.v\

31—4—4. 47.....1——-2,

14*] ”—2,
I 6—11"3

‘33-~3-_-.=I

 

...—-——n-u

41—4—3»

17...]...2 ;

38—43—1

54—4—2 '” .

Jéé—Z—I
31—?le
913—2—3,
3 DMZ—I

 
 
 
   
   
 
    

226—u—I—e-1’

153*0-‘3

....._.._.——'———-——2°3-4-.-—3

 

##w

 

* 1 56;— 3‘-— I

W

Ptoof—ea—w—ibs—fifi ,j

 

- Additiom ~
 
      
 
 

       

 
     
   
   
     
   
         
   
     
 

:4 , ’ : Eddz‘zm

. .‘é” -
O

. I Chap.1L j
Addition of Wifie Meg/2:73: , _ > . /

‘ 'IV. the fame: order that is fat down in :
the fecond Scfiion of thisChapter, is here ‘ "
to be obferved, and likewifeinallthe Ag- j.
ditiensfo‘l‘lewingr , ‘ .

»_ _ Example. 4 :

For 2,.Pz'm: carry 1 Quart, far 2 erm g: 4

a Pottle, for 2.,;,I’ottle: 16411071,” for 63 Gal:
lam ,1 .Hogjhmd, for4Hogjhmdr 1 Tm

T umJgag/h. gall. patties 773°"Pi7m' A i

, 321-1———16—.51~—-o—e~1:

 

 

 

 

IQ:‘7""I~—IO——~ Ie—h—o
31-7—Iv.+,—-115.—-—o~_1-—~1 .
. r 24.1:H2'7‘”3Q~r~1"°‘0¢-—V~l,
.‘7317——-I-f-.-:4o‘-r-1-}-.—-’- 1V--—-x ,
171—3 NIOmO—uI—mg
341;?‘24TIQ—"1w9~i _
...131.'”""1":-I7-—~_I"'“I——0, 1. .

 
  
  
 
 
  
  
  

  
  

 

 

 

Total 174s~—p¥—.:-.27::t0-'-—-0-0 .
5»: 14‘234——:1-izo-—0——~z-‘-—+1 I. _,
17$‘35‘0'*“2‘7--°"i‘°'i‘7°~ t

 

 
     
 
 
  
    
   
  
 
 
  
  
   

 
   

W

‘37,

Additiom . 154. ‘
Additiaa of Troy weight. -

,; 1:0,; 24 Grain: carry 1.P«gqy-wevéglat,far 20’ I
f Pen)! weight ,1 Ounce, for I 2 Ounce-s” 1 Pounds ,

 

wfi‘» % pm 97- Tb‘ 3' m.- gm
6 371:4 15"“19‘“"23" 41"“10—’.I:7“'IO
102—1 o—-Io-—-I 1" 3 1—51.1—«14—«5- i I;
413—1p—16—f—IO IO———-I.C——~,I';_--I§
175—03f—19~—II_ 11—11—11—105;
912710—18—10 Io—I.0——I7-16
341—11—13—5-22 7- _.-r-"“"~"
‘ . www— y‘07—907,__26——-14,
2 3‘2o——oo—-—18-.-,-IS ’

 

 

 

Addition of :Averdupoizq - .
” Weight, ,

‘ Far 16 Ouncescarry I mango-mg- Poum’s‘
carry ‘1 Quarter, for 36 found: 2 Qanrtm,
for. 84 Pamdr 3 garters, for I L; Pound/:4. 3 _
Qflflrteri, (drone :Hufldrtd Weight) forgo

Hiandrcd ITW»,

    
   
     
 
      
          
        
         
  

15,; 31424245»; Chap. 11.:

Example. E

  

C qr: TEE Tum. (7'. gm. t5 g
914.3...27-«15 91—19—3+——I7-—-—l§£‘
10—»1—16—14 Ié—I 1—1—1} -—--14
‘1 1———2—-—:o-—-—Io 9 I-—-11-—-2-— I 1,—— 13
313—14.: 1—4-12 ,60—11-~—‘—3-—10-—.—I 1
7I—~1——1.I+—Io' 31—10-—-2—-—I 1-—~I 3
~:to---*3-~--~.15——.1 I 78—11-4—1—13—3-13;
41e—I"I-—-2——I 1—1 1

__

 

 

  
 
    
      
 

  

Addition of Dry MeafurcsL .
for 16 PM: carry 3' Peck, 13926419314: carry-p.
' I Buflael.

   
   
   
  
   
    
   

/ “an“?! peck: pint: bnfiel: 1::ch pin“?

 

       

 

 

 

 

 

 

 

, 10 4 cm! 10
IQZ 3—4-91: 103 2, «m:
413 2—45—10 .710 11
I7""""“I“"""'-“1II 317 ‘I go.

 

 

IO6——-—-—3-,-——-.——IO I u6-——~—3——~§- I 1;
Wm“

11 114.2“:

04 ,;_

 

Addition- 4
geek’Chapill. , ’Jdditiwe. ‘ . , ‘ 17

  
     
    

Addition of‘ Time. 5
‘or 60 [Minutes carry one How ,for 2.4 flours
one Day, for 3 65 Day: one Tear.

    
    
  
   
  
    
  
   
     

If: , ,. yum day: hour: mm
5 f 37 Isomuu—wlz,
3 531" IIo-—-zo mam
3-; ” , 14. -—-—~175 “Is—~23

‘« Io——-IOI-'-—- ill—WIPE :7
i, , It—~—-137-»———-12—-—e——14 .\
‘ ‘IOWIOIMII «mew-«‘13;

 

 

 

 

 

M

115—..046—~23--——23 ’

 

 

«23»vmwmmwmwwwnmmflw~

Addition cf" Long Meafurc.
For 12 Inches carry me .Fooz, fur three Feet /
one Yard I

yard: feet inches 5; yards feet Invoked»
SlWI-s-r-IO , 3_90—.—..2...._1 L,
I7-—---2.——--II IO".——.1fi.._.._§§)
iO—~2:—~—~f)7/ 6Z—-———2_._._. l ‘1
9; 531 I-——--——-IO Ito._—._1..__._lo.i
3 41,._2_. 1 I 101...... \-_____08
IO———-O-—-=-—-—IO ' 7FGe—]_+_I[
~~~ ‘ 3310* 2w5io
Ig5+-~lo-a1 1 5 ‘

rttrgy'tfi‘

v .3 .. 'W um, m MAW mi

 

 

   

 

 

w

CHAR;

 
   
Chap. III.

,5!

CHAR. 11-1. ‘ ah

I

‘3 1‘

SUB TRA C TION
ofMa-my. [J

Ubtrafl'ion'» teacheth to take any‘lefier .g:

- Number out of a greater, and how-t9
know what remains.

I. Subtrafiz’sn of one Dena.
:m'mtz‘ong ‘

Firf’c, fer down-athegreat number from, -

which you would 'fubtracft,‘ and then place

the lefl‘er number to be fubtxaéled under it, a

as in Addition with a Line drawn beneath "

theme
Example. Received ” 3 '7 9‘
Laid out V. ' 136

M

Then take the firfligfigure towards the:

right hand in the Sum to be fubtrafie’d -
from the figure. over it; as,,,-6~Afrom 9 and,

there remains 3, which gafet down; then ‘

azfrom *7, and there remains 4;. L‘z‘il’dy, I: '
from 3 and therexemains 2, which 2- fet. ‘

down; 379
136

M..

And there- remains». unpaid W243

 
   

   

Sfiétrafiim. 1 9
, But I {hall give you one or two Exam-
ics, wherein the figures of the Sum to be
b‘trae’ted, are fome of them greater and
fqme leffer than thofe you muff fubtraé‘t
I fmm; therefore if there be only one De-
no nination, borrow Io and add'to the up-
per figure-7 as: in this example.

  

' * Received 130624
Paid out—-—-'-IO4I46

 

Remaineth #7026478

' W m
M) . .

.“vla .,-A- V.

Say 6from41eannot, but 6 from i4and
there remains 8, which fet down; 1 thatI
_ borrowed and 4, makes 5, g from 21 can:
not, but 5- from 2:21 maytake, and'there
remains 7-, which 7fet down. Then I that
I borrowed and I is 2‘, 2 from 6 and there
remains 4-, now 4. from o Icannot, but4.
~ from -10 and there remains 6 ', then 1 thatI
borrowed and o is I, now 1 from 3 and

«a [WT’VW‘VWV‘W "mum—- WY “m"? "finds“

there remains o. ,

'4‘?!"‘ 72: - r! . a / rug-m

thereremains 26478,

e i ‘ 11t<5u9-..,._

‘there remains 2. Then laftly ryfrom rand"

So that if you take .104 146 from I 30624., _,

    
 
     

 
    

  

Suétmfiéom Chap. HI.

        
     
     
       
   
 
    
     
    
  

If

U. Sablmflion of fewer-4! Denomina- = $1
tiom.

 

’I
But if; there be feveral Denominatiotfl,
then obfervc as before in Addition of Mo—
ney, how many of the firfi make one of the
fecond, and for on. And if the figure or E-
gures be greater thanthofe you are to {ub-
traét from, borrow one from the next De-
nomination, and fubtraét from it 5 ans} add
the Remains torhe upper figure. '

 

 

I, r... d.
Received—an“: 1 _——-03_
Laid out «---~ 196-” 12-9—20 Si}.

IV

 

m

Remains -—-—«078~-— 18—— IO.

 

 

 

 

Example; Take 51d. from ad. I cannot,
but gdgfrom a Shilling or 12d. and there
remainsq- d. which added to the 3 makes,
rod. r . _ _~,
Again,one5h§l!ing that l bowrowed,(for‘ , '4
you mufl be {ure- ro pav what v-zeu borrov- )
and 12 is :3, wh'uh to takci‘t’o . I lean-
not; then (Ky 13 from 20;. and {here re,
mains 7:, and the r; ,makes 18, WhiCh fer _
down.- ‘

 

 

Again /
  

   
 

Suétmifz’on. 2 I

Again,t that I borrowed and 6 is 7 ;now
from 5 I cannot, but 7 from I; and there
emains 8 . Then I that I borrowed and 9

g to; now IO from 7 I cannot,but IO from
_ .. and there remains 7, which fet downa
L 'Tiien 1 that I borrowed and 1 is 2', zfrom
' 2 and there remains nothing.

-

 

 

l s. d.

So that-“~— -——- 196—12— 5
being taken from m... -~~— 275—1 11-—— 3
there remains 078—48— 1 0

And thus in any other of this’nature, ob.
{erve that the fame that you carried in Ad.
dition , the fame you mufi borrow in
Subtrafiionz, as 12. in the Pence; 20 in the
Shillings, and min the laft Denomination.

I need fay no more, only “hall acquaint
you how to know whether your Work be
well done orno.

Proof of Subtrafiiofl.

Add the Remains to the Summ fuhtraflz
ed,and if it make the tame Summ with that
which you did‘fubtraé‘c,’ it is true, elfe not.
As in the [apt Example, 78 l. 18:. 10:1.
. and 196i. 12.3.2.5 d. being added, do make
the fame‘Summ with the Summ received. 6
r I Sp; .

 
  
    
     
         
       
     
      
      
 
   
  

 

Chap."HI.

 

Subtrafiiom

Subtméi‘ian of C lath I‘Mmfitre;

  

Tardy. qm. 7m. Ell: Flam. quiz. .
Bought-.37sc.2.~—I—-z BO.-—-4171—-2-. I '
Sold-— 1913~—2—-1 ‘So.-—1317-~2—‘1~3 (‘

‘
m~~h~ —..‘——~I——-‘_-—M H

 

 

Remain. I798~3~I Res—2853 “-3..“2

Proof. -—- 3,712. - 1 -—z ,

   

_ Ell: Efig. q“. me.
Bought-4716220w~2~~~~1
Sold ~——.- 1-0913 17 —--—-3 “M3

Remains ——3 624892 ————-- 3 ,_.____ 2

mum—am“ aw “nu—"n—

   
  
   

Snbtmfliafl of Awrdupozfe'
Wengt.

For the better tin-demanding of the Rule
obferve (as you did before) the Title of
your Account; and where you‘cannottake
‘one number 0111;: of anotherfi, take it out’of
the next Denomination; as you fee here,
Iofrom IO “1 cannot, but IzDrams from
I, 1 Ounce there rel’cct'hr4,and the 10 make

14-5 ,.

      

~ “v.
  

  

Suéitmfiim;
_ 14.‘7 14 from II I cannot, but 14. from 16
nd there remains 2 ; zand II is 13. Now
thatI borrowed and 14 is 15-, Irg'from
. ,‘fi ,
1‘1 1 cannot, but I 5 from 2.8 and there re—
F mains 13:, 13 and the 11 is 24.. Now 'I
_‘_’ th‘rt »I borrowed and 3 i543 4 from 21 can-
3 not, but 4 from 4. and there remains no-
? thing, bur 2. is 2, which you mufi fet down.
Now 'I that. I borrowed and 8 is.9 -, 9 from
' 7 I ca‘nnOt,’ but 9 from 17 and there re-
mains 8. Now I that I borrowed and! is
2, 2. from 43nd there remains 2.

  
 
 

C. qr. '15. NM. 6177'e
Boughtmm » 2—».1 rr—-1 rum
501d 18»—-3-———I4—~13~——12

 

 

'-”"“ ”moan—g.“

Remainsw—28 ~2-24-~13-— 14

mum-m...-
m

 

 
Chap: IV. j 5
C H A R IV
MULTIPLICATION
T he Multiplzmtian T able

J6 times

I
I;
>5
I
I
.1

‘ ' 3times

"

I
3

S
6
7
8

I, 9

.3,
4
'5
6 k~
’7
8
9

If"

f"

4_timcs-

/

xg cos] 9‘ V1 4“

 
 
  

25

EOr the clearer underfiandihg of this
a Table, obferve the Figures in the
‘ b: argin, 2,3, 4, (M. and the Word [times]
_‘ ar'oyning to them; fay 2 timesz is 4, 2
. times 3 is 6, 2 times 4. is g, 2 timemis

Io, (35°C. After you know well he Q' to read
it within/Book, you mufiof necefiiry get
it very perfectly by heart? before you car;
make any farther progreié in this Art.

    
  

  

[.

 

The ufi’ of leriplimz‘iafl.
Multiplicationferwtb iii/234d of marry Adv

515150725, 47251 tmdoeth, 0f trro fifirmi’yrrrtqiwrz
to increafi? zhcgrmtrmz: affair mtherc rare Us»
m’tes in the leflrr.

There are three things firmly to beoh»
. ferved, viz.
r. The Mrhiplimrd, or Sum t3 be muiw ,
tiplie".
» 2. The Malripfier, or Sum by which you
in;- muitipiye
3. The Fredric? or Sum produced.

Ask how much is 7 times 52, oringz

f Weeks how manydays there are ?

' If you would add 7, sztimes, itweuié
C , he

 
be a tedious work ;' but Multiplication wi
do that at once, that Addition fhould do _
many times. In Multiplication therefogf’
firlt let down the greatefi number and tile .3
lellet under it, beginning at therrighth 41¢":
and multiply every figure 0f the Multx‘li-
(and by each figure of the Multiplierz‘g
then (do as in Addition) fetdown allthat 3
is under ten, or above ten, or tens, and for
every ten (or Article) carry one to the next '1
place, and, in the lafi: place fet down the ;

tens. ., _ K

EXample.

» 5 z Multiplicmd.
7 Multiplier.

3 64; Prodwfi.

m

7‘; Begin with the Multiplier, taying, .7;
timfis 2is 14,. fet down the4 under '7, and I

carry I to the next place, fayi‘ng, 7’times 5
is 35, and [thatlcattied is 336, which fet:
down as you fee in the EXamplez' fo that;
7 times 52. is 364,. ~ ' ’
3;; In 3712 Shillings'how many ,FatthingS,
off'howmuch is 48times “37-12. ?' ,
Be careful intetting the figures of the:
3&nltigliet' under the Multipliwnd; {0‘33
_ , ‘ _ , 1' ’ ' _ unitefi/

z
"a

.v , W, ‘ :3

 
    
  
  
     
 
   
  
  
        

g Chap. IV.

   

Mdtiplimtim.
a: ulfnites mufi be under unites, ‘ "
,gfl‘sens under tens, hundreds 37’2"
*9 nder hundredS'7 and having 48

 

? ; tfightiy placed your figures ; 2,696
' then proceed accormng to _
your former Example, faying, 8 times 2,
f is 16, fet down 6 and carry nne to [he
next piace, the-n fay 8 times 1 is 8, and
I that Icarried is 9, fer down 9, andcar-
. ry nothing, faying 8 times 7 is; 56, {a
,’ down 6, and carry gto the next piace,
faying, 8 timesg i524, and 31529, which

. fer down. And having done with the firfl:

, figure of the Multiplier, can-

? eel it with a dafl] of the Pen,

' and proceed to the nextfaya 3712
'ing , 4 timesz is 8, which 8 48
fet (fnwn diremy‘undetthe . 21%;;
Multiplyer, then by 4t1mcs 1484.3

‘ I is 4, which fetdown, then mé—m

, 4t1mes7'is 29, which 8 fet 1:78:76

z‘» down, and carry 2., then 4.,

“ "times 3 is 12, and 2 thatl '

carried is 14, which being {Ct down, you .

t fhallfinfi 48times 3712mm 178176.

z
I

1'1

c Haw
e.

28’ : fiflgltz'plimtim. ’ Chaé} IV. .1

I. How to [Wigipbrby [0, 100, 1000,
’10000{

fa"
, w
, Look how many Cypherswou have/gin 7
your Multiplier, addthem to vourMLQti'» ‘3
plicand, and the total thereof than be the
pi'odufi. ‘ , ‘

Example.

, '(63 > 10 , 630
‘ " 36 2100 3600

85 byfelooo 85000

1“.
D
W
92 5:0000 "\ 92COOQ

73 100000 ) ' 73co'00‘0
How toflfyltiplj by 20, '40, 303,
5000, @‘6.

As many Cyphers as there are in the
Muitépiier, fee that: down towards the g
, I‘igi’gt hand, and multiply the ref’t as before "
iyL-itigbt. « ‘7 V

Example; " 37 , 232’
‘ 20 0 300

II-‘M

740 ’ 65,6

 
    

a.» v

Chap.IV.

A "IK~'“: ”'77" “I" ‘._-.

MthtéPZz‘catéom 2 Q ’
if” [Vow to prove flfltltipiicarz'an. h‘
\ n o r:-
l ’3 Full call away the nines of the Multn
l picand (in your former example) 3712,,
‘ lag, ing, 3 and 7 is to, wit away 9,3nd there
l remains I ; then I and Iis 2, and 2 is 4,
which fet on the right fide at” a croft, 3‘
thus + 4.. it:

Then caf’t away the nines of the Multi-

plier-v, faying, 4. and 8 is 12, cal’c away

the \ nine,

crofs thus,

Lafily call away the nines of the Pro,
duet , faying I and 7 is 8, and 8 is 16,
cal’c awaynine, and there remains 7 2, then
7 and this 8, and 7 is 15', call away nine
and there remains 6', then 63nd 6is 12,
call: away nine and there remains 3, which
place at th-tg» fanttem ofthe crofsg and if the
top figure ‘ he bettom be like, your

3
3wh4

' Work may he true.

3’

This is the common way to prove Mill-Q

tiplication; But the melt certain proof

C

and there remains
place on the left tide thus 3 +44 3 then
,x multiply the one by the other, i‘aying,
times 4. is i2, call away nine, and there
remains 3, which place at the top of ihe

”

3 , which

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 

3‘5,
is by. ' Divilion, as hereafter 1 will {hawk-
ou. ' ‘ -
. 11. Yet for the more pcrfcét underfland}
ing of Multiplication, I have hear laid git ‘Z‘
flown in. the Nature of the Golden Rnl‘é’,
which though it be not according to tile
,, nfigal method of Teaching, yet the. expc- \;
ricncc I have had thereof, lhewcth me, ,
hat it will inform any one morcthrough- "
ly in the Nature of this Rule, than any di-
icaions I have yet read ; for tryal hereof "
take fundty Examples, wrought only by
multiplying gfccond and third numbers toge—
ihrzt, as thel'ofollowing. I . .

Example. .

if 1 yard toll! 17 d. whatcol’t 4G ydrds?
. 17

2“"9

4.0

W

facit 6930 d. '

awrw» mm

fad; 2.1728 _

 
  
    

 

Chap-IV, 4 . flfyjfllg .. , x;
‘l-‘If 1 lhillingmakc 12d. What will 20:?
2.0 ' I - I

     
  

 

   

facit 2400!
ll 1 {billing make 48 4. what: will 20 3?

  
 
 
 
 
    
 
  
 
    

facit 960 wfdrthirzgl. ’

If 1 Crown be 60 :1. what goo Crowns?
' 60

30000 d.

*3 Ifil Yard be 16 Nails, what 576 Yards?“
, _ I6 7

 

313'?
92 16 Nail:.
If 1 El! Eng. make 20 Nails, what 24.6 Elk?
” ‘ 20

WWW

facit 4920 Na.
If I Gallon makes 8 Pints, what 6; Gall,

1W v~=rwwrvmrrw .. 5,. w. ”4.4m,
w

, facit 504 Pint)“.-
If I Hogfh. make 63 Gall what 4.210ng

facit 2 52 GM].
C 4.

    
 
l . Mgzzzngmian; 1 Chap 1V;
1’5 1 tun makes 2 52. gallons, What 20 tun 2

‘lo ‘

f4“; 3040 gallons. 5 gi’

3?: inclL 1.3:: 3 barley corms, Wl‘atL
lyncg? '

If : foot be. 12 Inches, What; 79 feet 2‘
' 12 '

facit4548
ff 1 yard lgel; feel, Wham-78 yards!
, ‘ ‘ ' 3

fkflil434.

If I furlong be 40 poles, what 846
furlongg? _ 4o

ffzcit 3 3840
If x mile bel8 furlongs, what loomilcs?» ’ /

jhmtSOQ

If 1 pound be 12. ounces, what 176
pounds. 12.

,mét n

‘ , facz't 2.112. 3

x If -‘

 
 
       
       
  
 
  
 
  
 
  
    
    

    
  

Chap. IV Maltzplzmtzm I “33

If I ounce be 20 penny weight, what 12. *
20

fad; 240

7‘

If I penny weight be 2.4 grains what.

 

52 penny weight? ~ 20

fizcin480
If 1 poundibe 16 ounces, what 112.
,—j p9und?& , . 16‘
-' " ‘, 672.,
% » 112
, ' fm't 179.2 -

If 1 quarter be 28 pound what 4 quark » >
ter's. ? 4 I
:facit 112. .
If; a Cbel 1:2 pound, what’zo C ? °
.» " zor
facit 2240
HI Tun be 20C. what 846 Tuns 9 ‘4
20 ‘ -
fad: 41359-20 ,

 

C15
v

"’34,; -7 Mdifzplztatwfi * Chap IV
if C grofs alloweth 15 pound tare, ,
what'13172C.grofs? . 2""
I) '
360
72

facit 1080 tare.

If; I C. grofs give I3:- pound tare,
what Will 96 C grofs give. 3
I3

.2 88
. 96:

.facit 1248
{'32 If 1 Dollar be 5652. what goo DoUers?
56 V“

3coo '
3503

fasitm 28006 12mg:

If I French Crown be 6 5. what 866. p
{ 6

Emit 5196' '

 
 
  
  
   
  
  
    
 
   
   
  
 

     

 

 

EChap V." Dzwfon ‘ >33 ,
g; If 11.: @096 37 d whatcof’c 4731.1 3

1 37

1‘ 3323

5 1 I42;

1‘ ' 1 . #6131757:

' C HAP. V.

DIVISI ON.:

Ivifion 15 that by which we know how: I
many times a lefl‘er Sumis contained;
in a greater. ’

E . The Part: of Divzfian.

I. The Dividend

In D1vifion 2. The Diwfor.
obfcrve,§4fi 3. The Quotient. _

. The Remain.

1. The Dividendis the Sum to bedivided. . '

:2. The Divifor is the Sum by which we:
divide.

: 3- The Quotientistie S :11 produced, and

containing fo many mes the Divifar, 3511;“

felf 15 in value. 7

127‘ i , .
v

1 36 ’ ' Dzwfafl. ' Chap V
, 4 The Remain is always Iefs than the.»
I Diwfar.
firfl‘, Set down the Dividend, andtigh
under it tow ads the left hand the Dmfori
Exam 1e. .1
Being to divide 4648 half pence by 1’): ,
number of half-pence in a penny.
. Ifirfl: fe: down the Dividend, and then ,
the Divx1or under the 5111’: figure thus: '
4648

But if the figure or figures 1111?; over the «a:
Div for, be lefl‘er than the figures under it, . .
.lhe Diviior mut’t be removed one degree or
place more towards the 1 ight hand

1 Exam [6. ‘ I .

Iwould divide 46481.2arthings by 4 8, the :
1 number of farthings 1a a 11111 lingzthen Imufit ’
_ fetrny DIV1101‘ thus . » ’

4 648 ( '-

4 ‘ 48 7 - .
’And at the end of the two numbers make
a crooked Line wherein to include the
Qt‘otient thus ( ,
Yet before yen begin your wérk,confide r ; I
three things, viz.
I 5858190137 often the Divifar 7': contained ,
m the D7177derd. .;;
2 21471117171} the 7.107767770717742 Dioiflzr tag;- :4
. ' . 3.574

 
       
      
    
 
  
 
  
 
 
  
 
  
 
       
   
 

Chan; V H ‘

   

mm. « 37 ~-
3 ,Srzétmfi‘ the Produfifrm» the Dividend. ,
To 'pr0pound then the former Example. f"
‘ ln- 4.64.8 half-pence, ifvl would know;
Elowmany pence. _ ’

  

\ 9648(2; J

l mull feck how many times 2~is conufl ’
mined in 4, whichistwice; thenlfetzin
the ‘Qrotient, and multiply it by~ the Divi—
for, laying-,2 times 2 i545 HOW4from4,
and there remains nothing .-, whichazrhap i

. ving performed its firl’t office, , I cancel with;
adafh of the Pen, and remove .i'tione place
. nearer the righthand, thus: _ :

£1648 (2.3 L L

3’ 2a

Then I-‘fay again, how many timer;
:’ is 6? Whichis 3 times; I let clown-Lgin

”the Quotient, and multiply by z, faying, 4' (I
3 times 2 i5 6’7 now 6 'froml6, and there»
remainso. , r . ,

Again Iremovetthe Divifor, thus: ~,_ ‘

~ 91648-{23
zzz ,.

 

Thus .,

/
\
  
        
        
     
      
      
      
  
   
    
 

 
 

'33; Divifiom «Chapvt ~
' # Thus." and try how many times 2 i114,
Which is two times, therefore I fet 2 in
the @otiem, and multi‘plyit by 2.;(theDi7
vifor) faying 2times 2. is 4, now‘ztfrom 4g,
and there remains o. A ‘
5:169:80ng (
zzz '_
Again, {remove the D‘ivifor, and trY*’_
again how often 2is contained in 8, 'which
is 4 times, I (er 4 in the wotimt and
multiply it by , 2, faiying 4 times 2,4is 8.3:);
now .8. from 8 and there remains o. "

5:659:812324.
222$;

   
  
   

Aflothtr Example with Me F {gram

Suppofe there is; 398‘pounds to be equal-_ ,

13] divided between 6 'Men, the demand ié ‘

. What each Man :mufl have P
. ‘ Firft, I fet down the Dividend 398 , and

. 6 (the Divifor) under 9 thus, becaufe 1., I?
cannot take 6 out of 3.» “ ’ t _ '

3'98 (.6 f
6‘

., ’ Th?“ ‘1 try hbW mahy times‘6 I can, _
have, m 39, which is 6 times, I piaeeo

 
  
 
 

xn—“T

—..,_. .-;r ~-

h‘ap. V.“ r

1:. in the (gotient beyond the crooked line,

2 '
21‘ :

a
7 A 2

faying, 6 times 6 is 3.6; now 36 from 3

éever the 9, and cancel. the- 3 9 and/6, my

; @ivifor, thus, ,

3

25

\ 1‘

'5 :
298(6:
6

Again, I "remove my Diviforzto the next 1‘
place under 8, andfeek howmany times:

61 can have in: 38, Which is alfo 6 times,
Ifet 6 in the (gotient, fayinvg, 6times6

M36, 36 from 38., and there remains 2., ..
which 2 Ifet over the 8, and cancel my 6

thus,” (
3’- 2
39%(66,
66

So. that every man mufi: have 66 Land
21. over, which lmayturninto pence, and
divide alfo by 6, and the-ngientv. will be

80 pence, which is in-vali66pound 6 mild

li’ngs and 8 pence a piece.
The Order I inflame to divided] oneFi—

‘ game, but saffloe Dzwfly‘ do corzfifl of more :

figme: thin one, I mwfl take the firfl figwe
.9f the Divg‘ar naeftmr mt aft/o: Dim-512224
‘ i an

D‘s-mpg»; 39 ..

. , .. 92 .1
and there remains 3, which Ifet down,

       

   
 
 
    
   
 
 
 
   
  
 
 
    

   

2 'f '49 Dielzflm:

.. Chap. V. '

   
   

212622 I 6472. Wife take 411 tbe‘reflof the Divi‘ '

. I 7 for; 9212 of the 1911222de that flamd: above

2193mm in the Example: following may np- 2

84?».-

P But before you proceed to divide by;
Figures or more, be careful to underi’catid
Well how to divide by one.

How to prove Multzplz'wztim.

In Multiplication I‘told you, that the
mofi certain proof for that Rule, was by

Divifion, l [hail therefore take the Produé‘t 1 .

of one of the Multiplications before going,
and div1de it by the Multiplier thflereof to
try the former work , as for Example.

I would divide 178176 by 48, which

Was One of the former Produéts 1n Multi-
plication, which numbers place as in the»:

Example following __
17,817‘6C ‘
48

FirPc I feck how many times 4. is con-
tained in 17, Which I find items , now
4. :times 4isy16;16_ from 11,,and there
remains 1, which makes the .8 to be h,

, .183now 4 times-78 is 32, 32' from 18,,"
cannot, therefore 4 timesis too much. . '
   

  

am 5-.“ .,

 
  
  
  
 
  
 
 
   
 
 
  
 
 
  
 
 
 
    
       
   

E 2.31 fee}; whether 3 times will do it,faying,
3 3 timeS4 IS Izgnown szrom I ,andthere
I3 , . 3 v .

gemams 5, whxch makes the to be 58.;
"then I fay 3 times 8 is 2+,now4from '8, _
; and there remains 4, then (2 that harried) .
:frdm 5, and theré remains 3 “

._.1.
a m’nmnpz «

3W

‘ ~ ‘ ”WIWWWW

2,4-
14781766;
9:3 '

? 3 3. Ircmovc the Divifor oneplacencarcrfi,

a the right hand ,’ faying, 3 how many times

4 in 34,, which is 7timcs ( bc’caufe 9 or 8' /

times are toomany) thcnd7 timeS4is 28;

now 28 from 34, and there rcmains6 gthcn ,

7 times 8 is 56', 6from 3,31 cannot, ebut 6,

"Rom II, and there I'Cfll'élinSS'y’thC‘n ; I; .
carried, and 1 Iborrowed i536, now6fr‘om_ -

, 6, and there remainsnmhing.

3‘75", 7

was ,

X78176(3'7‘
51:88 ' ,
:3 ' .

“ Againfi' Iremovc thé Div‘ifor, fayinggg

' _, 3 how
  
 

‘V - _.. .--_,.. ..«-»-- "'

    
     
     
   
   
   
   
   
   
   
  
 
   
  
 
 
 
    
   
   
 

 
   

e 42 Dibifioa..l Chap. ’5'

i . how many times 4 in '5, which is once ;, if?
i then» I: faionce 4iS-4- NW4 {mm 5' and
there remains .1. Then once 8is 8-, no .
8 from 17 and there remains 9,and I that
lborrowed from I, there remains nothing.
” 361’ V I
Sޤ9*
X73175 (371
$888
fl? , ‘.
Again, I remove the Divifor, and feek ,' s
how many timesa4‘is in 9,: which is twice ;;. ..
faymg, 2... times 4 is 8,,Tnow8from 9, and ,
there remains 1,. Then zitimest- 8 is 16 5, ;
X‘ > now 16 from 16, and there'remains'nm
thing. So that I find the Quotient to be"
3712, the’fame as the Muitiplieand was in
thCMLfltiplication, which is amol’c certain;
proofiof- thatRuIe; ' ’ ‘

How to prom Divifiom
352:
5%59CO ,

178276 (3,712.2
98888 7 ‘ 48 -

.4315? 23.6.96' ‘ _
;.14848
Proof 1.78176

 
 

 
  

“"1"" '“W w - :

Chap. V, Diw'fiorz. ,

And as Divifion is afure proofof Mul-
tiplication, fo Multiplication is thefurel’t
proof of Divifion, which is performed by
multiplying the Qiotient with the Divi-
for; and if theprodué’c thereofbethe fame
with the Dividend, your Divifion is well
'- wrought, otherwife be fure fome error is
committed in your work. -

Alfo if any figure-s remain after your Di-
vifion is ended, they mufibe added into the
Produét of your Multiplication, according
to their feveral places, and then (if true)
the Total will be likewife the fame with the
Dividend; as for example doth appearein
thelaf’t form of this Rule.

Q

A more eafier may of Diwfion, and
with 1%) figuresa,

T here are 4648 flailling: to lasagna”)! di-
aided beth‘xt 34 Men: I demand what i:
. mob [Mam proportion,

I will not Fund to {hew you moreof this
common way of Divifion, which is indeezl
very tedious and burthenfome to the memo-
ty, and hath caufed (to my knowledge)
many to defpair of attaining it, and fo’
grow.

#1

   

    

  
44 / ' Die/225%. Chap. Vi,

proceeding further in this Art. But pron ‘V
ceied by the Method foiicyw‘ing,~ which will;
enabie one to‘go on with far moreeafezmd "é'
delight than commenly is feen. '

The Qgefiion being fiated, is to be fet _

thus.
46%4<
‘ , 34" -

, ‘ Wherein confider how often 34inch-
tained in 46, which is once (or rather fee
firf’c how Often 3 isicontained in4, which
likewife is once) then fet I in the (bode-ht, "
faying, once/4k 4:, now 4 from 6, and
the-re remains. 2 guwhich .2 fet direaly oi
vet: its dividend._ . fi

9’5 (I ‘1 E

; _ . 35: f ' , .j,
, Then gdbackwaxd to the next, faying:
once 3 , is 3,’ from4 and there remains I, "
Which \al‘fo fet over the 41 , and cancel it,
and,3 the Divifor, withsa daih of thePen,
as yon fee in the fixample. ' ~-

‘ Then remnve the Divif‘ors' one degree . '..:
further towards the right hand thus: . I

l

I

12‘
[e684(1

 
      

k
y: ‘C

if '

Chap. V. Diw'fion. ' 4;

Then confider "how often sis contained -

.in 12, which is 4. time5°7 but4timesthe
~ next Diviior cannot be taken out of 8, and

you mufi: never take one of the Divifors . i

y ' oftner than you cantake all

the ref’c 5 feeing then 4 times 2 i

is too much, try (in your I256

mind) whether each Divifor gawk} (13
can be taken 3 times,‘if f0, 34%;}:
then place 3 in the Qioti' 3X

enr, faying,» 3 times 4i512,

12 from 8 1 cannot, bur: 12-fr0m13 and
there remains 6', then 3 times 3 is 9, and
1 that I carryed i510, 10 from 12 and
there remains 2.

Again; remove your "Divifor toward?"

"Your right hand: thus,

2
X256
$684CIS
MWM
53
Then confide: how often 3 is con»
tained in 26, which is 8 times, and 8
times 3 is 24; now 24 from 26, and
there ren'sains 2, which 2 Wiii make
the next figure "to be but 24; then 8
times 4 is 32, 32 out of 24, cannotbeé
an a

   

 
"" ‘»* .--,~

4-6, biw'fion. , , ‘ "Chapy:

and therefore ‘ian, 8 times is too much“);
which feeingxfov: try (in your-mind) whe-~ "
that (7 will do it, faying 7 times 4. is 28;

28 from 4 lcannot, but 28‘from 34, and;

there remains‘6. Then7 times 3 is 2 Land __
3 thatI carried is 24-, 24 from 2.6 , and
there remains 2. Canceleut the Divie‘iend
and Divifdr’, and fet the remains over head;
«and yourworkis done. , \ ‘

2’ (2.
226 (6
W84:»(137
3¥%%
3%

The Quotient {hevveth that 34 men
muf’t have 137 {hilhngsva piece, and 26

, {billings over and above to be div'ded a.
’, mongfi them. » ’ .2
Which Remainder-5, and all ohter: of may v '7
Diraifimyl flue/l flaew youwlmttloey are when
Jon pmfiice Fremont, mtheplace More caflve- ‘
m‘mt and proper. -

4- Example. 7 ‘
There 13: a Ship taken by 346 Sedemm

which 195‘ valued at 87654.1. to be equally di. ‘ h
t __ ‘ 4 , __ Wilder.

 
 
 
  

P;
55

    

Chap. "V.

 

Divifion. 47

ti‘dirvided among/E them, I dcmmdiwba‘t sac/o
k [Wm muff have.

87654 C

346

it

' Confider how many times 346 is contain-
‘ed in 876, which is twotimes 3 or rather
“how often 3 is contained in 8, which is like-

' wife '2 times; fat 2 in the ({notient, and

K
‘r”

it

 
 

‘fay, 2 times 6 is 12, 12 from 61cann0t,bnt

/ 12 from 1:16 and there remains 4.

Thenz times4 i553, and :1
that 'I borrowed is 9 59 from 18+
'7 I cannot, but 9 from ’17 and ' 87634 (2
there remains 8. Then 2 times 3&6
*3 is 6,and 1 is 7 5 7 from 8 and
there remains I. Then having done with
the Divifnrs, remove them tolthe next place
towards the right hand, thus;
Then fay,how many'times 3

in 18 6 times ; but that being I, ,
too ni,uch,(becaufe all the refi 87:24 (2’
cannot be taken in often)rhere 3:;

fore fay, Srtimes 6is 30, 30

from 5 I cannot, but sofrom
35 and there remains g.

’ Then 5' times 4 is 2.0, and 3 thgtibor.
.- :34: V

‘ i e ‘ rowed

  
 

   

 
V " :-,.;~ y.-._v. _‘

“Dig-wok;- '1 ‘Chfip~V-“’; 

Mfi23fl

‘48 .
rowed is 2‘3 ;/ 2-3 from ,4 Icannct,
from 2.4, and there remains I. "

I/' -II
ages ~
>8762#(23
[3&66‘
351*

_ Thea 5 times 3 i813, and zthatlbora
rowed is 17; 17 from 18,1an then re-
mains Ix.’ " . ~ I '
( Again remeve the Divifors-(pondering-
"in, your mind) how many times 3 can I have
in I], three times; ‘by‘which I perceive 3 ,
Will doaic, therefore: place itin {he @oti. 3;
ent, fayiri‘g’, 3 times ‘6 is 18-, 18 from 41
cannot, but 18 from 2.4”! and there remains
6 : then 3 times 4 is 1 2, and two that] car-
ried is 14:, from g'Icannot, but 14mm
15, and there remains 1 : Then 3 'tiil‘lfCS3
is 9, and ithat l'carried is '10 f, 10 from I x,
and there remains I.
(2
n” (1
£343(6 ~.
375544253.
~3§666
3%.?
3.

'\

 
     
 
 
 
  
  
 
 
 
 
 
  
 
 
 
 
 
 
 
 
   

Dz'w'fim. r . I 49

  
  

, 5 Example.‘
There M a Cary 54km 2m $533 WW: 5}; 9334 5
Soul'dz'm that 1/: mm}: 7 3 9624: I. 1 05mm 2:! '

gym: MC]? .30 “Miter nuts/i h we 3

f ’ , 9034 ,
Hate you fee that 9034 ('31th be mn-
tanea in 7506, therefore remavc your Di-
gvziox to the ncxc place towmd the right
hand this:

  

7306942

*' 9934

e ‘ I. Ccnfider how many times 9 can be
had in 73, which is 8 times, pfiacc 8 In the .
(119mm, Paying 8 timszs 4 is 3:: , 37 out” ;
of 2 I cannor, but 32, out of 32,, and them
E'l‘emams O. 7 _ .

E Then 8 times 2, is 24, andg that 1 bor-
Frowed is 27, 27 fwméicaamt, burg-y;
from 36, and that: remains 9

. Then Stimes 6 is@ but 3 that Maria”,
[is 3 , 3 from 19, and Ellen lamains ,.

   

790 ,
"" 4.?{CX52’42 <8
9P3? ‘
J Then 81 times 9 i572, 366 I thatlbor-
rowed 1573517093 73, a.d then: re»

8135 O.

 
 

A gam

  
  
  

M, “a. i

5  ‘ pf ,  chap;

' Agaig remove your Divifor.

1.,“

   

   

Va
Here; youlalfo' fee, that 9:334:11: Divifor E.’
cannot be takeg out of the Dividend; there— “
fore “cancel, it, and remove it to the next . '
place, fcttinga Cypher in the @otiem.

          
   
     
   
   
 
  
 
 
 
  
 
  
     
       
 

K. 790

7345625312 (80
gflgtfi

~»_9¢3

Then try again how often the DivifOr is
contained in the Dividend,which i528 times. t.

Then fay, 8times-4is 32; 32 out of '2 I: 3
cannot, but 32. out of 32 and there remains
nothing. , f ’ 7 E
, Then 8 times 3 is 24., and 3‘ thatlbor-
rowed is 27; 27 from 4.1 cannot, but 27
from 34., and‘there remains 7.

‘ i (6C7 .
‘ V ’ 29?K7(Qh i ;
72;,Co’éz7t'2f 808 , E
aflgg “
£33?)

The“ I tim€50550abflt 3 that I Borrowed )
S c’ ‘5 3 s 3 {tom :3 I,cannot,but 3 from 10,;md;

Etrhctcremainwc _ , , I
  
   

ii} ,
‘ Chap. V. Diwfim.

Then 8 times 9 is 72, and I that i borr-
rovyed IS 73 ; 73 from79, and there re-
mains 6. So that every Souidier muii have
_ for his [hare 808 pounds.

\

f .7, < 3-"... ,mWaw W

6 Example.

[What is the fitment of 563374 8,
dividedéylgOégog ? 7

Cfinfider how often the DivifOt is con-
; 181061111 the Divtdendmhich is here twice.
37 ._ ,

990141
e 362%7s?8(2
' 23268¢3

,. Then fay, 2 times 3 is 6 ; 6 from '7: and
there remains 1. . ‘
Then 2 times 0 is o -, o from 4, and there
remains 4..
Then 2 times 8 is 16 316 from 7 icannot,
but 16 from 17,and there remains ‘2’.
’1‘ Then 2 times 6 is 12, and s. that i hor-
rowed is 13', 13 {mm 3 I cannot, hut 13
I from I 3, and there remains 0.
Then 2 times :5 is o,hut I that Ibortowed*
is 1-, 1 from oi canner, but 1 from Io,and
~, there remains 9. ‘

 

D 2 ' Then ‘

  

 

  
 
   

 

‘ 5.2“ ‘ Diwfim. 8 Chap V.
Then 2 times 3 is 6, and one that I hor-
rowed 1s 7 , 7 from 61 cannot; but 7 fmm

16, and there remains 9.
Then 2 times 2 is 4., and one that I bor-

rowed is 5; 5 from 3, and there remains

, nothing

Remove the Divifor

Ag11n,C0nfider haw 11151117 times the
Divifor is c011171ned1n1h€ DIVIQCI d which
,is 4times.

67427
777 :77 7(77
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"Ihgcn 41 timcs 6 1527,7667 3 that I‘hor—

T617773 is 2.7, :27 fmm. I IIIIIII'I8I7 but37
from 3 73““ human: 12-41

    

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1

'6'

.
7‘

'7.

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hap.‘V. w ‘ Diwfiom ,5‘3 ‘
Then‘4 times (5 is 0,. but 3 that lbar-
rewedwi’skg :, 3 {pm 6 I cannot,‘ but 3 from
10, and {here farming 7“. . . ..
Then 4 times 315 12, and I4 that I by:-
xowed :is 13:, 13 fromg I cannot, but 13
from 19, and that remains é.- v ‘ ‘ '
\Then 4, times 2, '13 8, and 1 thatl bar-
' rowedis 9, 9 fmm 9 and {hercrc‘mains (2,
fit; that that: ngiw: is: 24.;01' the Divifor is
mntained Enthe Diviéand .24 times. ‘

Habigg laid dew . the latter part of th: far- -
my? Rule, in the mtwe of firm Rzale‘of Three?”
; ~ and @yrebmdmg it «my maeflkryfizr ymmg ' 4‘
* lawman, I flaw! therefore abjérm thefamw
have in Divifion, which i: ptrformm? by divi-
ding the [wand numéer by rlocfirflg cm’dtlae ‘ A
«fitsotiwtis‘tb; Mfwcr to'tbe 5Q; im. *4

If 63- Cations make 304, Pints, ”what '1
Gallon 3

 

 

Mvwwmww ,
, . A

'z’ 7%” am»:

, " (T3 “”2; If "Ti"

Sdfiflf 8 pints.
5}

 

If 4 Hogfizcads make 2. 32. Gailons, what

I Hogihead? ‘ A ‘

, I .

3'52 (63 gal.
flit“?
. v F .,.,.~-.

" g4 ' = ~ Diem. , . Chap. V\
if onuns/makc 25040 Gallons, what I '}
Tun?! . X p . m
" 5.6554,”! ( 252 Gallons.
2125275 > _
" If 72 CC. grofs allow 1080 pqund for
Tare, what mall: I C. allow? '
' .%5
138% C 15 Foam: flair.
92:2; ‘ C,
If 152. ,C. col’c 760 pounds, what I C ?
$65.2” ( 5 pazmdsfdcit.

' .. X132 ,
1f goo Dalian be zgwo‘fdwhat I’DOII'M?

3’
28¢,fip’ (5 6 pence fair.
{59’

"As in Mult‘iplicationmhm the Multiplier
» - is 10, 100,1090, (33°C. you add to the Multi-

' . plicand on the right hand f0 many Cyphcrs
{ as are in the Multiplier to [make the Pro. ‘
9 “ -_ dualfo in Divifiomwhcn the Disifor» is m, 1,.
, £00, 1000, cm. you mufi cut of? f0 many
. Figures from the Dividend to the right 7;
, ‘ hand (with a perpendicularLinc) as thcic
. at: Cyphc-rsin the Divifor, and the Figurés“ "
‘to the left hand are the (humicnt: Divide .
373900 by 10,-01- "100, @“e‘. ' '

‘ 1 Qwrv37590l0£4m 3759bQ

 
  
   

     
     
   
 
 
 
 
 
 
   
   
     
      

Dz'w'flwe. 5% ' ‘5’

I [ha/27ml.“ (I hope) need to trouble myfelf, or

Learner to flJew all]: Working oftbis S “272,07” any

whenhewz'ng ream/m I fuppofi )feefifciemiy treez— '

tee! of DiwfianJ—ut will leave it to the cenflere of

' t/ae mofl experienc’d to judgmhetloer tkie mmmer ,
ofdz'vieling be not p!4in,linml,and [0 be wraugkt

L with fewer Figures than any which i: commonly

: taught : A’: far Example appearetb.

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D 4- C HAP
 

   

"36' ”Chap.VI\

 

; ' CHARVI,
,‘R 'E'D u .c T10 N";

 

   

3. 5 for Redfifi‘ian, .thwgh it be m)
‘ _, Ruic abfoh to? of it feif, butmema—

‘ "iy wwught by Multipiicaxian and Divifim
‘ (as 1 have hm: manifcfied ina plafinmann
am) yet 1 mm}: good (mm; altogmhcr t0
omit it, 169% any would cenfizrc we (03" {a
{icingg in ragard it islveryaufimfly prafii~
fed) :0 dfiiiver ,ibmcwhat thércfbrc wann-
magfit. . . ’ ' \
,4Rcfiééxfi'ian zmafiwb km: {a firing (xii/grail”, ark
grmz Dmbfifiimtiam ifltafi‘mfl, 41M fméifi in“? L'
groan , ‘
Eras}? greaiflcnaminations are. Ezgrcgughr
mm flag? in Multipiic‘ation,/as -
I ,Pwmd: nudnpz’z'edr’zy .26, are fibiliing‘n
\ Skiit’ézqgs mmltipls’rd by 12, We pmce.
Pam: wxmzilz‘épféssd by 2, fire: balf'pmcm
3:35.3255—3'fififiiigfifli by 4, are nrtbiqgs’.
P935515 mmfiflied é; )1 2.450, m pawn
meds mfltiplim’ by 480, are lméfipmw, A '
Pmmdmmltipiiyd by 960, are fartlaiflgJ.

. Secondly?“ '1

 
           
    
     
    
 
         

b/Chap'w? Redézmbg} 3'7

Sgcnndlv,a” final! na‘mesare brought im»
great byDivifion. As, " x ,

Shilling: dividedby 20 are pmmdt.
Pence divided by 12. 22!}? flgzllmgl. ‘
; Halfpmce divided by 2 are pebce. ’
‘ , Farthing: divided by 4 arepe'me. ' ,-
Pmce divided by 2 40 are pounds. I ‘
Half pence divided by 4.80 are powder.
Farthing; Divided by 960‘ are gimbals. "
\ L000
20

 

* 20000 5';
13.

, y ' 24o©00d§
4..

I

 

960900 ,7.) ,

’ i‘. Confider whether the film propound’.
ed be to bc‘brought‘into a greater or Ief’ncr ‘
" denomination. '
‘ /2. Canfidcr how many of the one can
A make the other, as heré how many {hiIJ
. \ lings can make: a poundwiz. zo : and CO‘flti’é,
' ' how many. {billings a pound makcsm‘z. 20».
5 ' ' D. 5 ' ‘ b, There; _.
  

 

#2157161:

Therefore of neccflity there mui’c he 20
times f0 many, which being multiplied by
2.0,m makes 20000 fliiliings, and by 12,
24ooco pence, and by 4,1041% 960000 fare
things, as 111 the Example. 1

1n 9612090 fatthings, how many pence

fl1iIlings and pounds ?

.r . , .
95955929, (zgyz’xafifb’aaooio .1.
51:71:515115151: z::::z 1,oool.f11cit1

To bring {billings into pounds (or to di-

7"; yide by 20) cut off the firii Figure towards

Chap VI ‘ F

{is

   
      

1

.._,¢:

the right hand witha dafh of the Pen, and: y

i . rake half of the remaining Figures.

In 84717.1 3 farthings, how many pencey

= gums, and nobles ?

- 22 ( I 22m / (I
82721122 (22278953 (1211110
fl’fléfiffiifi‘fi‘é #9994“?

, f“

fagz't 26472. Nubia f;

  
     

. 1"er 1511!? 174‘: " ;

   

..’ Chap.VI.

Here you fee the fum is to be brought into
a greater Denomination than it felt, which,
is therefore to'be done byDivifion. ‘

Then you are to conficier What; your Di.
vifor mul’t be, which is here-4, becaufe t4,"
farthings make a penny 3, and asoften‘asa
is contained in the faid fum, To many pence
there are.

Your Farthings then being brought in-
to pence, confider the next Denomination:
what it is, and how many of the former
make one of it; as how many pence make’a
groanwiz. 4.; and look how many times
4 is contained in the film, f0 many greats
there are.

Having brought the pence thus into
groats,endeavour to bring them into nobles,
by confidering how many greats makea no.
ble, eiz. zo ; therefore divide by 20, (by
cutting off the firi’c Figure towards the right
hand, and taking the half of the refi) and
your @mient will be nobles.

I {hall fay novmore as to-Reduftion of’
Money, only leave two or three Qqeltions
for the Learner to praétice upon.

In 100 1. how many 5‘; d. 5. 3. dandy 961.;

In;

Reddfii‘m‘. 5‘9“

    

 
      
        

1- 6rd Realm/{fan Chapfll'gj
”In- 47162. matks,‘ how many nobles, é
~ .. p’oundfisgroatsw ‘farthings, 6 d. and 2. d.

‘ In 76.6311. 11 3. 10d. how many fhfl.’
j ltings, penée,«and‘pounds,farthings,crowns,.
1 _ and 01,7. 1 1 ’

. Rett’ttfiiéntf C lath Mmfure.‘

    
  
 
 
   
   
   
 

U, Ola/Ewe in this 521261.411 the Redufiiomfoti , é
having; hm many of the am Demmindtim do
' 1 "take (me of the other? antifo multiplyar divide
. accomflt'ng to the two Rule: afaregat'fig, in 126— i

 

 

«Mitten of Money. , :3
In 43‘7zytzrd5,1how many gm} & Elsi/em, 1
174.88 gm. / , 11%

1 1 2952: (I ' ' ‘1

X75158 8' (5 82.9 fztcit.
1 107862ElltEnngowf-nany qrtga‘ndyards?‘
.393 w

 

agar/2319827 .
. In 85: pieces, each11191EUsfidemany 1'
quartets, ngils and yards. ? 1
  
  

    

  
 

   
       
 
 
  
   
    
   
   

i,

,6

V “Ream”; t

a": ‘ , I
7 Rednflian of Wine Arlen/bra.

' \ III. 1:133: Tans, how many H‘ogflkadéfi .
gallons, pottles, quarts and pints? ” '

35‘
4.

3 4-6 13031.29,
63. ,

420
2 8:0

 

 

 

8820 gdé’amg
4 _._'
3 5280 qmrm
:2,

 

w

' 70360 PM”.

In 4:712:68 pints, haw many (gallons: 1
and Runletsv, cad-l2 11,-gallons3 , ;

 

Ingz7 Bag/gig, each 32.. "galions, how
many hogfhcaci's and was? g:

   

I
   
    
     
     
 

    
 

. v
_. .4".-

Reduflim.

' Cha’p. V1-1:
,Redufl'ion of Time.
IV. In 1659 yearsggég days a year.

 

how many days,h0urs, 24. hams aday. ‘ ,, ‘
and minutes? 60 minutes an heur,
' 1659Kyeanz ’
x 36; -, i
.8295.-
~9294 _
4977 g

A 6:; 55 5 3 day,
3' Jr

 

2422140
1211070

1'43 3 2 84o beam.
6 o

8'7 1 970400 mimm.
W ,

 

 

In 817 1627 lagsminutes, hmL many hours, .9
7‘ days and years P = 1;

In 2.0 years and a halfkhow many days,
hours,.§nd minutes 2. x 7
 
  

         
   

’— Redaéi‘zm; “'7 "’ i 7 »~'- *

ham“ '6;

     
  
   
 
 
   
    

  
 

Reduflion of Land Meajfwe.
E? ' 8 F url'ongs a Mile.
E hoIn 51:: D4938“: Poles 3. Furlong
i, w V I6“; Feetgt Pole

3 Fezct a Yard. ,
I 2 Inches at Foot.
3 Barley Corns an Inch. ,

Inches and Barley

longs, Poles, Feet,
COrns . 8

100 miles.

mm»wim 1V "' " '

gmurltmgs.
40
32000 Faith
'33
96000
96000
72: 1056000 balffi’m

“m..—

 

 

52 8000 Feet.
12

 

 

6-3 36000 inches
3 _

’319008000Mrlay corny; ,

  
  
    

   

\ ”Redm‘zm.

  
   
     
      
   
    
  
    
   
      
 

Redufi‘zan of Troy weight.

VI In 87 pou mi and ;, hbw many can» .
ccs, pfinny weight and grains 9 /

. .87W%

.12

gmmwiwmmwww131W»,r”. .. ”kw” r ‘r . 1.
M -> _ M . H: 9,.“ - ‘ a“ _._ .= . v.5

 

 

 

52 m4 *’ _ t

i 3'75 L I'

I. 1050 2 1
’ 20

7' 023000 dm 5

2:4 5

8460.3 . 2

+2000 5

.._..._.__.. 5

504000 graim. ‘

a

In 71§1213 grains, how many penny 5

Weight, ounces and pounds? 5

. / . » “i

In I; Ingots; ca’ch‘7' pound and i, how, 5

‘ many ounces,,penny weight and grains?
 
  

. /
k
2,

 

 
    

Chap. VI.

yam-vap- 2~mmm«ww 72.22,} 7.2 5,,
7 ‘2“: ~2wa «MW;

«mm, W «wwflhmmmflfi-“G'Ir V':-“‘_’“”""_:

  

522252255202. ,4 ',* ' :65"

Redufiian of Averdnpoid IVeiaht.
V11. Ingé C. weighr,how many qr: 113?. ,
4- (and 5?

3 9 4 quarter/’5. .
2.8 2 '

3372
7768/

m P5522745.
16

. 31257 ‘23.
‘13752

mum

1 72632 55552555

 

 

~ It! 400‘!“ z 19 pounds 11 ounces,I10w manV .

,4 _ ($5.153, and?

1 6 “' €55.25? 5575.
28

1305
32. s
4555;205:5556.

I 6 '

 

I

 

 

“~—

37331

‘4556
72 89 I 02575055.

/

In 8 2 14 ounces; how mamV 3522:522d5 qml I

  
     

  
   

  

Chap-lg

1v
\ .':
K 5 ,
I

 

'« b 6-6 , Redué'z‘im ' V,\

, In 20 Bags, ‘ .Each .3..C.~‘5, bbw mafly 77‘5- J {i
and Pounds? 4 ' 4 J:
14. ‘ V "i
28
,1 1'2
, 28

m

392. paumlr in om.
ZED

 

 

 

78.4.0 pomzd :in all. ' ,

 

Where you find the word [each,] have a
‘fpecidl regar'd to it, and reduce the particnlizrs
which it implz'ezh; firfl‘ into one Demmimtim,
then when you know how much .1}: contdified in
am, you hwy eafily know how much I}: in all. t
, In 36 Barrels @f Figs, each 3' Oi grafs, '

/ Tare 19 peund perBarrel,how many pounds
neat? ’ ’ __ , .-’
Whether the ward [Tare] imply per Bag, a.

per Barrel, or per (3. (five. it i4 411m one, if
you keep to yourformer Rule 2'72 Multiplicdtion, 1
{7y ohjér'ving which, you cannot mifi of what
you would kzww ; at here Tare 19 pounds per 1
3

 

 

Barrel ?' - ‘ , \ :~

, , Say, if 1 Barrel give 19 pounds, what V'
. 36Barrels? ‘ 7 , _;
. ' ‘MUL

 
     

Chap. 1V. Rédfia’i‘iwz.‘ '67 f

Multiply 19 and 36"together, and the
Produé't is pounds Tare; then fubtraa the
n \ pounds Tare from the pounds Grofs,and the
fiemains arc pounds Neat. "

 
    
  
    
   
 
  
      
   

36 Barrels 3C. “:1

F , 19 anefar I Barrel. 4.

, 324 V 13

36 \ _ 28

'7 684 Tara in all. , O4.

M ~ 26 ,,

; ’ , 364120142751: in an: ' .

' 36 (Barret;
2184
1092

I 3 I 04 pound Grafs. /
, 684.
Iz4zopaflndnmt. \ .L _

 

.In 45 Bags of, (5‘6. each 17 Cigrofs’,
Tare 1 5 pounds per Bag, how many C.Ncat ?
In 4.7 C. i grofs, Tare 17 pounds per C. ' .
how many pounds neat? \ ' ~.

’ WU" 1mm” , .m,‘ H , \ w ,; ow” J u. “Hwy
a ,f ’3 a v n“, MM an

«In
wm-uyq

‘ IVI‘WV’V' , V.
,ng
, VI

“ Number

raw-.WJ-«N‘ he“ L.w..-n.n,.z.:.«.a:W.WMfiua.a-wm',wammmw muriM-un.

5'8 ‘ ‘ ” {‘Redzifiim. , Chap VII 3

In 5 Hogfheads of Tobacco, each con~
tainmg as foIIoWerh, how many C. neat P

«vzz.

IE
11 fl ,
Jig 72“
16 ram“ 56

298 g7;

27 ”6+

{3
IQ
. V
H.

w

q’”W

W3
“'3 N033

cmmamin g

Mag. nib... m

sand haw many Father

I, N M
”’3
It'll

Ifig713fe
at 19 C;
In 5671 Pigs OIL tad, each7 C. 5, haw

0

‘manyFotherm 19C”, ‘ ?

facit2181 Fothfir r55.

C H A P. VII.

Numeratiw of Fmfiz'om.

TH E next thing to be treated of, are
Fraf’tions. ’

1 Cenccming which IflxaIl Ifhcw what
a Fraéfion 15 ~ '
" 2 Hm it 133240? 6?:

3 How many {03: of Fraé‘zionsthere are. 3
A

-, .m-...rw.am‘$

 
 
    
     
    
   
 
 
   
   
   
  
    
  
 
       
   

    

Ch. VII, Numeratzm omeéhomn 69

A Fmfiion, (2r brokenNflmbtrw apart or
9 many parts of a whale Number: For 522'
whale‘A Number: take their begimzzmg fram‘ (
one, (and continue in 22222221722“ 122251222213 mdv ;;~
, ft) the [22262 whalel‘v 1229711367! 5); zmégmatwfl,

, may be 421712125221 or broken mm 12356633 27212222225,

5» mfinite.

1’ The'efpre to attain thf: knowlcrge of,
them, acquaint your 12!” with that: two
terms, M2-memtn2' and ‘Dmamimmh ; ,,

' Th2 N22memtar cxpreffcth the number of
2 the parts
'1’th Dammimwr giveth chore parts their .,
“811,335. ‘ A , _ X '1: A

" I 2 3 .Nmneramfin
E 3? :22 ‘2D22120212ifi22wr.

1‘

5—; IS the 0222:3121? of anything

)5; netwothxr pm‘s cfamy thing.
2 three gunners of any thing

(i; IS 20221 five parts of any I: ling.

‘ Pro; er
V—\ F} 511,11"
3 (ms.

P22672022: of Frafiiona

13225220225 23f Frafiiam 12252222 6022222202201 that ' L
Ed, 2225-202 bet-22222225252252, .125 3 2f 43222222 25,2120
E 22222222 2f 2222556 51522222 2225.

If .
\

underwent». \

.“ ummmn «who? but-aw”... » .m , "w. .,.

e. - wear-(L

' :70 Redagiofl omeéZZam. Ch. VlIl.

\ , Improper F mfii’am.
If the'Numemtar be greater than the De.
nominator, the Fraé‘tion is improper, and con-

\ taineth a Unit: or Unites, or fome part or

parts of the Denominator,as 5" 4" is 3 Integers,
or whole, and 3 quarters; but when the Na.
memtar and the Denominator" are alike, they
make a Unite. \

Though Addition in whole Number: be
immediately after Nomemtion, yet in PM-
Eliom it is not fo, becaufe there are, as here

you fee, Emilio”: of feveral forts, which ‘
muff of neceflity be reduced into one De— ' 1'
momination, before they can be added.

Therefore to avoid diforder 1 than firl’t
{hew what this Reduétion of Fraftions is;
fecondly how to reduce all Fraétions to one
Denomination or likenefs.

 

C H A P. VIII.
Redaél‘im of a Prac’h‘om.

A What Racing-ion is.
R Edu-Ction teachethta bring Integer: into

mehom, or contrary ; yea F Mariam o f
dzoersoDeflamimziom into armor whatyog lijf. '

:‘Msflmfléfismemwam ,‘ ,

   

  

5

a}

J
51
a

i

 

‘ . "5.2",

r ,

 
  

”I... w

E Ch. VIII. Redufr'im of Fmfiiam. 7 I
l lwould have reduced :5, f; ofan Ell; or
what you pleafe into one Denomination.

To Reduce proper Fmé'liam.’

For the efi’efting of this, and all other
of this kind, multiply all the Dcaominators .
, together (which produft take for acommon

‘ Denominator)as 2 times 3 is 6, and 4times
6 is 24., your Denominator.

Then multiply the. N umerator of the firlt
in all the other Denominators, except its
own Denominator; as once 3 is 3, 3 times
4 is I 2, which take for a new Numerator to
the firfi Fraction.

Then multiply the ,fecond Numerator in
all the Denominators, except its own; as
2 times 2 is 4, and 4times4is :6, which
likewife take for a new Numerator tothe
Second. ' .

Then Multiply the third Numerator in all
the Denominators, except its own'7 as 3
times 3159, 2. timesg is 18,which alfo place
fora new Numerator to the third, and your
work fiandeth thus:

12 16 18 50 that ii, ”24, “‘3-

5‘“ iareequalton 32, 4

,2_
3
2+

 
   
 
 
  

 

 

72 Realm/72022 of 17222272022115.1Ch1‘VH." 1

II; To 1222213122222 Fmfiiom of 152222722225
into one Denomination.

Multiply an the Numerators together,
and take the 1912121118: thereof for a new Nu—
meratm, and Iii-2 gewife multiply allrhe Geno» \
minators tog ther, and make the Totala 2

Denominator. _
6
Example,; of? of f;
1, 1 22 '

III. To reduce improper 172422242:
, mo whaleNMfléers. ' 2

K

‘Divide the Numerator by the Denomip
11211012., '

Exemple. 2:;
z: (514-
4

IV’. To reduce a whole Naméer mm
222 zmp220per 1222229072.

L21: the number giv2n he the Numerator,

and 1 the Denmmnamn
Example. Reduce 131ntegers into an im-

p: oper Fraé‘cion. facit *1
* ’ V. To

    
 

    
   
   
      
  

- , in...“ g: ant—"erx ::~,::T‘:: :; er “

" Ch.VHI. Redufiim of‘Fmfiimxzst
‘ V. To reduce a whole N umber joyrzed with
a mefiog into one Benomirmtiam

‘ Multiply the whole Number into the De
. nominate! of the Eraétion, adding thereto
t the Numeraton

r»

Example, ; yards and g; flo’il‘ “aria

VI. To reduce a greater me'l'ion into lejfér
term: equiwhmble to it feéfi

Take die half of ' the Numerator, and

half of the Denominator, as o‘ft as you can,
and when you can take the half no further,
take the one third, or the one fourth, or
the one fifth, tic. both of the Numerator
and Denominator.

Example.
' Iwould abbreviate fiéléélgo‘e I‘Hfl

Take the half of 24, which 'is 12, then
the half of 120, whichis 60; again, the
half of 12, which is 6, and the half of 60

" is 3'0, then the half of 6 is 3, and the half
of 30' is 1;; here you fee that the half
cannot be taken both of the Numerator

{ ,a’nd Denominator, therefore try whether
it will be abbreviated by 3, as thus: How

‘ E ~ many

7;

 
 

u ‘ “it myW'Mammufiarmmattwmim».wkhkmwamoi...‘ , x ‘ V '2 '
. . _ i ’ . t, ‘ ‘21:”) ~,

  

75,4. Redufiz’an qurdC'inflflt Ch.;VIII~§f
,m‘a’ny times 3 in 3, once} then how‘many .
i times 3 in ; 1;, five; times. 'So thatiis in

the‘ lowef’t Denomination, tyct it retains
the fame value; for 3*“ is equal to T’fét.

I A ficondigkind of .Axbbrwiat‘viari.’

"Though by the former“ Rule alla‘FraC-tiotts

might be abbreviated, yetwhmy’ou can- '

l l I I 1 I

‘ “013 ta!“ :3 E3 2) '5‘: Z: 7—1 315‘) 013913 (350-. TIN;

fcem more tcadious than by_\this'fec-ongliway

as may appear. _ ‘ .
I. would havethis fum abbreviated, figg

info a [caller Fraétion. ' '

For the reducing twhereof, J-divid: "
the Denominatorby the Numeratot, and-
the remain of the 'Divilion will be Ib86,
by which divide the former Divifor, .2 3077,,

and’there‘ will rcmaingog, bywhich di-
vidc your laft Divifor 1086, and there will

:rcmainAIISI, by which tcmains" lichife‘

divide the Divifor 993, andthcrawill re-
main 0; ’ \

Whgre note, that having tliv'ided-..your._
Denominator by the Numeral-or, an} the ‘

Divilbr of .cvery DiviGOn f0 Often b‘v the
Remains,~that»n~othing will remain; Then
that lafiDivifor will divide-both your Nu-

merator band‘Denominatorof , your: F rattio‘n.‘ '

 
 
   

,1,'fHaw to reduce or alter My'Fmflzon 1044119—

‘tend, dividing the Produé’t by the former
:Fraaions Dangminator, whofc @otient

.. *«lafi chofen. "

What 15 8 10f 21 Flam. EH?

Ch VIII Redafizm of 171111520111. 75 M

" fig 63 facit,§' equal 10 the former.

A5 111 the Example.

tiger Dmomirmtim, m Mamy, Weight, ‘or‘
Mmfizre, @0.

Multiply the Nurhera‘t‘br by fuch a new 1
DenominatOr or Number which you in-

1 16‘: " "

{hall be a Numerator to the Denominator
‘ " Example." , i
What 15 g of 12261. ‘
e ~ 211811. =
. 3. _ ‘ 7
What 1139 of 20 Shillings? '
What 15 i of 2 Yard?

’ ' What 15 6 10f 21 Tun of Wine?

What is 11 part of a Tun of Iron?

, 7 What 15 the 1-5- part of a Hogihead of Sack?

What 4 of a Dollar at 4 5 8 d.
facit 44. d. i.

9.1: iWhat is 71—05% of 2; of 5 flfiihngs?

 
‘1MfiilflLA ~.

rflvliwz'ifli'lifl.‘muluwkhmbllh an“, t .14». but .,

 

75 -Q451ditio';z omefiiom. Ch. IX.“ '
‘ Reduce \Fmé'tiom of Frabiiom to am fiflglc‘ “

Haitian, and work“ before. ~

l

 

"$2.;- 2‘: 9f;(15.&4.
fl! 1
1‘!
What 15 5 éofaDollar at“. 84? l
fflCiI 44-4,.5.
CH'A P. Ix.

Addition of Fmfl‘iwrr.

1. % Edition of Fraélzions is the putting

of two or more broken Numbers ‘

into one fum, or principal Fraétion.

In this Rule and the next, obferve, that

all Fraétions whatever, proper or imprOper,
mui’t be of one Denomination, or reduced
thereto by the former Rules.

2.. Being of one Denomination only, add

all the Numerators together, which Total
fubfcribe for a new Numerator over the f:
\ common Denominator. '

Example. .

Add 5‘— and 1 of any thing together

,3 tandi farm? ‘,’ or onewhole one. ' ”l

 
  

   

. .f‘ "/K'V‘F‘H‘e‘ W :7", ‘ r- y "ffi’m

__£Eé________

(0l80l90l96 f

» .fimiéiggggiflfi fiwit fig-
120

Reduce them into one Denomination by
the firlt Rule of Redué’cion, then add the
Numerators, as in the bait Example.

A’ more fiwedy way.

Multiply all the Denominators that dif.
fer in quantity each from other , and the
Total thereof {hall be the common Deno~
’minator, aud Dividend to each particular
Denominator, whofe .Quotiem multiply into
its Numeramr, and fet it direaly againfl:
its own Fraction; and, in fine, add them
all up, which Total {hall be a new Named
rator unto the common Denominator; and
add as many Integers as they make to the
whole Numbers.

Example. Tb. (2.4) or 12

620-}; 3 ,
271 3‘; 4.
103-;— 6

 

017% 9
716‘,"

————-—_

1723;

6

£3.
12.

 

 

’ ChJXe Addition of Frat/790m. '77 .

 
'1- '- .2.

‘78 Addition; 1,0"171w63121213217,~ ‘_ Ch; XI.

m M... ym‘. . ‘3 1

I III". Tet aware fiwfl way.

Cali «your Eye upon theDenominatorsg; é
and imagine what number will be divided *
by them all, and that {han beyour common 1,
Dendminater and; Dividend unto each par-

- ticular Denominator; then work as before .
in the laft Examples. ( ( u)

. Y 313-459 “

Number I 2 will be, 917—s-i 6

divided by ail the 106~§ 3"

fimomime. . 317-— 2.

32—5—3 3 ,
2398~§Ii~f " ' Io:

1’2: _

3. ‘”
7‘“:
§ 7.
3
i”
1

 

P33 1"

 

IV; Addiiz’m of Ema-ism of Frafiionx..,1
1' Reduce yourFrai’cionS'into a fingle Fig.4,
aion, according to‘the fécond Ruie in Ree, '
dué’cion, then work asbef'ore. , , ‘ "
eExam. Add 5— of f of iunto % of 53.39
6 I 24; f I 219’226. .
gofg ofé unto? of 7931-: 3% $1373;

+ 1W; 1 arc/3:313.“

 

WW

 

 

. 2334'

      

  
 
   

V. Addiiion of improper 2222222222: 2

Reduce your Fraaions into one Dena-j“

1202f mination, and work 222 [222222.
12 5222222212122 Addi + andi

 

2%?
~HJ~U~3
Equ
E“.
(32
u
N
PM
“Hon

532022 of F 2226220225.
Example . Add 3— and; ~ of i“- together;

  

ing to the fecOn'd 82522022 in pan 72, and
work as before. \_

 

 

4- 16 4S"
iof'f ’ . 7;? and
3.;me
/ 601‘" 2 '

‘ WWW-3211111: ,2 —- : 1n— vmuman _

,2 ‘ C H A P. X
32222273522022 of 1722522222222

UBTRA. C T ION isthctakingofone
Era.étion_, from 2122022262,; a. leis from

E222. .. Ȥ

ChX » Séétrafiibn of; Frkfiz‘bfin 7,4,7 ’

226‘;

VI T22 2222122 22 f 2212 272225322222 22220 ‘22 F222»

A 112% of 3' 4r¢Vd12ce intoa 43tingle Eraé‘cion accord---

‘ 715k

 
 

. .“a,Wmm‘muwofmuowmmkama» w“ um ix.

.. «- amuumhm-H...‘

  
  
  
 
 
  
  
 
    

' nation.

.

cnnx: '
a greater, or an equal from an equal. “

”Ir. Becaufe Subtraé‘tion teacheth to take
a'lell'et Eraflion from agreater, it will not

' be amifls to {hew you how to know the one

from the other. ‘ .

2. Thole Frafiions are accounted the
greatefir, whole Numerator multiplyed by ,j
the: Denominator of the others Fméz‘z'an', ""
maket—h-the greatelt number.

And as in Addition, fo here, all Fmfli-f
am. to be fubtrafied, mutt be of one De-
nomination, or reduced thereunto‘. '

II. ‘To Subtmfi Fmfliqm of the Denomi-

Subttaé’c one Numerator from the other; ,
and fat the Remain over the common Deg
nominatort ’ " ' ‘
. * ‘Exzzmplet

Subtraé’c—fi~ from ‘2‘ re‘in‘ain 3". I

_III., To Subtmzfi a whole Numher and a ‘
Fmfiionfrom a whole Member and a Fmfiz'o-m

Firl’c, reduce your Fraflz'om into one De—

nomination, then Subtrré‘othe one Nume-

rator from the other: and from the Integer
Sub-traét as you were tanght in whole

, Numbers.

, Example. '
Receive 30!. i. Laid out 201.43..

  
O'Ch,X.‘ Suétmfiion of Prairie)”.-

   
   

2

 

 

6 4
3. .1.
2

4 Remain e or i

 

 

8

IV. Another way.

Multiply the Denominators together,
and let the Produé‘t be the common Deno-
minator, which common Denominator di-
vide-by each particular Denominator, and
multiply their Quotients by their Numera-

tors, and fet down their Produé‘ts direflly '

againfi its Fraf’tion, and then fubtrafl, as
if it were in whole Numbers.

A: for Example.
Received 1001. £25?
Soent 93 13% 18

Remains 7 : 3;}

V. When the Frafiim to be Subthfied, is
greater than the F militia you are to Subtraf}
' from,

. Reduce them into one common Deno-
minator, (as you did in the lai’t Example)
and fubtraét the greatcfi Numerator from
, the" common Denominator, and add the
Remains to the Numerator 9f the lefs,

' ~ 3 s. ‘ which

 

 

7:
i:
l
1 ,
l
4
i
l
,l
i

1
2 twnn...’ ..,ymn,,..-,u ~44 «.1,» ,. .... my‘“ 7 <.

W‘th“?! A 3W5 7 I a: I . , v ,
:ub’

 
xmmwhmwuwummmw' gym “and; 1‘“ u m." . L-

<- Wan-3.3;“ .4":

L. um»

   
  
 
 
  
 
 
 
 
    

,whOlc numbers...
' . l

«we»

the common Denominator, . thén... carry one

    

: 82 Mamas” a ”(Sham Ch x1

" Which/fubfcribe forwa flew NumbratOr. unto '

tothc ‘next integer, and..yfubtra€t as imll.

:. . I C;

: .\ Received—4wro , Bought. 165, 7..

Remains“ I—e-i- Remains? reg-é

VIE-i When .Fraéti-Orxsipf anaions 3‘? to. ,
be fubtraficd, they mufi be réduccd,....1ntq

finglcanafiions, then fub’traéied as before.

. Examplg, 7;» of; % rt0» be,.._fubtra&ed,frgm fi-j ,
. am, being.»xeduccd>into .fin’gl‘c; Rafi-tong...

they. Jam? and in.) g

‘ ' 5 9
3— .3.
3

 

IS "

 

Multiplic‘arimaf Frflfliaflfl

.\ N ., Multiplicationpf Fractions, «whether;
\ ' . they bepmpcr,impmpcmmixt, or ,com-
paumh they muf’c li‘kcwife be» reduced to ‘
i/fingle Efrafiims; amuitiply the Namcraxors-n

thcmfoxctogcther, and the produ-é’ciflmall,

beancw Numeratorfi; th‘en'multiply'; allvthg: .
Denominators,’ and the .Produft themofi‘:
flail b“: thc.,;£5)cmrgzigewn . Ema-r

5 Remam 7 ,1 I”: .
    

Example. 6; . 7'
Multiply :4 by. .3. éXi‘fdcit-tét fit if. .
‘ 12 i

_ Izt‘might feem (fomewhat) firangeizto

meet 'to acquaint them, that as whole

‘ #1??? *

‘ young Leamm’, that? of a pound being -
multiplied by f; of a pound, {hould make) i
but: :. There§0te to inform them, I think:

‘ Numbers multiplied by whole Numbers,

dotincreafe the Pro‘duét, f0 proper Ft‘aé‘ti—

ohs multiplied by proper Fraélions, do diet.

minilh the Ptoduétt. For as 1 multiplied by
1,:makes but ‘1 :, f0 that which is lefs than

I, .heihg multiplied by that whichis lefgi .

than I, mul’t needs make lel‘s than eithet bf?

. them. ‘ Orthus: :-

 

44w

 

EQ‘

To" Malt-i1)! y- F 742525 072: of F mfiiom.
Il‘.iReduce them into {ingle Fraé’tions,
then work as before. ‘
Example. *3— of g— bv :- of. ~31 being reit-
duced theme; and 3%, and beingmultb
plied, fair—g.
To 'Multz'ply 48 whaleeNamber and a v-Emfiz’mt

In

.3: 3 together.

 

‘ llh Multiply. the Numetatoe by the w

whole?-

_. {git

" 'Ch‘iXI. Mammy,Tofmmom. 83‘. I

a?“
 
 
      
   
   
     
      
   
 
 
   
    
 

  

' r 84 Diwfan of 17114672045. Ch XI!
7 whole Number, and divide the P1011110: by
' ethe Denominator.

8x44112111. .
Mulnply 4by3- 4 . ,, 121(3 fmt-

fl‘ f

To Multiply 4 whole Némber and 4 PM. ,
E'I'irm by 4 whole Number.

IV. Reduce the whole number and Fra«
é’cion into an imp‘mper 13111611011, then work
.as before. 4

5x474? e. z and 1% by 4 facit~3 3—4" or 10; 2;

To Maltiply 4 whole Number 4224’ 4 F 114672-
on by 4 whole Aflzmber and 4 ch’lz'on 1
_ Reduce each Of them into an improper __ .
FraC’flon, and work as before 1n 54132.1

- Exam [6.
4 Multiply 3 ~and- by 2 and?
”#133113 f4cztfz or 7 1'1;—

.1 , 1. v.1.1mmnaumw amismwumu1111.411wu»‘.&w1'4,.11. n 1, an ..- 1-; 1

,1r.,

 

, G H A»: B, XII;
Elvifim of Fmi'r’iom. _ , 1 j i,

..AS in Multiplication, {o in this, all i

13113151111115 that are to be Divided, l".
mui’c be reduced to fing! e Haitians, both '
For the Dividend or P11111111 Then fer that

1 Eraflien which is the D1vidend on the
1 left
  

.: J? ,

 

.. Ch.XII.

left hand, and that for Divifor on the right

hand; then multiply Crori‘s-wife the Nume-

rator of the Dividend by the Denominator

of the Divifor, and fubfcribe the Product

for a new Numerator : Likewife multiply?

‘ the Denominator of the Dividend by the

Divifors Numerator, and the Produflz- fhah’t
be a new Denominator.

_ Example. ,
What is the @otient of % divided by 3;?

Place yam mei‘iam

 

flew, with #2:}: X C’Im- @Xi
rafi‘er between them, and fig
War/{according to the di- faciti, or 1 Whole
reciiom beforegiven. ( am, and T;
I demand the flatten:
of %di.vided by i .? §2X3T
facit 34.

in Divifion of whole Numbers, the Big. ‘

vidend muf‘c be always, greater than the Di-
vifor, otherwife you can‘make no Qapzz'enr.
But in Divifion of Frac’tions it isorherwife,
asin the fecond Qiefiion pronounded, g to

be divided by %: for—3; is greater or more '

than g, yetit may be diVidr;d : for as the
Multiplication of groper Frattions ( as was
faid before) doth diminiih the Proouét, f0
Divifion of proper Fraéiions doth increafe
the finafiam. 119 2’0

A r‘li'T'ffiWf urge-r, :- ( v-r.~w~~--,_. _ ~
7 , in, “._V ‘_‘ i .

Divifion of Frafiiom. 8 s".

   

em

 
  
     
 
 

3.85.» 192214272 omefimm. I, ChXII‘ .

  

, I I To divide 22 22/2012 NWber by 22 19221837272

I demand the Q191icnt 0f 20 divided;
byfia

zo being the whole Number, convert it y -
into an improper Fraflion by placing an . “‘3
Unite for a Denominator, and it f’cande’th ;.
thus: 1

    
  
 
 
  
   

-— 22.. ;
2' *3

fan} 3‘9""

 

 

II I To divide a whole N72772122r 22772172 Em-
1512072 , by 22 221221: Number 22721713 Fmdion. . '

Idemand the Quotient of. 5 and ifdivir-i
dad by. 3; .

21%): 1—12. _
. ' 11‘}:
fag.“ :2;

, . 1V1." %“d-ividc F mft'iam of Frhfiié'm. ~:

 

g g, Idemand the Quotiem of GI 3101' 3—, di-
vided by 3 of‘;

I - R2422“ 2b: Dali/Mend 27222 072:
fingle F 7722522072, 217221 12km” fly the
-.D2wflzr,2h272 workzu [21797 e.

XII-"é- T;

4-,

[few :3

Q31»

 

     
    

Chap-axing;- _ 87

 

CH A P. XIII. ; .
The (Rule off/1m. , - 5, .

L's'TH E Rule of T'Threeris‘commoniv‘
called, The, golden Rule; and in...
deed it might be for termed,’for as Gold -
tranfeends all other— Metals, fo doththis ~.
Rule all others in Arithmetick.

II.-.N.ovv, for your better: information
concerning it, 5, youmufl obiérve, that there ‘
are “three Numbers-known ,1 by which a .
fourth that is unknown may be found out,
which bear like proportion to the third, ass
the fecond doth the firfl. 5 ,

Iii. Here aifo is to be noted, that if your» :-
- Sums confifi .of fundry Denominations? ,,
then the firi’t and third numbers mui’t be of I
the fame Denomination, as alfo the fourth" =
and the fecond : As thus, if the firi’c num». i
bet he Yards, the third likewifemuf’t be ,
Yards; «if‘the fecond be» Pence, then the.
fourth mufi be Pence. ,

IVt But the greatci’c difiicuity ”lyethi in u
the {hiring ther‘efiiono

i There ‘

 
   
 

  
  

  
 

».v

, 38 T/ée ébldeh RaTe; Ch.XI’II. . K

Theteforeobferve firlt, That what you ‘

‘ iodefire to know,’ or to be refolVed in the
,, fqiueltion, malt beyour third Number; and i
' 'you have commonly thel'c words before it :
as, Wlmt 60/1 .31 How long .3 How broad .9 How
much? How deep, 81c. ' '

‘ i 2. Your (Qeltion being Rated, bring
‘ firl’t and third Numbers into one Denomi—
\ nation, , ‘ ‘

3. Bring your fecon’d into the leaf: name—
mentioned , or as law as you dcfirc the
@efiion to be anfwered in. _

a 4. _ Obfe‘rvewhether your third Number
; reqfiire: more or lefi; if more, then multiply,
' ‘ . the middle number by the greater of—‘th-e-
; ' two extreme, and divide by the l=ell‘er,andf

' - the (Motient anfwereth the Qgeflion.

' Buttif it requirelefi, then multiply the-

middle number by the lefi‘er of the two ex-

treams, and. divide by the greater.»
Thefe two words more or [6]}, being well; ,
obl‘etved, the Scholar will underfl-and what
7 he doth, and need not to make‘two diltinét-v
'1 4 Rules: of Three, as moll- do, I ,
The four fixlt Quef’cions are [la-ted four:
feveral’ways, by which the one is a proof:
of the other. '- , - ‘

 

  
 
 
 
 
   

 

   
 

  
  
 

   
  

      
  

,‘u ,4“-

‘Chap; XIII. T126 Wide-fl. ‘ K ’“8 :

And thus You may eafily work all the tell; '
which will be advantagious to the SchOlar,
and likewife an eafe to the Mallet; I {hall
thercfore only give you the facit: of the
’ following @efiions. ‘

‘lf 6 yards soft 10:. What 12 yards ?‘
o 10
I 2.0
‘ 32¢(2o fhilling‘s.
66

 

If 15 yards—~20 J. ---— 6- yards?
20
zzgfl IO 3. . -—---
zzz 1.20
«r
20 :.-=—bUy i2 yards, what will re 3 .3
~ 112
no.
2253(6. yards.
2:05

N H ice—~46! yards --———20 s?
, 6»

”M

120,

.rzz( 12 yards.
{and

 
59 The Golden Rule Chap X1117-

If Q11: men will be a- finifhing a piece of
' Work ten days, how long time will 12. men; 5‘

; . be a domg the fame ?

 

mam: , days. mm.

6......“ 10 9mm 12:1;
101-
' 6071'. ég/(S diflj’fi
' ‘ " «1’3" .. .

\

11:12. 11111111. 5.111511% 5 111111 1’
s .

 

, N

36° £2110 111; 1 - \

If 5days-—~ 12. mam-10 days?
1 12

61! 61.5116 211:,

, 1/ij : /

N 1’0 dails'wat-w 6 men -- 51.111315?
, ,6 , ,,

W~

. 1v 5 . 1 _ .
69::- ’ 65$” (12.111172;

 
  
  

 
   
        
    
 
    
  
  
   
    

.Chapg‘XIHfi T336012» Rule; , ' 62.,
7 * madame: 931.233,. what.;co&,2;C;-;3r;-?s- ; \
I 4 :4

I ,3 an. _ 1c);
9: , 7 ~28?

ruin—52.

   

 

2* ‘ V 3- ,
- 2325223336460 533; ‘ 80 .
$21.2: , _ 20

MM ‘
2 89 “b
39 .3

 

' 2320
84.0
I 32920

If; 280 '15.”) 4.50 21 1E“

 

' I 092:;~

Z 39
2:592Q)( 32 qr: facito
”)5

If 54605173“ w283i’b «m—ggqm \‘ :
, 2 )0
J'fing‘CZ’fb. fade)“ -———--:
3253* ' \ 3120
V /~
2, W’ y

992' ' ”660mb M. Cha'p.x111.'t_.
If 39 g”"‘"‘“f'2 Tb -'-+—~ 5460qu. '
. _ ‘1 . 2

     
   
     
         
    

 

‘ 31’ 1092.0

IQ’Q’zfi’ (280 Tb- fac-iz‘a

, 3999' ~ ' _ '
33‘

If I {pend 476315. ‘11}. ion]. a year, I'
' , demand how much that is one day with
> another? ' * ”

m. 5:. ,. d, M; 4
V ! 2° , ’ ' v . -.,

9"?

9s§1 v“~b' %

 

v ‘11:. ,mury m: S".

114382
(I

22(3 7 ‘2
#820 , ,. ~13
M’fi'3’32’(313d. '

, 3625;;

366‘
, 3

 
2:15;; .4; ;

' 31%33z(*d- ‘ 9393

. ‘  313
1095
, 3657
10953
> I

I , 1;,4382 d. \
If i‘i’sidp'FI 4.7114382 :11.
¥ I .

13(3
IZM¢¢

zrgggzgss days,

3X33?
31x

3’ .
7 days. ( f

1565

18787

xxggSzI 7 , ; fl

, 114382

 
   

s ;,Chap. XIII arr/madden My '

‘AI

 
   
   
 

     

 

”94 - 552400 w R212 *Chapkxm':
_ At 13d .2,. perTb how manyC. weight} ,
for 111 11:. £121

    
   
 

fucit I C2 22 '
If 9 Eli-11$“ j cdfli 27:. 27:521. what coi’t 89

pieces, each 21; yards and2 , and .12 pieces, 2

each 1 9 E113 2 .

 
   
     
 

facit 2751 16:. 821.22
If 100 25.91? Cloves cofi 881 11:. 104’
and 1 C. wzcight of Mace 991.102. 32!.
What £09: 3",, 2012: with another? , _
,. facit 3:. 341.3326
If I pair 9f Stockings coi’c IO greats,
how many dozen pair {haul have for 190
Marks?

 
       
   
   
   
    
   
    
   
 

 

facit 33 dozen pair ’3'. ,
If 7 Tb-ié‘ of Currants COR 2:. 7 d what \~
‘coi’cg Butzts, each‘ 150 2, I4Tbgrofs,tar’c '
319Tb. per Butt?
-_ fwzt8818: 02152
If 5 E1153— 3-— of Cambrick £09: 21 5. 82!
What c9i’c 120 pieces, 7222:. . L
. . E112. 77:. 2222.
A 3032. 272—2.———I
Number EB 5° qt. 4oI_—.3__I '
C. 40 qt. 341—1—3

Mm

 

3015—4—1
fdmtlgfil 85.991.31.922: 7, '

5012 “

  
    
   

1—: ,~,,,. ..- -r .,. _~ .. .- ' w"‘>—'

5 3 Sold SBags of Pcpper,-cach,viz. tare 43
.15 per Bag,and trct 4113: pen-104 1‘5; at 1-5 d.
_ 4 per 1% meat -,=what comcsmit‘toneat?

 

 

 

 

 

 

 

 

 

“Alfo I demand howmanyDollars-of 4 5-
E 8d. a, Piccc Will, my forzxighe. neatwcight“?
i . ‘ "C. qm.
' qut. 4 I

M qt. 2 I.

0 qt. 3 “'3

i‘facit 5915 Db”, I
19 ., '2.

""So¥d 10 Packs OFCIoath,~’cach Pack‘qt‘.
<10 Cloths, and each Conh 39 yards, at
It 5. 1-1 d. per yard: I demand how much

, zit comes to in "all? facit 2352.; l. 15 5. 0d.

yrs. TE, _

' Bought of fevcral peffons 43 3—-—*3~—-*17
OF Currants at 4. d. per 15.10 whom I have
infald 512 C. grim“ 7 1b. of Sugar. 31:2 61].:
per Tb. Now I would know what remains
{of me to pay, they having taken the Sugar
impart ofdpaymcnt. '
“ 8091.195. 09
3 -, 6671. GI 5:10.:

 

 

. f,,_itRcm. to pay 1421.317 5. or};
. . A

l" ‘Chapi’Xm. ThexGbldekg-ué—J s

cw

 
  

 

Chap.XIII'." '-
./ ‘ A Merchant died, being indebted to fe-g
' veral Creditors (viz. ) to A. 4.01. to B.

t I 4 ' 56’- ‘06- 801- Now he being dead, his,

 

Eflate was Worth but 30.1. I demand what
each man mufihave? - '

l

 

‘ facit got.’ ’ _
Bought 160 pieces of Cloath for 43’! l.‘
{I I s. 1 1 d. what containeth the Cloath, the 9
yard being valued at 7 s. 8 d. . ‘ ‘
7 ~ ' facit 1073 yards 3%.
‘IT 7 1' pound of Virginia Tobacco col-’c
’ ‘10 d. -;-, what cefl: 3 Hogfhead-s, weight 17 '
C. i I 2. Tb. grofs, tare 37 Th. per» Hogfhead,
and14'fb per 194mm“. ‘ _ _
} fatit 781. 6 3. 3 d.

r “math I gleman-d how many Duckets of
‘33, 9. d. 4’1 will pay for the neat weight?

' ‘ .--.fhcit4.13Dmk€t: 35g}.
, ,_ ‘ A ‘
      

inChap. XIII. The GO/bft’fl Ride,
‘ A Merchant hath owing 357,1. 9:. anti,
“his Debtor doth agree with him to pay
him for every pound 13:. 5 d. I demanei
what mufl: he pay?

fair 2391. 155. 944.2%

g, ' AMandicd, having three Sons and two
Daughters, he gave to the eldei’t Son 2000 I.

’ to the fccond 1960/. to the third 1000A

to the Eldei’c Daughter 7001. to the fem

cond 500i. Now, he being dead, his Efiate

.was worth but 20201. Idemand what
each Child mufl have?

,‘ 1.,
Eldeflc Son—«—-—~——--—.662 3%
Second Son——_—__._.629 {3%
Third Son—————m-_.331 3%
Heidi Daughter—~43: =3
Second Daughter—.—165 235%
facit 202d

5 ‘ If I buy a piece of Cloath for 841, I 1:.
‘ and I fell the E11Eng.1for 7 5. 8 d. I demand
how many yards were contained in the faid
piece? . ‘
'w- facit 2‘7 3 yards '37 <3: i"; cf a qr.“

F §old

.97

 
98w m : s; y _ .-c11pxm
'1 ‘ Sdld 4 ‘Parccls of Sfigar,‘ centaining as j
, touowesh; . a " 1 , ”

' ‘C'. qrs. ib-

7 - The fi'ri’t containing 86—2—2 1" tare 84 ‘
Thefecond containing 76a——1+—12 tare 56
The third containing 98——3-—-I I rare 9?. f
/ The fourth containing 75—1-5517 tare 8; .f

M H i’

\_ A: 3; hper Cmmtficit 5851.65. ;%%or 3 d. a

If so C. 3 qrs. 15‘ ’Ib- of Sugar 'cofl 211.,
19:. .1 1 d. how many Chefis of 86 C. —;a
fin“ I have'for 1000 Marks and 4861. '

‘ facit 30 Claefl: and %%%% of a Chefl.

If 5" penny weight of Silver cafe 7 dxfi,‘ ;
what‘coi’c 3 Ingots, each 11 113.5? a
, ‘facit 5'01. 0:. ,6 d. T’

If a Gent. hath 9601; , 12. :. per mm,
how much may'he fpend {one day; with ano;
ther, to lay up 100 Marks at the‘years end;
to ,purchafe withali? ’ , ' ~ '
. facit 1463704” 3“}? per diam;

A Merchant bought 376 ~Cloaths, at;
I] l. I I 3'. I d. per (II-oath, \thh be {hip’d
. for Spain, to have returns from >thence,
_"the one half in \Wine I," at 281. per Tun,
“and the . other half in Sugar, at, 27:.

. m.

 
 

 

‘Chap X111. 71166011551211. 99"

‘ per C. weight,l demand how muchof each 1
111119: be returned for the {aid Cloaitlis?

’77 77571: 7%}: of Wine
-.16C9C 2 ib-g fafSttgar

There are 101 Pipes of Oyl, that con-
tain 115307 Gallons, IWould know how
much 59 Pipes andto‘f will contain , and
what it will amount to at 361. per Tun, the
Tun being 2 36 Gallons.

facit 1105 l. 185-. 714.12%.

A Merchant bought 98706}; of Lead,
which COR 7!. 8s. 5d. per Fother, (or 19
C. ‘ ) the charges upon the lame amounts
£01251 2:. which he ven 1' esfoerecc,
to receive from thence French Wine at
13!. 10.1. per Hogfhead: [demand how
many Hogiheads he mua’i receive for con-
ICDI?

facitz 87Hagfl.ead: fi 13%.

A Grocer delivered 76w 15b. of To-
' bacco in the Roll to be cut and «dryed ,
and when it came home, it l'l'ClCl out but
5639 15. I demand what'is lOfl: in the.
,pound, and alfo fuppofing it coil in the
. Roll 8 d. g;- per lb. and the cutting
E z. 1 .
. v

. mo. Te of mge ¥"‘¢113a{7;;“f

I d. "I; per pound, I demand what it how
fiends him in? ~ '

ll. '—--9 al.23t.---——-—-7657 l. '
It fiands him in 21 I I. 1:. 3 d. :3;

'7657l.l—-—‘————18181.———-—-——tle ,

. fate-it 3 fieefi’g-‘g-Z: loft per pound.

 
  
     
   
 
 
 
 
 
 
 
 
 
 
 
 
     
     

 

 

- gCHAP. XIV. . ' We
‘ The Rule of Three ireFrm‘fiom.

S in the Rule of Three in whole '
Numbers, I‘ laid down certain Prin- _“
eiples both for the better difeoverizng, and

7 more eafie work thereof : to in this of Fra- 1;
(Hons, 1 [ball endeavour to make all things [I
.15 plain and familiar as may be. '
And firfi,’ bec-aufe‘ many queflions feem
very ambiguous, whethen they-_,belong. to '-

_ theRule of Three dire€t, or indirefl. 7 i
That you may be rightly informed 'con—
,cetning them, \ cafi your Eye upon the third f

, Number in the quefli‘on, and fee whether't
" it be greater or lefs than the 519: Number.
But if you cannoteafily apprehend which ‘
is the greater or leffer,‘ then work accord— ,

' mg to~ the fecond Sefli‘on in peg: 80. ~ ~'

 

     
    

E

t

.ChapXIV. 1'72 Fmté‘z‘hm. : 103:

'3 If the third number be great»-
! er than the firfi, and the An.»
\vI/Vl’mt fwer required be greatest than
qttefliom the fccond, it is upon the Rule

belong to ‘ of TthC direét.

the Rm’c' And likewife if the third
of Three number be lefs than the fit-{hand

'_ direét. the Anfwer required be lefs than

the fecond, it belongs to the
J fame Rule. ]
‘1 But if the third Number be
lefs than the tint, and the Anv
lVImt fwer required be greater than
fine/lion: Y the fecond, it is. pertaining to

d’ balance to " the indireét Rule.

the Rule . And if the third Number be
of Three 1 greater. than the firl’t,and the An-
indirecf‘lt. l

E 17:11:;tr’33,§ t is according to the fame

l

‘ J Rule.

Having thus found out to what Rule it
belongs, firl’t confider {liligentlyt viz. whe-
ther-the fiti’t and third. Numbers be both
of one Denort-inption, if not, theymuf’c be
reduced into the lead of thefe Denomina-
tions.‘

2. That your feeond being a compound,

Fraé‘tion. muft be reduced into the lowefi,
or lead name mentioned. *

. t l E 3 d The

twee reunited let‘s than the fe— .-

 
 
  

f Muitipi y the Denominator of
the (Mt Fraflion mm the Nume-
rater of the tecond and third,

With??? of Dividerd

direél 1 minazorofthe fecond, and that

Lthe Divifor. ‘
the 11111111111101 of the firft and

the Rule{ be the Dividend.
fla’ircfl-

 

Produé’c that arifeth therefrom
thail be the Divifor.

, \

Example. 1

 
    
 
  
 
    
   
  
  

f 51112 711R11111fT/1111 Chap. 11111. 1

{ice 0911- and the totalthmeot {hall bethe

WW 13111534 Multiplyah‘b theNomeratOr '*
of The:1ofrhefirfinumberbythefleno;1,

Prodruét by thfiDcnominator Of'
the 1111111111111 thetotai (hall be. E

1‘ Butiwhen the queflions belong
to the ihdirefi» Rule, multiply

fecond together, and the whole "
“Tm ape- thereof by‘ the Denominator of
ration of- the third, and the Produét {hall 1

9f- Tier 1, ‘ Multipiy alfo the Denomina-

tors of the E19: and fechd toge- '
ther, and the tota’l thereof by the ‘
Numerator of: the third, and the -

 

j
j
”i
i
1
Chép.XIV.v\ I in Fmfiz’om, ~ 103

Example.

I

 

”7“»me

.. z“ ‘ ——-—4—.,. WV": ”up

 

:1: ”nut: Ell ._._....._...__. 31‘
,kA 3 1-0 K
7% ”6%
. 2.7:: ~ \
-‘ 1253B“; If?“ If: E” facia-
‘g, For proof of thcfe and the foliowing
' (Aie’fiions, the fame method is to be ob-
‘ F 4. fervcd,

 
     

     
   

1,104 V TIzé-LRiiZ-Zfe‘of‘I/Jreefl/ ChXIV :

errved as in the Ruleof Thy“ in Whole ’
Numbers. . X ,

      
   
  

7 r Llffibmfifiofa {hii.whatcofl:§:0f'a?}b?'
’ .1. sea , ' -

  

 

1‘3 ‘ 2.; 5. ' 1
.28 (I fifaclt,’ %
16’ / _

 

 

' If iib. 60% 145;. 2%, whatcofiéfb?

‘ 3% ””27
§
filififilfiié of Wm.

 

I: i :éwfib. :

V ‘ .2 -

7 < ‘ as “3% '
.'..3_ ——--fl: V ’
:1 ‘44- 72 2§_\»3.n/
n machxgali (0‘41?)

To prevent_ difcwrsg’ement to Young:
Scholars in the QJei‘ciom f this Rufe,
which indeed are ' {Omswhat intricate, '
~ I: advifc thcm to turn to the Rifle of ‘
~ 7 ~ , ‘ Three:
 
   
     

   

“.Ch“ XIV 212 #2135072!“ 55 I07 .

Three in whole Numbers, and exercife
themfelves well therein, and efpecially in

’ fuch Qgel’cions as are (130?: plain and eafie,

, , till they throughly underfland the natme ot
the Rule; by means whereof aH other Q1:-
5 .fiionswill be more eafily wrought, be Ihey. .,
3 never f0 difficult.

If 6 yards and; COR 8 {billings what.
w col’cgyardsand‘k? »,
5 facit 11 s. :2;

If 1 Dollar be 56 penceg, what 506
Dollars? . '

15"5'6 d. é—goo faeit I 17 1., 183.4;

ff 2 Ounces and; col’t 16:. got. what,
‘ cof’t i 73’”? »
fw‘t S9 4- If;

_ When the Bulhel of Wheat 15 fold for
5 6 3 3,the half penny whiteloaf {hall weigh
2: I demand how much it ought to

weigh When the Bulllel 15 fold for 7 5. i ?

65"?” 52%“; .---712':-
5 ‘ , ’ fzczt 5 § 3.];
”7/.

;“" "' 5“" ”‘ ~ >~ “a “wk 3“; - 2e

 
  
  

ma mike afrhree‘ Ch XIV; '

If 1 yard COR 9:. what cofi4yardsi? 6.
’ ' fam 43 s. ;.

      
    
  
  
  
  
  
   
 
   
 

1f 31335: cofl 15d; AwI1at oofiéEIIs.i}?
facit 2;. 7 d 5%..

If: ofayard cof’t-g‘of a! what coI’ci éof.‘ 1
a yard. ? y
. , fan} 10 .1. '37?-
If gyards and: FcoPc4l 145 212-5 , what“
COR, 30f an EIIFlemzjh. ? , .

. ., 1...‘3:3‘2b.§,
5—%—} Ali-343i , 1% de'ZI. 17 :9. 767570"

15' 1111.101 64’. =,—;—, what :03 41. £2. '
faez't 30:,.d.f§‘§- I

If I ElMcofigs g,‘ what co& 1 yard}:
faczt43: 1 ~§..

' Iilcnt my Fficncké o£ amfirwclo Crown for _
' thagec weeks, that:heihould.do.as much for ,
, mc.,anothcr time: but when l camcgto bar-
rowof. him, he. Could lead mebut-é—éf a
(310an Idemand how long timc‘l muf’t
keep his money to requit-e my former kind»
mfg? _
féiflf +W€€kfl 5.

If:
  

Ch. XIV It.” Fmfi‘iém.‘ ’5 107 I 5
If a Piftolet be 55. .5, What {hall 430
be thUS, ‘ .
I -—-—.55 1-0 M430 faczt1261175.~

  
  

If 1351‘). col’c me3l how manyfl‘). {hall
Ih‘ave forg7dP ,.

E 3 facit 1.7155.
“2551310159615,Whatcofi65b.9§.3;?
. facit 34. 275‘:

If 5 yards of Velvet COR 4]. 351.5, what
«aft 4. yards7 5‘ P .
facit 31 I7 5. 11 51.24255?

If VIC. 3* coft41. 12 5. what cofi5C?
1-5:.“9'2 5. g facit 33 5. 55.;

 

WV. .......,..w._..w.. a"... ._. ._ . r . ,

1‘12 1.42.18

.“fl ol—u—‘d—é
n

‘ If 1C. C0fi111553,WWhatC0fl4§ P.'

If 10f aniEll c0951] 25. What coI’c5P
facit 325. 18.5!

5 If 10 E115 COR 3!. 5‘, what cofi 1 yard. P
‘5‘]: '5 : sor 50——18——-4
3/ If i- G.‘ £09: 1505 I. what coPc I C. 5‘?

7%..7-‘5 facit

If

   
   

    

’

m8)- leé'Ruléof’Three chap.~xv.',
If‘% Of CQcol’c I? .Whatwillg.s.ébuy? I
34.12.?“ ’ 'I ‘g‘ C. 3"; 5. facit.

      

  

 

 

, ‘ 1f {gof axyard of Cloathin length, and ,- f
I \Iyard % broad make a 'Childs Coat, I dc. '
mand how much fluff will make the fame._  ‘
\ Child a Coat, when the Raff is buti of a; ‘1:

yard broad ? '

12'
,7,f"""""5

 

3 fazcz't 1 yard%‘%‘

‘ , 'f If “Silagflc'ofl 1: £115.52, how many 15.. ' l
, \ flaallll buy for 41%.? ' l
fflC‘ita ‘ _. _

If %’of I C. colHé‘of l, whiz: col’c‘ 5 of '
alpound.?s ' -
’ facih > '

7 ' r \If :f-of a gcol’c fi- of, a pcnnyfilow much
mall I‘buy for ,9—"0f 20 5.? , l ‘
7 ' facit. , ‘_

y , If 1%?“ of‘a’ pound “cof’c IiZ'Of lg haw many, ,

plpundsihall Irhave for; Z. 7:. 341.334 j V 1

\ . I ‘ facir. ‘ ,.
How'lmany yards are bOught for'142 In

115:. 2d,, thlnhghci— of): of va‘ya’rd col’c

 
 
  

       

. Temp. XIV. 22 Fri"

If 1 C. 3 I2. Tb 3cofi2l.3, what cofl:
30f an 3? ;

 
    

faint 5403333,

   

If 26Tb. at Afltwerp be 27 Tb. §afLan-. .'
don, how many pounds at AntWerp are 56,.
Tb. at London. 3

   
 
    

facit 322 2%
If 8 E115 at Antwerp be 5 E 11s~’~ 5 at Lem:
£01712, how many E115 at .Afltmerp are 159
S 1'17" ?

 
   
    
  
  
 
   
 
 
 
  
 
  

3926i! 2.31 E115 333;

If“; Ji—times 3%pr c013 I v:- times; i l." _' ,
what {hall amount [unto 3 timeséof the g-

of 121.33
“1

 

 

'3 33 «cit? ‘3301’91.
316153 1’15. cofi 2.3L andtheggof Tb}
1 .1 Whlaft 1113111610315 16153 5 and 2; of 3; 3Tbe \_ '-

,‘amount unto? ,
3: 33

.9.
4.

 

m1~a

 

~331¢)fiatrz'tr 135-17 0-3 ,

If a: French Cgown be worth 52 $573

 

flerl. 316w many muf’t be received for 1091.3

 

 

     

3/1167}. 1 Crown. .
215.; , a; » » 7253,29. ~-
22; a .1. - '7 J ‘
13 fazvit 460 Q3333. ' , 
- ' «When

  
 
 
    

r0 T In Ruleiof TIiréee, 86C Ch XIV '

When? of 5 E115 lefs 3— of an El! coI’t-g'
‘of 9 ;l. leis 3‘ of 211. what then {hall‘g ‘ of
6 E115 lefs 6 of an EU. 9

    

I

 

 

 

5- ‘fzzc‘k I 3%].

lfé‘of 20Tb? coI—Ié 36L Ieisiof gosl. I
demand to how much g-of 40113. and— 3-}, =5:-
i. 4 _‘ Willé amount unto?

27

   
  

. 3—715 facit 35 135
_ If: an Ingot Of fiIver: whofe weight is
I 60.15;- be better 16 g. 5, I demand the
Standard weight of the ingot, alto the bet-
terneis; hate, that the Standard is l 1%
, 2dw¢. Firfl, fubtzaft the Standard weight
from the betternefs, then it follows .1
. 11;..121 .300
I , , , I

     
  
 

, ,, "a“??? 56 tterm’fx,
/ 728; fif wczaIJtaf the Ingpt:

.xfiq-

 

1086 a; g? andardmigbt in aimed."

—-——-—-—~‘1‘b. 3. 4m

90: 6 :iggggizfaczt;
An Ingotgof fiIver, weight 47 fit, and is
work 14-; [demand the worfe‘nefs of the _

Ingot, aiin the Standard, weight.

’— 0 &.§. 0 5:1;
10 o 0

I5 I i—02 1—6 dwt. 7F;- warfmefi f4. , i
11:» 344—06; .—..1 3 m3} {)2de fat
' CH AP

 
 
 

€113.12); XV , E

  
 

ECV'HEA P. XV..,, ,
Rule: of Prdfiz‘ceéh

     
 
 
  
   
   
   
       

 

EE , TIM/esof Pmfiice.. ,_

E 5. d

E - [10.0 is i1? ‘ d."

2 6—81 is 3‘] - 6 56%;:
E “The 621m ESE—o is :1; , 7726611672 4. is ~;-’
E partsafaé: 4—0 Es Eh) aftfofdgtg Es 2';

E Pound. E 13—4 15 *6 fivallwg. 2. 15 ~15

E2556 is é " 2153' *3
L-I—-o is zéJ ‘ Eris 7%
E pEfore the Learner ‘ 2-»1»z:-—2
U can we” procefd 3—4—12--36

E further, he; mufi get.“ 4—42—48

1E5 thefc Tables very per-r. 56—12-669.
E/feé’tly by heart; lmight 6—42—«72
E'puzzle his Head w1th " ,7-—-v12-——84.
form: other~,wh1chb~:-~ ‘8—12—«96-
‘E caufe I Conceive. would 9—4‘12-408

be noublcfomc and bur» 10-—-~1’2—120
dcnfomc to his-vmcmo—E I 1—-——12—I;2
ryEEthcr‘cere-‘l,fl1allomit ‘ 12—4 2.144

‘ thcm

      
     
         

   
    
         
 
  
 
  
  
 
  
    
 

V1512" ".'Ralrestof|Pmfiice., " Chap.XV:v

them and obfe‘rve this piaim and eafieme---- ‘
thod‘follewing. . ~ ,_ ' - e 5
' §And firfi; lihalllbegin- with the even. ‘7
parts ofafhilling. ’ ‘7 ‘
1. When the price isvan even part of a4
fhilling, confider what part of afhilling it, J
is; which being found, divide the Sum.
- propounded by it, and the, Querient will ,
:‘iihe (billings: Asin thefefixExamples fol-'- '
‘ ‘ lowingwillappear; ’

Jazzy. d. , 1b.. 21.
8468 "at 6.1m" £11,4-;— 3618 at 2., per Tb.)

 

 

 

ul-

  
 

 

 

 

 

m 1 4.: , m F~

‘ 3,0“ facit.‘
yard: d.

2i1—14—dfaeifi. ,.
867 at 4d. per EN."

.51

 

 

 

 

. . g}; ans-oat 17*; per ya )
28- i 9 1 a 34 1 5'
I4—9-O/fdw’t. ‘ {7-3 facit;

, $327631? 35!- P69’ Th-E‘Tf‘i-Sg-é at: I pert-B. .

 

 

 

".3615 ‘ 401-8 ‘
j 349 fetch; peg-758' facit. ‘
7 W h . Having
E

A'ChapXV. Rules of P7457266. 113‘ .

Having gone thus far upon thofe even
parts of.a {hilling that are mof’c eafie, I
mufl: intreat the Learner to return back to
a farthing, an half. penny, three farthings,
036'. the other parts of a ihilling.

11. When the price is Fat-things, or
Halfipence, bring the given Sum into

t Pence, and Work as before in the laft Que-

fiion', butwhen they are uneven parts, as
pennyfarthing , penny—threefarthings ,
two-pence—farthing, or the like: Begin
5m with the even parts of afhilling: As
for infiance, 63,96Ells at 5 Farthings per
Ell; work firl’c {or the penny, as before ,
then confider, if at the price of a penny
they come to {23 many m'iilings, then the

Farthing mutt be the fourth part of them,“
which being taken and added together,your«

work is dome,

 

 

 

Ell: £1325.
flue at gr dprrEH. % 716 at“; d. per Ell.» '
E -. —‘--v_.————-——-..—-—-<
r3280; “1-3358
829d. facih 2 I 9-1001.

' ——-—'——~'
“W ‘

t 1- 9- I 0 facit.

Ell:

    

 
 

 

 

 

19-19-9 facit.

5712 at id]. i

 

19—1 5 chit.

           

. 114'- Rat/emf Pmfiz’ae; . Ch xv,
’ £95.. kt. ¥ " ¥ £15. 3 d;

6.396 affirm]... 5;: 72253t1§perE1L
«531198 (I I? 903;}?
--~~—----—-—-- 1150-63;
133—‘3‘ 10513—F7fi;

————' ~W~ ~ tau—fl

\ 52«13—7.%fac¥r~« ,

, III. ,thn any thing doth remain Of
any Divifion, it is-of the fame? Denomina—
tion as the Divjdend was, as here in the
laPEExamplc 722; three half pencebcing

divided by 8,. t’
~ ancc.

 

here remains one three half

_‘ 864.,
Clla§.XV, RM“ of Pfacfice, “5‘

{3716 at 3d; :7?

f5.
i'4-I712at3~d.i
‘ $1042.39
1738

6086—0 fucitr.

4 817 at 3 d5;
4. 2'04_3 d5
5-1—03;
2'5 15—3-3;

mas—saw.

. 7138;

 
   

 

116 .Rzz/eI-éf Piafiz’ce. , V Ch. XV

7,138,344.;2.‘ 3‘; 712M541.

:. 1189+?» ”8

1189—8 3

148—481;- . 1‘
i

   
   
  
   
   
   
       
     
       
      
    
 

 

G\ {M

 

 

W.“

W“:
4: an-
N
~‘9)
T
+3

 

mm . W\

2523—: L ’ L

 

 

 

12!; 8“: I Zfaczt. 3114.316-8 facit.
3716 at 74’
‘ 3'171ac4d.% . s—--——---

NIH

mp

 

 

.. r-—w--~-+« g1858
_g 55* 1723—8 , , “é 309—8 -
% 213—5-5 \ , 4 ' nwm—M—n—c—a— _,

 

.—~—-—~. W 21617-3 u
I-93‘m9“'1-i’2:.. “m ***** w
. 9619.16. fmt. .7 ‘ JCS 7—8 facir.

\

8716 at 8 d.
82905—m4
2905-4
381£O-8

w” I .

wlu

 

 

290- 10-8. facil. f

 
 

637:8:
 

Chap XV Ru/ewamczce 1

  
   
  
  
 
     
    

: 2716 at 12d

W

 

27116
l I35-16 I. deit.

3762 at.12:d.i. I

I 1881 ' ,. .A 3
940-2—6 _,

3’“ mflhfn'éw , 'Trrw - 7..

"fl-u—I—I- nil-fl
‘ '4‘

384IO~4 1‘- t,

5 , lane-sam-wmm3

 

 

v , :, ”.m-qurnwvy-JWT ’W'YJM 323%:W7 ‘ mu
1 A V ‘
‘ ,
  

 

‘ - 5627 Evils at 133. per‘Efl. ‘
IV. jAsfof the '12 d. that is‘done to your
hand, there beingfo many {billings as there

are 15115:- then‘for the penny, canfider that

12. 4. ”per Elli: comes to fo much“, ‘ and the
odd penny take 75;, of the given Sum, which

wi‘l‘l make likewifc millings. And thus you .
majy'do, touching any of the following Quc- _

'2

, (lions, by “taking the. even or uneven parts
as you have learned bcforc. , ‘

 

    
  
 

 

 

Fi§2584a113¢~ ‘ 7‘ 7684atzgd. ‘
ii 2684 ’ i 7684 '
2273—57 1921

. 5901797 960‘;

 

~‘———'—

I. 5. d. .i
143-7—47 facit. ?

8642 at [4 d.
; 31'. 864.2
I 1440—4

«a. »- man-u «Am.

 

m

480—; fuck.»

M

3716 at 16d.

_—. u-‘w-‘u—d

 

3716 .'
1238—351.

 

 

 

 

 

 

mow:

 
 

wof p

16082.1 ,4.;3'5|4_:.8’ . ; ‘ j
504-21. facitf; 24744-8 facit. ‘ 11
1' .hoVT'Rzéleiw mm}; W

i. 1
A";
:3].

E ‘

E e

3141 at :17 d.

.Iand“

 

41.7 at 2.1 d.

m
M

 

21021 at 22. 4'.

MM'
“he.“ _‘

'1236 at 18d.

m H.—

 

26812 at 19 d.

“Mr-“E

317at23d.

‘w mm

1213 at 20d.

;_--'_- MC“;

[71231211.

“I‘M—.fid—(m

V. Obferve'that as many yard; as there
are, fo many two millings; therefare mu!-
txiply by 2, and the produfi are flliilings:

“ and this method you may obi‘erve in all

others.

Or this, if you Wili. '

For thofe even parts of a pound that are
mofi familiarly known, as two fhi‘flings,
you may take the 7%, for 2 {killings and
6 pence the 32—, for 3 {billingsand .41 peace
the 5;, for 4. {Innings the ~§—, for 5 {hiilings x
the i, for 6 {hiflings and 8 pence the i, for
10 {billings the r}. >
.17 12'.

 
 
      
 
      
       
  
    
     
    
  

3:26“ V’Rwleyiofmfizce; « Chap XV'E, ‘

if) ‘ ; H 3672 M2224.
'1712 atznperirbw
2‘ g~1222
"*""'~--~'—- ' ’734-4
342M- ; 612.

    
  

 

”awn—~—

795l6

‘ s—u—nF—fl

' i7Il.——4.s. fdcz't.

 

£11,, '1. 397-165. facit. \
,a-g .7260 an 5. I d. ‘
\‘ / 2 _ If pcjnce be re-
~—-_—~—-—————.-..-.—__ quircd m the que-
% 14520 flion, the partsfor
605‘ I ‘pence take out Of
...-._-._.__.............. " the glven fum, as
151er ‘in thcfe three lat-’6

Examples do ap-

756-5 :. facit. ' pear.

4512 at 2:. 3 of.

“mm

14.10 atzs. 6 d

 

u

,106 atz .v. 4d.
71m--___-

m‘iu‘ ~

 

712at2:.7d.

I713t25. 561.

V Ww.r——I—j

11:06 at 2 ’5. 8 d.

 

 

2‘6191

 
 
 

Chap-.XV- Rufesof Pm'zz'w. m

,Z {6101, at 21. 961.: 6109 atzx. 1-1 4.1-) '

 

 

 

   

‘3 a. _ My
: f

u . , Z . '

411.306 3t .2 5; 120 d

E Z rm”...m_w. ail—- )

r

4672Elsan‘dr‘; at4d and/.313. perEEI.

g Qefiions of- this ham as that do con fig. ‘ \
offeveral Denominations, as .,3,4,,,6"c -
Ziarc wroughg as b‘efore, only for the half
Ell take half of the givzn price of an EU
céw for a quarter, takcaqua rter of the:

E prise, 6'6. and add it to tha format: Sum. Z

 

 

    

 

 

E Example. . -
E 1511}. 9 C. _7 1-. 701- _
é;- 4672§at 4.1. 4d. :- 17fiat 1'7-7pe‘rC’4 '
E7 4. 2 2 I7 -
18688 . 119 4-45;
fg [357—411. _ .- 17» _~ _‘
EW- 2,———2 f; 8—6
E ~--——---~—: pr—s
2c 2417—6 ‘4-‘4 if .4.
[-012-7"'6 fflCit; 3
i

   
, m “m 57152452252; may

If the? price required be concerning
pounds neat, you muff reduccthc hundreds ‘
. grofs into pounds grofs, and fubtrafi the
‘ pounds tare from them, and the remains
will be poUnds heat.
32C. grofs, tare
172 TE. at7d. per
Tb. neat.

32

    

36 C. grofs, tare‘
x94Tb at14d para
Tb neat.

.1 -.—~ m’w

36
2112,

    
    

    

 

       
 
  
   

 

4.72:
36

.403 2 Tb. grofs.

94 Tb, tare. '

391-38 Tb. neat.
ib- ' V o

 

   

: 13384Tb grofs.
‘ I72 Tb tare.

       

 

   

 

”-W‘

3412 Tb. neat.

   
  

  

~‘ In». » - vs. ,. .

99- 10-4}. facitg -

   

229-144. fam.
VIII
  

I
g,

4.. .,,~t""

riff-n": F511"? W ‘-

" Chap; XV. Rule: of Prdfiice.

i atare be abfoiutely fo much as in the lai’c Ex:

‘ ample, or whether it be fo much per Bag,

1, per C. or Barrel, Cé'c. If it be any of thefe,
multiply the tare given by the C. Bag, or
{Barre}, and the (Produét will be pounds

2.? tare, which fubtraft from the pounds grofr,
and therremains are pounds neat.

fill-mf—

Example.

56 C. grofs, tare
17 115. per C. at
9 d. per “lb. neat.

56‘ 56’
I12.” . 1'7
112‘ -392

S6 56

56 '952

6272 T8. grofs.
_9_52Tb tare.
532.0 Tb. nezt.

  
  
 

gzzofbm 9 per 11')

 

199-110 facit.

 

Ni-

12C. grofs, tare
13 Tb. per C. at

p 1.48 :1. per it"). near;

12 , 12
112 I;

24. 36

12 12
1215:11ng2;
1344115. grofs.
1;61‘b.tare.
1183 E. neat. ’ V

d. , .

1188at18 perih." ‘
1188 ‘
504. _
I78I2.

 

893-0 facial

. I 2 3
VIII. Again, obferve whether the pounds

 

if“

 
.r 2 4 T 194299.999]? P9459929. Chap. XV

lX Obfervc whether the given price re- .
quircd be at fo much per C if fol, then bring
your pounds Tare mm C. and fubtrafi them
1mm the C. grofi

Example.

 

 

E17 C. Grofs, Tare
; 9.11 IE. perC. at
‘7 I155. fiperC. Neat.

, I7

17...... A .
7(; C. q”. ”IE.
1’ 70—2—19”;

ems?“

, I7—-o———-ogrofs.
1"‘2—12m7'6. ‘

EMI§~1~91162L

EC. qr. I673.—

. 13—-1-"9at I; 13676.

IE IS

E 9—9,

922E9——-—! I I.

m; w—— '

Eng-11 Efimt "

‘ (3(6C qr. Ib.,

  
   
 
    
    
  

20C. Grofs, Tare
93 IE per C. at 9
1'2 ..f perC. Neat

 

V v

” 260

mm 2 _— LENS m.

Ej C. gr. IE
. 20—‘—-o~o grofi.
' _ 2~I—-—8 tare.

”an—M - ....,..,.

:”C anE

17-—~'=-2«= 20 at 12 s. ‘-

 

 

 
 

  

45 19— 129ml 91.: fa”? :5

,XC’H
\-”,
a
 
 

”.
ll

ChapXV. , Ru/ewf Pmflim, 123"

X'. [thing thofe former Rules ‘well ob-
ferved, to he fnfiicient for your Ini’twé’cion

- touching Tare, only if the grofs hundreds

' have feveral fpeciesaas 51, 3,14 A odd pounds,

 

or the like; then confider, if" one hundred
give fo much Tare; then aquarter of: a C.
will give aquarter to much; and it one

quarter give to much, 14. pound will give
half to much; ‘and if I4pound give f9,
much , then 7- pound will give halfv as»

much, o’er. .
Example.

. Tare 12 pound grofs, Tare 13 Tb.
:, PerC, agzy. 3d. perC. a-t35.éd.
er pound Neat. per pound Neat.

 

 

”In
L,. ,. - _, _ . W. in”:

What Treat is.

 

XI Having- thus {hewed you the way“

of finding out the Tare, I come in the next
place to {hew you how to find out the
Treat, which is a certain allowance, of ,4.

Tb. per 104 T5. upon many forts of Com"

modities.
Example.

I 39C Grofs, Tare 1515. percent. andi

415p” 104.115. Treat, at4s. 6d. perih-
Neat. G 3 I Bring

13 C. jg t0fs,l 96C}: upo’und'

    

 
:26 A 12“!“ 0f Prafiia‘e. 1* (HUN 9

‘14. Bring the C. gen-{s into pounds grofs. .
2. Multiply the Tb tare by the C. grofs,
and the modem is the pounds tare. ~
3;. Subtraa the Tb. tare fmm the Tb.
. grofs, and the remain is vfubtil pounds, 5
whichpounds dividebyvz6, becaufe 2.6 is
, l-«contained- 4. times. in 104, and as often ’
A j ,as it is. contained, fo many pounds Treat .
' fiber: are, which fiabtraé‘t from the fuBtil' ’
,- pounds, and-the remain will be neat:
' ' pounds... ‘ “ ~

1112. -» , _ I;
{3’9 , ' - 329-

‘58; $315779; . ,7 ‘ .
( I ‘ . ~ . .

 

     
   

{4368‘ Tb. grof}. .
38.5 Tb. tare. A, gal/a: it)" .1 .

' ’ * I '378(3(14S_trw~.3
43783 15. fubn‘l. - .2555 ~ I
; 14.5 Tb. treat. ' 2:9:

W

“ ' 363-8Tbm4t. '

 

 

 

       
 

  

X;

  

At 45.364. ‘1’” Tb. ‘fécit 82:}1.‘ I 5.7, \

 

T an 7". ,
 
  
 
 
 
 
  
 
 
 
 
 
  
 
 
    

l-ChapXV. Rule: of Prafiice; 127

f , Other ways there are to find out the

if Tare, but I conceive thefe are the molt
plain for young Learners :- However I {hall
give them one or two Examples of ano-

’ ther manner of working, which is both:
very commendable and fpeedy.

' 1.. _When the Tare is I4. pound per com."
take the g“ part of the pounds gtoi‘s,and the
Qtotient will be pounds Tare.

, 2. When the allowance is Tare 161. per
amt. take the;- part, or divide it by 7,andf’
the Qiotient will be pounds Tare.

3. Suppofe it were Tare 24. pounds per
cent. work firft for iéas before, then take
the“: of that which 16 cometh to, for if 16':
produce. f0 much, 8 mull produce the i of
that, which» being added will make the
pounds 'Farse for 24 pounds per cam.

Again, fuppofe it were at 2.") pound per

'“ cent. you may work firfl: for 16, and then

, 4-will be-the i of that (flotient, which be-
ing added" maketh: the total of your pounds
Tare for 20 pound per cent.

Again; fuppofe it were for. 12. pound per
cent. Tare, work as before for 316, which
Qintient is for 4 too much, therefore take
the j; of that, and fubtraCt from that of

J16, and the remains will bepounds'l‘are,

K or 1.2., pound per cent.

CI. 4.,

Again,

   
£7128 .“Riu’es‘of Pmé‘ficé. / Ch. XV”.

~Agaia, . fuppofe it were .7 pounds per:
Cent. tare, Work {01:14, and if 14icomesto
[0 much, then7wiߢbciof that: and you J
‘ may with cafe work a” quei’cions .of‘this
kin-d, by making 14 or 16 your {fending
"Rule, adding and, ‘ihbtraéling the partxorg.’
~.par-ts of it more or lefs, as occafio’n red
_,quires. I might fay more as to this, but
‘ {hall forbear, only I will give you two 01‘“
three Examples ready cafi up, and figure a
.few others to exercife your ilnganuicy j
‘ therewith. ‘ '

. a:

 

48 c. Gmrs. Tare {4115. pg; cm; at;
»x;0»d.;‘- per 15.,Ncats. , ’ '

‘ 48 4.704. T5. at 10d?" '2} Perm‘

    
   
 

‘ 112

3525‘53761‘b.g70fig ".7; 5
6721b.mre.‘ ‘ :

47041.5.716’151‘; .

 
 
  

    

q56C 4grofs, tare
316 pound- per cem.’
Eat 9d. per pound

 

 

   

 

900 Tb. tare.»

Wm hw

579335400135. neatat 9

 

 

‘ i —- 42.700
- 1350
405k),

.fl—W «M -—.--

202.« 10- offing.

 

T” ‘ ChaPaXV. - RfilEJ'Of‘ P74672176. 1:9 .

eat. T
c. ‘”‘ '
5.6 '4;
4.
2.25
28
g f 1800 ‘
5 45.0
2 i“ 63 oo Tb grofs.

d: .

 

97 C.’ 411 pound”?
grofs, tare 24 ft.

per cent. at 5 4. per
pound Neat

 

 

 

 

 

9-75-11
4.,
391
28’
’ 3129
783;

 

 

“M

1565“
782

. 2347Tb tam:
3861sz. Max:561

‘MM

 

 

 

 

 

 

 

; 2870——8
717—8

 

 
 

 

 

330
' W19 C.;‘; 11 pound

\‘l

 

Ra&£~0f'flrafiire.,. Ch

      
 

sgme, ‘ T3126“ 18 4 17

, pound per mm. a ,
7 ..1,.,,1,,d.; per ibnn‘cat...

aw ' y, n- _ J 7f?!)xn -~

9 piXV... ‘
20.0:- 13 pound; -
refs ,.>“Tarie 1‘2.
pound patient. an
10 d. per-j pound», .~

   
 
  
  

neat. . ‘

86C. 3- ”Igvpgundy
‘ grofs', ”Tare 13...; ‘
pound percent. at

8 d. per ib.vncat.;

\

Wm”

19 'C.,i- 19 pound:

2 grofs, Tare 19 it).

  

 
   

CHA P. XVI.

7721: DOIJ&[€.RZ&ZB of Three.

Aving fomewhat at large infil’ced up

, onthe twolal’c Rules, viz. T he Rule
of Three and Piaflice, I (one to the fe-
cond Rule of Proportion, commonly cal-
led The D able Kale of Three, which hath
its denomination from its double work-
ing: And 'as I did in the former Rule of
Three proceed with one plain and eafic
. winking of the fame, either direfi or in»
direc’t: So I {hall here ali‘o obl'erve the
lame Orcer; b 1t heie firlt a diligr: nt heed
11 mil: be had unto the fiiting of the (belli-
on, becaule under this Rule is compre-
herded divers Rules of Plum! ‘Praportian.
Therefore o-blerve as in the former Rule
of IThree, f0 in this.

.That F1191 and third 111111 bers be both":
of one lpecies, viz. if the full: number oe
Principal, the third muli bel ’1m ipal; ilthe
fi1f’cbe lnterel’t the 11111 mul‘cbe Int: relt

If thefirf’t be time tl‘ .e1hi do. 11* be 11me5
1;; 1f the firfi bemen, the third 1:1u=3. be men» _.

1y " ‘EW
5:3 1 "lg/1}”

 
   

   
      
  
 
 
 
  
  
  
    
 

the third term of demand.“

” maple... ~ ' . I -
‘ .fiz-all 276 Again in: 18 months?
V If 1:001. gain 61..

gain ? C ‘ . , , ,
_ ' 2.0 1440

 

 

 

12.0%., ’ 1.1040.
1.2 . 1.104..
W4- 2.76 ‘

. I440:
Cut off" the; two fitfl
. figures,gnd' the ref: are;
, acme—y viz. 39714 414 ,

M.

#3974140 ~ -

mun—w”

, 5 .Then-fay; . ._
M712 fiz‘aflQT53n974dr—What 18 mm},
. , V J fdfiz‘t., 596 1 d.

, in, 5 day/9%, how many Clerks can write 360:

; . 3.311ch

I . ChapXVi.
._ I257. Obfc-i‘vc that thcrtwo<firfl term/rs in“.
, the Qzeflionvdo cdnfifltof "a fuppofitionlands.

If 100157 in», 12 months gain 6-1. what-5'
1 . Here. you fecthé. fup.pofifion i9, 5

2. The démand igmhat Will'27,61.‘

, if 6’C‘1cfks canv‘m'ité 43,.5m'e-ets-510'f papcm»: ’

' gfijcets in, _13‘ days aftgr that proportion 3, I

  

- i
 
     

f‘Chap XVI The RuleofTbree '

3; Sheets. Clerksc - Sheets ,:
1800:

; 1 d '
L"? " ‘ .. X8 @2140 Clerks
9?}? ,

. 91": . , ,

Days-1 ’ Clerks. V , Days.

§,-—-.—---- 40 —‘---~ ~— 1333*“
5- ’

~. ' ‘ zoo _ " ‘

, *“Obfirw here, 532251129 7“ marks.

if? othz’rifllaet/fier the de- zfiflx I 5 ; ifdé‘iti.

. mzmd be manor lefi, a" (1/33 ‘ -
work 44 hatb'lyeen tangbt. ‘ ,3."

If the Carriage 'of §6C Weigh’f Ibo
miics cofi 141. what will 13 C coFt being
carried 29 m1lcs, after that rate?

C. E. C
56———-—-—-—-—- l4—-—-—-——-——Ig;
, 1+;
( (4 -———-~*’
1X8Z(31.513 52
13.
1/ 182: f
l“ “ ‘ 1f:

 
 
     

     

‘ ChapXVI.~
If :00 miles—3 I.-——5 ': ~29 miles.
‘ 2.0 _ 65 ’

:34 mum, .&c' 7

 

I74

.65,  14.5 !

fab-2:: 18:. If}.

 

If 8 Taylors make four Suits of (baths
in 10 days, how many will make 15Suits
in I4. days. ? '

If 4. Suits require 8 T’ayiozs, what Will

:85 Suits require. 3

 

g

252% (gofac’it‘ 1520.6
51“?

if Iodays waoTa w 15:13..

30
3.053“ « 35/336501 3;.
. ' 1%? _
V ‘ _ ,1
(Of What‘PrineipalX was 150/ gamed m i;
119 months, when :ooI. in 12.. months ,

gained 6 pound?

fad! I 528 I»; 3Prinéi'pal.
am 1

 
        

‘7‘” 7;.

R'CfiapXVI. T118 Golden Rule- 135’;

How long time was 9001. a. gaining-f
4201. when 61. was gained‘of reel. in
1~2~months ? -~
v ‘ facit 93 month: ~§-'

A Scrivener lent 7001; at Interei’c the i
22 of Ofiober 1639, and upon the 9th. of-
- Decom. 164.5. received for Interefi thereof
3301. Ideman'd at Wth price per cam. per
ammm it was lent ?'

The time is 6 years, .
1 month, 17 days. facit 7 l. fifif;
If I fow 20 Bufheiseof Peafe, and they,
produce inroneyea-r 2.76 Buihels, Indemand
how many Buihels in 6 years will 90 Buih»
eis produce after that proportion?
facit 7452 BhflMlLl
What is the Principal that gained 4761.
in 16 months, when 1001. in 12 months.
gained 613 :
59501. Principal. ' ’
In what time was 8501. gained of 940
pounds, whcniool. in 12.».months gains 6
pounds?
, facit I 3 yams, 25,114. it}
If loo 1-. in 12 man. gained 61. what mo-
nies was that which gave me in 8 months
./ 3-0 Pounds in .
‘ " . facig 25013 Primipafi

 
I3 5’ The Dow/6, 8&3, ? Cha’pQXVIég,’ .
7 If 4.6.28 dz pay one Soldict‘for? 1 week,
haw many Dollarsm 4.5.72d.,will~pa«y 83
men for onemonth? ,

 

' fhcitx358 Dollars f =
An Ufurer Imam: III of ffldy 1647 3a-
. film (If money at Interef’c for 613.3257: cmt.
and on the 27‘of'FebJ 16st received for In-
tercflz thereof 3181.125. I; demand whats.
was the fumlcm? _ .

- The time bet-weenw“
"the Inhofjuly 47.‘ I 7 ‘ 7.,
__ —‘ rajrlqe'27 of Feb. 3.51; facit 1448!;‘1735
zétfom' years, 7 mom, . ' ' » .

16 days?

A If“ 10 Brick—layers make a VX7211] of FCC? f
foot long, and .20 foot, high in; 1‘2-~days, ,
how many Brick-layers will make a Wall
of 236 foot long, and 20 fodt high in16 '
@3315?» 7 ~ ‘ ' ’“

" ‘ facit 173mm {51; i ’

Q! H.,;TA P;

 
  

M.Chap. XVH.‘ l 1,3 7

Ply? C H‘ A P. XVII.
, Ame]? brief and compendiom Waysef Warkiyzg
lll'; all mmzner of Qggfliazz: upon Intercfl.
6: Example.
r“ It‘ll, Rate your Quefiion thus 2"
5,, , If we 1.8ainw61. what the Principal 3’“

a. 2. Multiply the feco‘nd and third numa.
‘1 hers together, and divicl‘ehy your firl’t,
whith is done by cutting of? the two fitfi“
figures of the [mantis with a line.-
3. Multiply them by 20, by 12, and 4.,
i and all above two figures in each Multipli—
" cation, carry over the line to the left. as
you fee in thcfe following Examples.
If too l.‘ in 12. months gain 6!. what»
Will 3561. gain in I 8 months?

 

 

If 1001. gain 6!. what 3561;
6
,. _ 2'I\;6
l. 3.. d. zo
'tz man. fa. 2:1—-o7———2 4:; ..___.....
6mm. f4. IO--13—-—7 ' 7720..
FM ..——--—- I z
ale-'0 0—9 *2, ~---
2140
I ’ 4
‘ 1160

  

 
     
 

' '12 33:? 2 ‘ hare/f. 2‘ Chap.XVI‘I”IQ:
2751. lctout for threeycar523t5pound I,
per 0222:. per 222222222222

    
    
     
  
    
 

 

1005-2-

 

2'75; 7 '
'6

- l. 2. rd. :6 75o 7
1» year fm: 16-—Io—-o Then

.4

3 years will be 101500;; -

3 times this fum

72361.10 :. 52!. let Gut fér 16 months;
at6l. per cent. per 4222mm.-

1_ool.-——-6«-—'—-—.——- 2.36—10—~5
, , . * ‘ 6, ~‘
. "222.115.2221. 14. 19~02~6
fmit m 112.. 2 14--—3--9 f 2

3 ; 4- 14*73 M“""""
2220. ' 12;}

fizmin 16. 18:18-24,

 

 

,9 90‘

33.1? 6.0

  
   

lid The fame order obferve for Intel-eff u
- Interefl', only add'the lafl I‘nterefi: to

l as before in thefe Examples following.

ll. ’Ch.XVIIZ. Interq/l'upon Interefz‘. I 39;;

pon s

the,

third number of the laft queflion, and work;

417‘]. I 1:. 8 a’. let out for four years,”
-~ at 61. per cent. Ber amum. Interefi upon Ins.

terelt.

- I; 5., 51..
too lam-361;“;417 :‘I 1 :8

WK—a—

252.03: 10:0;
#120

 

fim‘t 25!. us 14'; ‘1‘10-
12.7

 

[80

W

‘x
- M,

Multiply fecond and third“ Numbers:
together, faying, 6 times 8 pence is 48
pence, which is 4. fhillings, for down 0
and carry 4 to the (billings, faying , 61

times 11 its 66, and 4. thatI carric

j is

70 fliillings; fet down'the 10:. and carry
~’_3 to the pounds, faying, 6 times 7 is

s 42, and 3tha~t I carried i545, fet dow

n 5,.
and:

 
 
 
  

  

’ r40 Interefl umemerefi Ch. XVH .;

and carry 4, flying, 6 times I is 6, and 4
‘-that I, carried is 19; {ct dawn o and carry ,
,faying 6 times 4- is 24, and I thatl ear- <4
tied IS 25-,w which fet down, and cut off the
two firi’t figures of the pounds, and multi- i
piy as before, and the Produft wiii be ac— 41
cording to the Examples, 251 15.14.
fimple Interei’t for the firft year, the which
aide! to your farmer Principal 4171.11:
- '84! and it wilimakc 4.421 1 2 3. 9d Then
Rate yeur Qei’tion again, faymg,

 
    
 
 
     
    
  
  

 

 

 

J. 5 4.43

If we l.----61.- "-442:—.-—12-9
. _ 6 4

 

 

 

. 2.6 55—46-56—54-
2.0

 

 

- 1136"
l 3.619.11'16
2:41 year26-11- 1 3 im

~-

1498..
4.

 

 

3i92 .
l. .5. 4’.
Add this Intercfi unto the 442—1299
and ti: willmake—u— 469—03—1043—4.
' Then '

 

  
 
 

“30114. XVIII; i 429"”

_ Then Rate your Quef’cion again, and
work as befOrc, faying,

 

 

 

 

 

 

_ »l.' ,5. d

VICO‘AZ. 61.‘ ‘ 469—3....10"?

. 6%

_ a l. 3. d. 28 15*2;+-‘«

' galyear ..28~—3— o: “LO ’ a
3103

,‘V'W'hichz‘o’ l. 3 5.10 d.;‘;,add 12
' unto the 4691.13 5. .10 4.13; o 40
facit 4.971. 6 5. I I (2’. then I 4.
'~ flare your Qgcfiion agaih,
1. . and work as beforeflayinlg, 14162

 

M

l y. d.

1 GO,I.———-§-—6z l. 49 7—6— I I
\ . 6

 

 

29184-“l—56;
20

M

 

'Wlfich being added to 16 81
the497 1.65. 11d.fdcit . '12
5271. 3:. 8 a’. “3;, Interefi:
upon Intercfiforéygags , 9173
[at 61. percent. per annum _ I 4.

- 3112.

 

M

Aéd

       

14:“ V

 
 
   

 

And thus yen may in a brief manner
Work all quefiions of this nature Other

Ihcm to your confideration. \

Example.

Iercfi upon lntcxcft.

Chap X;

 

 

I demand how much Ihe Interefl of 81 9 I. f
will amount Unto for 3 years,‘ 7 months, '
18 days, after 61 par cent. per annumflra?

      

l
a
i

/ ways of working there we, of which Ifhalil ‘
I give you two or three Examples, and leave

 
  

'w'r‘r'ffizzw W VW«
, ’ \‘ ‘V
2 . .
l

. facit 243000 4.

Iterefl uponlm‘er “1‘4- 4»

     

20‘

20830 5 3(60 firfl yam

 

1230118
2083530

 

_

2208540 8 Scare”.
106

m L

 

._ 1325124
2208540

 

234105C24. third year.
@025

' 1404630
2341050

" 248151C30 4tbyem', [rm ’
234105 wbicb film. the 31.

 

-—-_

 

 

1‘4046 axe 7cm. ‘

7023 : 6 me.
1170: I ma.
585:1; dzyx.
117: 3 days. .
23410; : third year.

 

 

tun——

 

 
 

 

Infamy} ”pm Thtmfl; Ch.XVII-. '
A Table to find. out what any Sitm of Money ‘
'1 wifl (mm-manta for 21 years, or and”, rat ‘.

. #6 l. in the Hazard, Interéflnpon Interefl.

The Table is f0 1
plain, that I fuppofe it
needs very little de-
monl’cration, I {hall
' therefore only give you
one or two Examples. l

 

. A's),
gal-urg— 9—1 If you would know,
1c I--—-15-—— 9/“; what 361.“ comes to,
IIQI.-——I7——-II-—~2 Interel-t upon Interefi,
122—.- o-— 2—3 for 20 years. ‘
-132—— 2-— 7~—3 Look againl’c Num-
14 z--' 5-—~ 2—2 be: 20 in the firlt "Co—
‘15 2—- 7-5—1 1—0 lumn, and you will find
16 2—10—- 9—4. what the Interel’c upon
{I 2—-—13—-—xe-———"o Interel’c of one pound
18 z—-—17,-- 0—3 comes to for that time.
19 3—~ C—-— 5—3 Then fay, by the Rule
2 ~3-—— 4-—- .1——2 of Three,
213—— 7&11—2

If _1-v‘l.--"3vl..4:‘. .1 d’. gar—361.

(2.2». » xiv-fflrngfliawvf“?“‘7‘... ”MA-who .A m‘ ... . _ u
          
  

'ChLXV'ILfiIMerw‘ypa/‘vz Imewfl; 14;?" . .
‘I dcfirc to know how much 346 pound
{Efwill ‘amomt unto in 13 years, Interei’c up- ‘
:Ti‘on Interefi, at 6 pounds per cent.

Look- againfi Number 13 in the firi’c Co-
gilgmn, and waill find L ’ s. d. q”
:i . 2———-2-—‘7--——-3

   

,5. Then fay as beforeg
, l. s. dn q

\ If’ I bew2,~2m7~3«w 346'
_\ ‘ ' 4.2, _
: \ 12

 

51 I ‘ ' I «
.4- ‘ 1

 

 

. 12404767. ' , "
346 ' /

~6-

 

12282'
8188
6141

 

 

708262
'32" ZCZ 50956 , ‘ \
5 WWW (WM/€56 (2:475:55 ',
MMM ”MM .* -‘
f. ' \ XIX/1’ H 737...;ISwSEffi. ‘ '

W

 
E 4,6 ‘33»A7tmtt'ties. '3 Chap.XV]i

A very brief and neceflk’ry Table to find out
the prefent Worth of the Annuity or Yearly
Rent for 2 1 TM?! or ttfidet,dfter the mm of
fix pattfid‘pfr cent. per annum. ’ '

Al. 3:. 61. q;
foo-m 18-—Io——-2‘“ For the underl’cand- '
210 I «16—08wo ing of this Table, the *
3302. -~ I 3-03wz fame order is to be 013- f
43033—09—‘3 ~23 ferved with the for-’3
j’ 1:,:u4.—-—-0:;~—-—02—~3 I met: As for Example.3

6 . 4-18—C4»—0E If you would know
'7 og-11-o-3 What one pound year—
8 ~6—~04+—02~_2 1y Rent is worth for7
900—— 6 oc—zfyearsin readvmoney,
mow—07 02—2 Look againf’rNum‘g,
, II 07 ~17-—-—092-O{ her 7 in the fun: C0»
12,‘ ‘8—-—n7-——»05%‘m-o§ I‘Umn , and you wifl I
13 r 8—-«—~I7—-—oo-——2§ find What I pound is“
1409—2—05—1 1——-o 'E worth for 7 years,
I 3c9-14~02-~3 é w’z. 5—11—73. I
16 IO-———OZ-—-01-——I Now to knowhwha't »
I7 10m09—~C6——-2 3' any Other Annuity J
18 IO—--I6~——C6.———I 3’ (3540 LCé’c.) is worth _
.19 11m03-—01~L~3' for the fame time,
20 11m09.__04_._.33 fay by the Rule 0f3
21 II—uI-5-03~—13Three, , *"

 
 
 

 

 
         
   
   
   
 

t

   

l

J

 

         
    
 

 

 
       
       

 

3 {help XVII; flmwz'ties.

;
§
5‘

L :. oi. q. i,
'If 11. heft-«swnwéi—fi what 49
5, do

fm‘it 2 Zgéusng

4 , ‘ v 2"“.m 3.17” laym‘s—Tfiyhm‘f "fl
, .

.I have a Shop, a ‘Place, or an 0.130343%;
fiWOrth 6c pound per 472an (or 21 ycas,‘
liand would foil it for ready moz‘ey; the
:"quefiion s, how much it is worrh ? "
Look againf’t Numberm, wit: my“
find one pound a year 1.5 oowh in: ma:
itimc II I. 155. 302’. I 9!. Then fly,

If 11. be worth II—ij—g 61.: what
{hall 60!. be? \
’1 l. 5. , d.
facit 7055—16—3

W hatis ’10 l. per 4717mm worth in‘ ready
money for 4 years and fto come, at 61.
.per cent .?
facit 381. 75,761.};

, Firfi, fee the Table what 1 l. isxworth
for 4 years. ‘
facit 3 l. 9 5. :33 d":

Then fay: if I I. be worth 5 l. 9 s; 3 6H;
, . H 2' what;

 
 

 

1118 171111111111 11112111111188 Chap-XVIII?

What fhaII IOI. faclit 34.] 123 “(5.1

Now to find what the 2‘ years is Worth, fee;j
in the Table what one II 15 Worth for "I;
years. fem 41. ~—-4. s. —~2. d.
Then fay, if”: he 4L 45.;2d. 3 qrure
From which fuba 5 years 42 I 2 s. 3 (1.2
11361 the 4th. year, 7 7
and the remains Will 1 4. year 341. 1273.1; d;
‘be for I year, then ~-—-- ‘

W

a—

 

 

 

take the g of it, :1 year 711951 41H;

 

which will fhew 7
what the 5“ War is ~ i year 3 I. 145. 8 d.
wmth, facit. 7
12/1. 14.1. 8d. ;, which add to thcfimto.

1111:1111 year, and 11 1112-11 erh 38!. 75, 7d";

11......1mw-mwm . ma; _:;, _:~ ‘ -» ..-.-.-—:.:.:: m
,. m, mm‘w mwu— a. va— warxr 1::

C H A P. XVIII.

The Rafe 0f Fellowflyip11.171801151171115;

LEN the working of thrs RuIe, 1111111;
no difference betwixt i1: and the RUI
0f Three, where every mans 111111111111;
Stock being added tagether, the toraI 11111,}

be the 51% Number 111 the RBI e (If 331111

the gains the 1111111111 and every 1111111311211;

ticuIar Stack the third.

1I

CW1

 
   

lJChap XVHL The Rule of Fallawfllip, 3‘
E The ufc/of this Rule is theraforc t0 givc

‘to each Farmer his jufi ané eguai fhaza
Ohferve than?

V, A: the Wicaiez Stadgéx 29 3595 whoic am,
[3 1:561’6'73’ 132,337.: pmfimim Smcé'éuw 6175?“? mm;
pflrfimlar £33221.

‘ E xgmpls.

Two Merchants Company, A. put in 2:: i
B. putia 401. and they gained :50}. 1 (Ea-n
mand each mans part of the games?

A. 201..
B. 40L

’Im

If 60!. gain 30?. whatfhafl 201‘?
’ facit 161. 135. 4d. A’.

If 60!. gain 50!. what will 401?
facit 331.65. 8d. 8.

M

 

5c——ec—woo

If both the {hares added together,
make up the whole gains, then isthe work
right.

H 3 Three

 
5 18’1””be Chvam

Three Farmers hired :1 Shepherd to keep:
‘ their Sheep for 71,10 5: P” flmmm. -
I The fiffl wmmi’tted 430 Sheep to his?
care, the fecond 357, ,and the third 500,;
Sheep ~' I demand how much each man mufe;

pay of this 71!. 10:.

l. 5. 5!.
x1, mufl pay 2-—-‘Io4-1
B. muf’c pay 2-,-~OI?—-—7
C, mufi pay' 2~— 18—;

MN

I prqaf 7—- 10-4—6

FourMerchants ventured to Sea a, Stock
of 2475 pounds, Whereof A. put in 7101. '
, B. putin 9601. C. put in 2071. D. put in 1’
' 598i. and/they gained zooo l~. But Tern—t

peflucufhefs of Weather arifing, were forq :
, cal, to caPc over-board as many Goods as -
amounted to 769-1. Idema-nd what cachg
‘ man mui’c bear of‘this lofs? ‘ . 1:

7 22' '

C.........»—--—-‘; 764-

247 i 5

“M”

D. ----..... 18; em-

faeit 769 .
" ' , ’Four‘;

 
      

ChapXVIII. The Kale of Feiiawflyip. '13 1

Four Grocers laid in a Stock containing

‘ thefe feveral fums following, A put in 1.20:5.
B. put in 1361. C. putin 1802. .1). put in
2101, and witfi it they boughta payee? cf
Fruit, by which they gained 3981!. I de»
mand each name part 4:2? the gains?

Z.
A-—-'73
B. —-33
C» 110 580
D.-.129 246‘

393 ¥933(3
.636

we 81v
Inn-8— E0

;=_
6
.9.
Anfiver 4‘ 510

‘7‘!» Gw-m
b

 

Three Mexchants made a Company, xii.
put in a certain fum of money, 8. put in
, as oftentimes 5 l. as A. put in 4 l. C”. put in
\ as oftentimes 7!.- as '8. put in 61 and they
have gained together a certain fum of money,
whereof A. his part is 100]. Idemand
3. andC’s part, and whole gains?

4 _—-—Ioo--———-§ facit 125 B.
6-—-—-125—-—-~7f4cit 145126.
facit 100 A.

7303
H 4, 1W0

 

 
  
  

‘ 13’; The Railcédela-wfljip. gChapXVI‘H. ,_
, ‘ Two Merchants made a Campanyi A”:

‘put in 3501. and ’thcy'gainc’d together
" .196 i, of which E. rat-UP: have f0 o{tentimes_,",- ,
‘4101. as A. mzjfi have’ 6!. I demand how
much money 113. put in the-Company? ‘ :

        
     
     
     
   
     
   
   
  
     
 

(:1 ' _
' A'vf‘ehfitrvc that e’vc’ry man xfiuft‘:
2 have awarding as h; hath put, m, then:
it‘onfider if éwm-mamggo ' um 10";

 

flair/583 : B. put in. ’ 7

Two men Company, and make a Sfbck
«335 P7003. whereof A. put in 3001-. and f

/ ’ they have gained tegcthcr 2401. I demand
» ‘Whatcam man mufi havcof the gains? "

fizcz't 102—~—17——I fiA.
facft 1.37-—,.oz-—Io—;— B; ,

 

/‘ L 240*(30-7-00

 

 

,ThrEe Mei-chants made a Company, A.
puri‘n 600138; pm in fo/oftcntimcs 50s.
- aszA;‘put “14:05. C. put in (0 oftentimes
'70:; as B. put in 60.9., and they gained
‘ ‘ 7 ,. “ together

 
    

Chap.XVIII. The R2415 afFe/[owflzip 15?:
together goo i. I demand what each man
put in, and mufl have of the gains? ‘

In quefiions of this nature, the particu.
lar Stocks unmentioned, mufl be found out
by that which is mentioned.

As for example, to find What Stock (B.
put in. n

l.‘

If-«mq. wméoo—w—g » t

' filcit 7501. B.

 

 

A Such reafon as 6 hath to the Money which
‘ B. put in, fuch reafon muf’c 7 have to the
money which C. put in: As,

 

If 6---~-—«730L—“-—-7
fecit 8751. C.
\ 630 A.
730 B. {3
873 C.

 

L ‘2225
I €2,225 «-———-Soo—~—-~6oo A.

 

2 222,5 goo—~7so 3.
3 2225~w-500m873 C.

 

2225

H 5 Three

 
  
  

  

232; m m f mow cmmm; i???

. Three Mé’rcha'nts‘made a Company, D
put in" 4371. E. “put in 2111. and they“;
_~ /_ have gained " together 5621. whereof F;
‘mufi have 2871. 15 5. *I demand D. and E’s.
‘ 'partgand What F. put into the Comgaany ?? '
, . To find what F. put in, firfl: fub‘trafi his "
, ' particular from the whole gain;
' I. 5. ‘
’562-——~¢0_ *
1 87am»- 115 '

 
   
   
   
   
    

 

 

;_ , W- —*-----" { _ , ‘ 1
“ Thenradd D. and ES Stock together.

'43‘7 D.

:211 E.

Nv 9......
w

as
\

6+8 / ‘ V k' _, If.

 

I Gain. , 'lSioék. Gain,
3741'. s 5...... 648m» 1871. 1 51«.
fmt 325’«;$§%

Til/ma to find D, and E’s part of "the profit.
\‘VSt'OCk‘t? l 5. > Stéc‘n’. V ’

649*374-w S ........‘ 4270.
“543““?3’74?‘ '5“?le 2 1E E-

   

m, \
:i V' 1:

 
  

Fellowjkip with! time.
_ III. The ufe of this part is the fame
with the former, and differeth not in ope.
ration, fave in this that every mans Stock
is multiplied by his time, and the total of
thofe Produé‘ts added together is the fitfl:
Number, the gain or lofs the fecond Num-
ber, and every means particular Stock and
time the third.
‘ Obferve then,

IV. A: the whole Stock and Time 135* to the
whale 10f: or gain :

50 is every 27mm particular 5500114121 "Ema
w 61/517}! mm; particular [0,”; or gvzz'z’u

Example,

Two Merchants Company, D. put in-
tool. for4mnnths. E. put in 1361. for
3 months, and they gained 501. I demand
each mans part of the gain 3

, Mo.
D. put in 100'. 4W4oo
E. put in 1361. 3 w408

sca ,

 

 
  
   
       
     
   
   
   
   
   
      
     

  

l.
808 “-50.1 4494.00 facit 2.4. g
8o8«-———501~——~4o8 facit 25 *3

WW‘”.
A

50'

~ Three Butchers hired a‘ piece of gro‘and
'fOr 121.105.601. APutm zoOxen 5
days, '2? put in 16 Oxcn ._7 days, C. put
in 25 Oxcn 4 days: I demand how much
* cachPButcher ought to pay for his p oporg
’110fl.’

.026. day. ,
A. put ingzo -'—— 5.--—-——r we» .
'3. put in 16-»:— 7--‘112‘
C. put in 25 “4...;— 100

"W'

312 i

J. 5. . ; d, _ .. _\

‘3I;W*~~12~XO—6_1c0
i . V i. /S. dz!!-

quzt 4»—-—C——-37‘;
31AW1’~10~6——-112‘
fmzt .f—gw—ij:
TIWIOM6~~IOQ 6
f““’""““r“‘O--°31‘§T

A“

‘\ i3 " ‘ ’ i \

 

3123

 

 
Bs'ff WT? A...» "(

   
  

Chap ”XVIII The Rule of Fellowuflj‘ip. 1’57 \

 

l. .1. d,
‘A'A'H'OW 37%:
b' 4"" 9-~11;~3
C 4““ON3Y%
proof 12. 1;: 6 134:1

 

 

«2'3»

Tlucc Merchants Company,fl .put in
the firPc of 73mm)!” 1201. 1111111 21/1..er the
22. B put 111 1761. the 1oofFe17.until
the IZOf April. C. put in 2951. 2 of 13.619
until the 25 of AFN], and they gained
800! I demand each mans part of the
gains. .

L
Amufi have 174 fig;

0‘ (3“

B mut‘t have 19;; Egg;

9 iv)

C. mufi have 433 Ziif‘é

In." w M

proczf’ 8 00

 

%fi5%5 (I
fiQéfifl

 
 

— ¢2§un _

= 2001.. and at 10 Mo. put in more 300 Land
at 14Mo. took out 1301‘. E. put in 4-001.
and at 3 Mo. ,put in more 2701. and at 9

Mo. tack out 100 I. and at 12 Mo. put in »

. gmorc 10:) I. am? at 1; Mo. took 99 l. P.
put in 900 I. and at 6 Mo. took out 2001.,
and at 11 Mo. put in 5001. at 13 Mo. took

358 , The Ride of F ollawflyip. ChaPVXVI‘II. ‘

Three: Merchants Company for 18Mo-
I). put in 500*]. and at 5 Mo. took out I

 

  
  
 

out 6-001. and they gained 2001. I de— 7

mand each mans paltOf the gains 3

D. mufihave $6 ’%
E E mui’c have 52'
F. muf’c have 87

NU)

w, W!

proof 2.00

328,734 (I
22873

Two men made a Stock of :65 pound
wherewith they gained- 28 pound, which
added to the Stock makes {93 pound.
E). his Money was in 12 months, and E...
his Money was in but 8 mo. When they
flared the flock and gain , D. had 67'.
and E, 1261. I demand what was each
mans Stock? ‘ V

Stato
   

  

3-”...

ChapXVlIL
State yéur queflion thus 2:
Asxzmo. (£01631, f0 358310. to “of.
for E’s. flock, the which fubtrafi from 1673
: and the remainéer will be 551. for D’sr
N Rock.

I.

The Proof.

If 55!. in 12. mo. gain 12L what rco L.
in 8 months? gams.
551. Izl.-——-IIol. facitE.161.
[119.12. 8 mo. fm': D. 1&2 I.»

 

Or,

Having the flock yeu have the gains-3
by fizbtrafiing each mans Rock fiom his
flock and gain, given without the Rufie of
Three. - 4

' Stock and gain of D. 67!.
Szeck Cf D. ~~;-~ 33

W

 

 

D. his gain. 12

 

Stock and gain of E. 125
Stock of F~ --—110

E3 his gain 16
So that D. with 35; 1. Stock gains x23,
.E.With 110 /. gains 16 z’.

12

“E? CHAPB

 

 
 

   

. "vegan? a“..- w... _ ~v, ,,

e Chap; XIX. ’ f

 

~ (3 H A P. XIXS
Of Barter.

Arter is the exchanging Wares for
Wares, or one Commodity for ano- ‘ ;

‘ther. ,
Example.

Two Merchants Barter: A. bath 3 C. 5-
of «Pepper at 135%; per pound; 8.1)th
‘ Ginger at 15 d. 5; per pound. (”I demand how
much Ginger mui’c be delivered for the

7‘ 4 ‘Pepper?

 

1. See what the Pepper is worth, faying,‘

If Il.coft‘13.d‘-:—, What COR 3 C. in?
fan": 22!. I .c_
2. Say, if 15 duf; buy .2 $5. of Ginger,

Whatwill 221. 15. buy?

» ' facit 34,7 3% Ginger. .
Two men Barter : A. hash 20 £115 of ‘
Cloath at 9 5. 6 d. fer EH ready money,but
in Barter he will have. 10 s. 2 61. per Ell: B.
hathj‘erfiey Wool at 21. 10:1. per pound.
Idemzmd how much Wool muf’c be deliver-
ed for the Cloath in Baxter? A
, s
 
 

é‘
1.

W 3'

Chap. XIX. ' Barter. 15:.
As before, {'0 here, ’
If I Eliot Barter be 105., 2d. what 23

£115 in Barter ?

fizcit 2,440 a];

' ‘ L If 34dhuy I fix what will 2.44051. buy?

, ”R

fight 71fha~f§

Two Drapers Barter, the one hath 472
yards of Canvas at 1651. per yard, the
other lets him have 38 pieces of Claath:

the qud‘tion is, how much one Cloath fiands

,himin?

facit' 16 5. i

20 Bags of H093, each 3 C. i, Bartered
for 336 C. @mezil, 3:18 5. a C. I demand
what price were the Hogs fold at?

‘ Anfwer 41. 65.-§§=perC.

A Merchant hath Tobacce, which he
will Barter at 14d. per 1. for Sugar at 10d.
per pound in Barter. I demand how much
Tobacco mufi be given for 8900 Th. of Su-
gar? . ,
Anfwer 6337 175.5?

Nutmegs '

 
 

 
  

.162 " Barrera 5 Chap.XIX.
Nu'tmegs at 4n 2%. per 135. ready mo-

ney, 5:. in Barter, how mufi: Pepper at

fit? ,
Anfwer 14 d. f

How many dozen of Candies at 3:. 2, d,

I 2 5!. per 115. be’i'old to make the like pro.

  

r

    

 

*1
i
i
1

per dozen mul’r be given for 3 C. 3 7n, 16 [.3 3

of Tallow, at 37:. 4 d. per C.

Aaner 26 dozen g'f- “

A Merchant- hath Stockings at 39:. per \ "
dozen ready Money, which he will Barter
at 4.6 I. per dozen for Canvas, at 13 d. f per ‘

ELI ready money. I demand What price the

Canvas mufi bear in Barter1 to gain 5,1. in
me 100 l.» _
“ Anfwer 1621:; and fig of 5 01.
Broad Cloath of 6 :.~ 8 d. the yard ready

money is Bartered at 7:. 90!. for Wool at 1,.

' 104’. per 1. ready money: What price muff
be made of the Wool in Barter to gain
1 I, l. per amt?

Anfwer 12 51.91053?

~ D. hath Holland of 3):, Per EH ready m-o4 ‘
ney. Battered at 6 5. per EU to E. for broad~ 7'

5 Qloath, at 95.645. ggr yard, which cofl:
, _ " , but
 
   

Chap. XX. qumiiorz. 1 6 3
, but 8 .r. I demand which gaincth 117103;, and.
how much per cm: ? ‘

Anfwet‘) D gains 20 l. per 667th
$18!. 15 5. per cent.

 

C H A P. XX.
0f ngztz'm.

TH E Rule of Equation of Pavm-ents
teacheth to reduce the times of feve—
ral particular payments, to one time for
the payment of the whole fum.

Exampic.
If the qaei’cion be of this Nature;

A Merchant oweth gco l. to be paid at
3 payments, viz. 2300!. at 4 months, 100 l.
at6 mo. and 100 l. at 12 mo. The Debtor
agtfes to difiiharge thc whuie Debt at one
payment. Now th’: quci’tion is,. at what
time the payment Ought to be made,

without damage unto the Debtorcor
ma

.. “a.

 
164. 7 .Egmiwz. . Chap. XXQ
Creditoig accounting ‘61‘l. fer cam-.3126?" WW"?
.lntereit ’ ‘

 

. The gym 3:; Mars},

{WIL‘Multiply each parlicular payment

by its my e, then add all *the Piodu‘t’ts to-
gether, and divide the total by the wholem;
: Llebtp ‘ f , 1

 

  
    
   
     
    
   

\ " Z. , Mo.

, a 30:5 multiplied'by’ 4 facit: 1200,,\i
mo multiplied by 6 facit 0600 g

‘ .100 multiplied by 1.7. facit 1200 (fl

 

W
W“ W

i , ‘Di‘wfir god 3 Dividend 3000‘
, - (B/Q’Qld /' _
WW

\

  
    

. ‘ Soithat theaaner to the quefiibn (ae-t .
I, cording to this Rule) is, that fix months _
, -isthe‘ time for. the payment of the whole a?
. film/Q ‘ , , ‘ , l ,, ~ . ‘
 

  

”leiia'pxx. 12311411111."

 

III. Far the praof cf this Kale, thmg

300i. ought to be paid at 4. months, and
' is not paid til 11 6 months, that IS 2 months
after its time. The Intereii: 01' 3001. for
2. months is 3 I.
Then 100 I. paid at 6 months, isthe
time Equated.
The 01 her moi to be paid at 121110 is
paid 6 months before its 1ime; and the
intereii thereof for 6 months, is Iii {ewiie
3 pound.
3 Which {heweth theR1~ ie to he true, and

at 6 mouths isti e 1i me for the may 11 ent of
the who? e £11111, and th era: by neither the
Debtm 1101 Ciediter is damaged accmding
to the Law.

A. Mcrchaht 0 weth 41; CI to be paieia
3 paj 1111111115, 1: at 3 months, 3 at 51110.:111d
3111. 8 11111. {mi the Debt 1111 and Creditor
ages, that the Whole {11111 {hiII be paid at
one time : The quefi on is what time
011ng 1i 1:: 11 Imie 111111 to be paid 111:,10 that

neithei the (1111: 1101‘ the orher may be dam-
hificd.

The

  

 
    

   
 

W _( q . J _ , W . 5-7 , f'l-,*~I"~’Zr’faf§-Tx~sy4 WALK

Eg , CthX

 

:5

 
        
 
 
  

* The little I}: to multipb/tacb part by its. ‘
‘ time, dam; ' r ‘-

   

3‘— by J;- facit 1 mon.‘

‘ 4. MMMMéMf flfikikuumu.mnr

  

1 . > 9,.
“3— by f?- faczt I mom. ii”

Wm
3,
‘ _ _ V _ V
‘1: O
3 by 4? famt 2 mom. %

3' ‘, - /. L} . .3.

   
   
   
    
    
 

 

“ facit 5 mon. g“

‘ 'A"Merchantvqweth 30.34. tobe paid gat ‘ x
,3 months, g at 6 months, and ~;~at 1.2 m0;

_ Idemand at what time the faid fum oughi g
{to be paid together? ‘ ° \
  

Chap. XX.’ Equatim;
3 Months":
éby “f“ fiz’Cit I

3 -
6 . I To prove the

certainty of this
manner of opera-.
I tion you may take
3 . - the fame courfe as
12.

”“4”“

3f- hyfi" fascit 2 .

Wm-

 

.‘efore, 7 manths
being the time for
payment of the
whole fumg

 

 

1% by 1% 152655 4..

m

 

3

Wm

 

 

fact: 7 mo.

k—W-WWW

Spc firit what the Interei’c of the money
corms. to, that thould have been paifi be-y
fore the 7 menths: and then fee what the
Imeteft of the money comes to, that {hould
have been paid after the 7 months : and if
the lntetefi: of the one part be equai with
the Ewen-(t 0f the other, then is the former
Operation tight; anfi 7 months mutt needs

be the jnfl time; As for Example.
‘ tool. {hould have been paid at 3
months. but now is not paid till 7
' months,

. . -\~_ “» , _ ---~_ - ~ '1“ .r-x. h.

    

 
       
   

   

' Jogwc‘p‘. XX

”mo. f0 that the Intereit for that’iooI. mun: 5
be accounted for the4monthsdeiay, which 5
Interefi' 1s .1..." 2i. 1......“ 00 s. f

11:01. more IhouId have been paid at 6
me. and now IS delayed till7mo. The In- ;;

terei’c for that is WW0 .___., 1o

facit 2. --———-~ 10 j_

The other 1011!. is paid 5 mo. before 3
its time, and the Interei’t thereof for 5 3
, 1110. is IikeWif-e 21. ~——---IOS equal
with the former, which Ihews the opeta- 1
tion to be right. = 3
There 15 owing to a Merchant 34.0 I. to i

be paid, 80 pound 1'63.in monty, IODI.
3 mo. and 160I. at 8 mo Idemand what 3
is the indifferent time for the payment of j
the Whole?

      
   
  

  

 

   
   

   
   
    

 

   
   
   

 

IV. In Queftionsof thisnature,fet down 11}
the particuI ar fums, and the feveral times f‘
of Payment, thus .

‘ ‘ I

 

 

 

   

. mo.
'80 00 ‘ 3
ice 03 i
'160 08

 

    
 

Then Multiply each Sum by itt‘
time of payment, and the work will ;
Rand

    
      
  

chapxx." @mim , 159

Rand thus, Add all the Produé‘ts together”

and divide the total by the whole debt.

I. l M09,
8 omo— oo 0
IO 0—.o—— 30 o
16 o—-o—-—Iz3 o
3.4 Divifir. 158 Dividend.
(2(2 ,
.I’f/c (4. f; fizcit‘.
3‘}?

There is 2431. IO 5. 9d. to be paidi at

 

 

 

 

:6 mon. §at 8 mo. and the roll at 12.111011.

what is the indifferent time for the payment
of the whole {um together ? . '
This Rule is laid down in the firfl‘ and

;fecond Examples, multiply each part by

its time.

ofizcit—g (‘ The certainty hex-m
y 8facz’t-2-§-)of is dcmom’trated by
y 12 facit 2 )the proof of the third
'_---—~ -—-~———‘~,Example.

facit Mo. 7 §-.

“C

& [HUB [n p [a

i ,
if A. is indebted unto‘B. 3001. to he
lpaid tool. at 4mm. and 2.;0 at 8 mom.
7 ‘ ‘ I And

 

 
,, ,-_ - —-.
fiarxf’: a. Haas» . “firm”;- -714? ”mew , w“.—
, .....

17o Eglmtioifi’i. I 4‘ ’Chap.XX.
And B oweth unto Agent. to be paid at

. . ii
10 months. It 15 agreed between them As?

1

 

{hall make pi'efent'pay for his wholeiDebt, g
and B {hail pay his fo much the fooner, as
{hall countervail that. favour : I demand at
What time 6" [11119: pay the 3001. reckoning
fimpie Intei'ei’t?
V. .For the refoiution of this, and the
like Qaefiions, firft fee by the former Rule
what time A ought to pay in his Whole
money. . . g;
Mo.
ijoo’m—at 4.~-w4
zfioomat 8~-=—16

 

 

  
    
  
  
 
 
 

Then fay by the Rule of Three,
if sew—6§m~-5‘ '

2m (4 mo. fizcit.
:3 ‘

Which 4 months is to be fubtraé’ced
from 10 months, (the time thatb’. ought
to have paid in his money) and therere»
maineth 6 months. * i <

(fly/arm?
;
  
   

“ Chap. XX. . Egzattém. 17g
h 05/3706, For the most hereof”, ee 8w;
f what the Intei'ett of get) Z. comes to for 6
“' months § ,4
3 Then fee what the Intereé’t of goof.
3 comes tofozczt mon. If both the Ennis be
i‘ alike, then is the former WOIii true.
. A Merthent htlEhSiCfl‘tfifl fum of money
fowing to him, to he gut at 7 month,
5 his Debtor {hath egzeeto p31",- him 3:2 tea 1/
’2 money, and g at 4;. mi“ . :ieniztnti
what time he mutt have to pay it; the «3“
f0 that neither party may have advantage
of the Other Without recitonmg intetefl
upon interefl? 1

VI. For the Refoiution hereof, it mat-
tets not what the film was, but you may
work the fame by any number that will -
eaiily admit of the parts mentioned in the
Quei’cion. And for our ptefent Life, we
will imagine the fum that was to be paid
at 7 man. 60 l.

Whereof if that is 302. mni’t be paid
icontent.

And 3fwhieh is 20!. mutt be paid at 4
‘,months; then fee what the Interei’c of
“ thefe two parts comes to, for the time in
which they were paid before they were
due.

1 I 2, The

 
"‘ xiii-$95”; 373%?" W. 4, My» .. *m—«M~-n~u,>>4 . ‘ A,»

  
 
   
 
   
 
   
     
       
 
 
     
 
 
   
 
 
  
 

1'72 ‘ vEthz'on. _ Chap.XX.'
The Interef’c for sol. for 7 months is a!
' ——2xs.”"
The Interelt for zol. for 3 months is";

~06 salt

i;

M

facit 27 s

a Now that which remains for a full Refoe

' lution of the quefiion is only this: _
’ To find out how long time the remain;
ing part of the Sum (whith is Iol.) mUl’t;
be retained, that the Interef’t thereof man
come to 27 9t ;
And that is done by the Rule‘of Three;—
thUS : ’ f
The Interefl: for 101. for I no. is 15;;
if -1 s. » 1 mo. 27s.?
Unto which add the facit ‘27 mo;
7 mo. allowed at flat. (:7.

W”.-- m‘ ;

 

 

 

 

   
  

, facit 34mm; .

A Merchant hath owing him gool.
be paid him at 8 mo. and his Debtor doth
agree to pay him 200 l. at 3 mo. on COUdi‘fi;
tion that he lhall let him have the rel’c for“
f0 much the longer : The quefiion is, when
he mufl pay the rel’t-m‘with Interef’t upon?
Ifiterelh -
l A

   
  

  

i
  

‘X Chap.XX'. Fig/anion. I 7 3
a As in the former quef’tion, fo‘in this:

fish Fiti’cflee what the Intcrefi of 2001. comes
to for 5 months, paid before the time.

. The Interefi of 2:0 I. for 5 mo. comes
2' to —~—-3L-——oos-—oo do
" Then by the Ruie of Three, fee how than
t’ ny months 3901-9-“00 s.——-oo d. mutt- be
' let out, that fo the Interefi thereof may

i come to 5 L

36

fl . facit "3 mg. L}
a To Whlch add the 8

facit 1 1 g-

A Merchant hath owing to him 146!“
7105. 9 d. to be paid g content, fiat 3 mo.
fiat 5 mo and the ret’c at 7 mo. And his

‘ Debtor doth agree ’to pay him all at one
payment. Idemand when that payment
mutt be made, that neither have advantage
of the othefi’

 

mo. mo.
’5 at «w o —-—-o
i atw—«g o i
4 4
i at -—-— 5 -~»-— I

.13.
4%?)— at"“""7"""““I 6°

\

 

w

facit 3 mo. 7?

 
            
       
     
       
 
      
     
  

 

, i 174 Eggmz-‘iwz. ‘ Chap’fXX \-
A'M rchamha “homing 21.31323. 19:. 1101.1

:0 ho paint; at 2 months ;— at 3mon1hs, _,,

- and tho 1:65:13: 511:6 months.- the Debtor (330111:

_ agree to pay; content, and tho other half
at one my}: 11.21515. 1: demand whom the pay—,3
mom muft he (11:16.13, (shat neithermay hcv

‘ 3.311111115ch 3’ ‘ '
Eirfi, Do assoroing tothc former Rois,
what 13 the indifi” orent time for the payment 3
of the whole 11.1111 together? "

  

3- .3 mammmom mm u- m. 1mm, .

I

 
     
 

mwmdwwm
3L ,
gm~W&wfi

p,

 

 

‘i

. ‘ fimit 4; mo.
Now in regard that}; is paid in 4 moh.

, . and ‘ before it isdue, it is rweafon and ac— j?
coxding to Rule, that he {houid have the 3
other : 4mg)... longer, which being added 3

to the jufi: time of the payment.

figcit Brno.i 9. _

»CHAmf

 

 

 
 
   

ll

ll

l:
303'

la1
a

l

l'

l,

Chap. XXL

C H A P, XXL

7/36 Rafe at” Beet/are, or DQ’EOfl-m‘,

J

1; kg lit-chant»; com: ionly ‘ vend their

Cornnzndities either for ready mom
nay, or to be paid at a certain time or times
appointed, at 3,4, 6, 12. months, or the
like -, but it often happeneth to be very con—

venient both to the buyer and feller, that-

this money be paid in before it be due.

A Meechant fells Goods to the value of
lOOl. to another, to be paid at 12. months,
but the other is willing upon an after-

» agreement to- pay prefent money upon Re-

bate, after 6 pound per cam. per 477mm, {Em-—
ple Interel’r. I demand the [urn paid‘and

‘ rebated?

Ola/Ema, Before you lay eleven the man-
ner of working, onlem, that in all ebate~
ments, there ought to be no more money
paid than WOtllt’l augment it fell~ to the {em
firfi clue, if it were put forth to lnterel‘t,
and this may all‘o ferve as a lure proof of
this Rule.

I 4 HOW

 
 
    
   
   
   
     
       
        
   
          
        
 
    
   
     
   

   

, ; 1:: 76 T116 Rule? of Remié Ch:XXI

How inflate the Queflzm. ;

' I Firfi, fee. what the Intercfi of 100L954
2::3meth to 80: the time demanded. ' ' ,, 2‘ ‘
1 ’2. Add. that Imeref’c tothe 1001. Much
muf: be the {1:13; number m the Qucfiionr
\ 1col. the famed}, and the fumto be rcba-w
1::(3 :hathi rd ; ; .

   

;- maxim-a1: Wmfi.aw mam: “an mum. _ war. ; ,, ,.

Example.
5. I; ' I.
If zcémw 100M 1 00'

100-,

«M

10009

  

which put:;}
‘- forth tOIntc-
refi, would i
‘ become IooL

‘ * ('3
95(5 . _

X:¢¢¢(9: 31%:

819-566 “

: :m: '
Idemand haw much the rebate of 289 L _«
:39 '3. wifl amount unto for 6 months, after
81; per amt. pcrwmm, fimple Intercfl? 51%
3‘s. v
‘ 1mm 16C: ”~289m I9

20

5799,
‘ , 100

\
W» —-—¢

579900

 

,\
 

    

a ChapXXL or Dzfiozmr. 177

 

 

 

 

 

(I
26(ov‘
542%?!(0
EMMW 5571;
Xafi’fl’ei’fi’ ‘
«I’WDCZ/ 278—1g—%§;
an»
l. s. d.-
‘ was to be paid 2.89 --—---19 o
Is to be paid 278 . IS “3%
Is rcbxtcd ~~—-~-~~ II-w3WE§

‘ I demand the Rebate of 3211. 18 s. for
11 months, after 6 pound per cent. per am-
mma, fimple Interefiz. ’

To fini the Interef’t of?" A
1001. for any number of] EXampku
mo. you may take the‘ m0. 1.
parts of 12 man-ths, as 12m6
thus: If 61. be the Inth Mum
tcrefi of 1901. for I; mewk 6 M 3

 

then 6 mo. will be the 5: 3M1.Io
of that; 3 mo. the i of; 2—;«1

that i, and mm. the: of! -——-~""‘
that for 6 months. j 5 L 10 5»

nose—“lo s,_——;onl.——321 l. 18 s.
1 fm" 305L~Eff
I. 5 Ide.

\-— .- ....... ‘_‘_ w. .r —.

_ _, n. ‘ .
--~ «.._,_......._.“ .- , .. _,‘__

 
yl‘m ,_ u v‘ .
—" me-s —-

173 71716122;le Rem, Ch.XXI..

7 I demand the difcount of 378 pound for ,
two 6 months,aftcr 6 pound per cent. per an:
7mm, fimple lute-raft? -

By two 6 mo. is under- mo. ‘1.
floodthatthe onefiohhe’ 12.—~-6._.a.:3 7-8
money is to be paid at 6
mo. and the other i at 6 6.....-37“... 118.9
mo. after that. - ‘

M

 

 

 

l. I. ‘ , I. _
L103» ' ”—100 ~----18-9.
I facit 1831. 3'65“? ‘-

l’. - . . ’

'1:o6~—--«-=}-——-__M_M we —« ———~_--——- 1 89
- ' , facit 1781. i?

 

’ I‘ demand the Difconnt of 7601.;161.
, for thrée 4. month, afier 6 pound par cent.
per ammm, fimple Intez‘sf’c?
‘ moo I. l. s.
12 .._.,....___ «6 3 760—...16

m Mg‘

 

4. ~~-~ ~---~ ~25? 2:53—42
r8-~*--v-—-—-4.§ man—12
,l'lmm’wé ‘ 253—42.
233 l.——-—1‘2.5. ~
flair 248 1-. 2}? for tha firf’c payment at 4. -
' ‘ (months,

M ':
u—... n" w om“... “W

M

 

 

3,202 mm 100

 

1,04

 
 
 

      

Chap. XXI. or Dlfioltmf. 179 e
104! «v-~~-IOOM'253 l. 12:.
fmt 24:31.11; for the fecond payment
(at 8 months;
106 l.~ loomnggmmlzs.
fim’t 2 39 [. g—g— for the third payment
(at 12 months.
There are other ways for the working of
Rebate, but I 011331 only infianceone more
after 61. per cent.
.14; firfl mzzalzipzfy the money, and the time.
Secondly, Divide that Prodzzfz‘ 19)! 200 and.
tide Time, and 2.195 Ethimt i5 the [14m Ia 136
paid 14pm Rebate. Exampfe.
Wth is the Rebate of 1001. for. 12 mo.
after 6 Z. yer mm. per 4777mm. 5’
100

 

 

EOOWas to be paid.
‘ 31% is to be Rebated.

 

 

1. 94%? is {0 be paid.
And thus you may work any ether que-
fiion after 6 fie?" 65m. 8R.
But if the Rebate be after 81. pm.” cm!-
then 1:31: the D‘ivifor be I so and the tune.
C H A Pa

 
 

   
 

'13:, _ Chap. XXII. I

 

C H A P. XXII.
Of Excbamge.

'1‘. H E whole courfe of Exchange is
T no more than to pay money in one .
Place or Countrey, and receive in another. 7
the like value or fum, with confideration of
eitherlofs or gain. I ‘

I might give you a Catalogue of For-
reign (Joins, but it will be to little pur-
pofe, becaufe they are not currant money ,
as our 1:723!th is, but fclo‘ rife fometimes
higher in value, and fometimes lower ac."
cording as the Exchange runs, I (hall thete- .
fore give‘vou fome choice Quef’tions, and‘
foaleave you to enlarge as you fee occa.
fion.

A Merchant delivered 34:) l. Sterling at
LOWdOfl to receive the fame at Amflerdam,
the Exchange at 345. 7d. Flemifla, the
go 5. Sterlirgg, I demand the fame in Flemiflz
. money. “ .

2, Confider that firl’c and third numbers '
mull be of one kind :, if the firfl he Sterling
money, the third mull be fo too : ifithe fitll:
Hemfla, the third. mull; be Flemiflh

i. If.
    

, \Chap-‘XXH' Of Excbwge. 18,1
’ 511 L dLFk. 14$
Ifzo—434-**'7”‘“*-"34O

12 20

__________. WM

435 68c0
6803 - .

m
, M

332000
2490

M

28220C10

 

 

 

ril4xlood;‘

“7318‘"451 .
M... .__.__.._____, ?
fkwt587——I8—~4

()r thus:
34oL—eat34s-7éj
34 '

 

1360
1020
170
28——4d.

' an“

 

”nu-mm»

117518-44.

Wm“

‘ 587-18¢——4 facit,

    

 
i - ' '46?" L" 7,- psi Pale-‘7' v .4 WV?

 

   

mm, 34......"A ~--.._..r__._..__a -.

I l 182 Of Exchange. Chap. XXII. .,
' A Merchant received a Bill Of Exchange -
of 8000 Crowns at 5 3.515;.975. I demand. 7
the {um in Sterling maney. . Say,

If I_ be . 3:. 3—, what ~-—---- 8000?.
facit22831.14.5. 3 al.53- "

 

A Merchant delivered 2451. Flam. at
Middlelzoraugb to receive the fame at Lofl- _‘
don, the Exchange at 295., and 54’. Flem. ,
the 20:. Sterl. I demand the Sum Stcr- 4
Zieg money. ‘ ’ . ,

If 29 5, 5362,1318)”. he 205.5567]. What;
2451. Flem. ' “

.. ‘facz't 1661. 115??? 7

AMerchant of Londonreceiveth a Bill”
of Exchange from Paris 4.601. Sterling, "
for the value delivered there at 84. d. Stew
Zing, the 60:. Tou‘mois. I demand how .’
much was delivered at Paris Tonrnois ,‘ ‘
when 20 5. makes one pound Tournois?‘ '

8+d.-—~—6O 5. 4601. ‘ . ,
. fecit 5942.1. 17s.;eTourhois;

 

A Merchant at London delivered 80!.
Sterling by Exchange for melefard at 4. 0!;
Sterling the Florine of 67 Kremzem‘. ‘ The
quellion is, how many’Florines of {63’
Kremzer: the Florine, he mull receive at".
Frankford? ‘
     

Chap—“XXII,

 

8o 1,.
jam“ 510 if-

A Merchant at Damzicé’ dath receive 21..
Bin of Exchange from Lma’arz 3999 7510..
' rims, and is for 3761. 51573in delivered at

Lam'm. ldcmand at what pace the pound
Sterling WES delivered, when 30 gz'ofs P0,.
lifh make a Florinc?

fa“? 319 33% grofsPolifln

At Arzmverp a ,Merchant rccaiveth a Bill
of Exchange from [40.57610729f 3751. Flew;
for the value IECEWfi} them at 27x. 5 a’.
Flam. the 205. Sterlizgg. Idcmand the
{um in Sigrimg mane}! that was deiivcmd
at Lox/2655,72?

fflm 2731-. II .r. 3%;

A Merchant at Lfifldflix doth deliver 3701.
Sterling by Exchange for 330372 a: 7392,
516242721? 1107:5(3 5. Tommisa Th6 demand
is, how mm 3% mm”; I‘ecsive at Rom
Tourmis? 1

#0163821 5.51% Tournois,

A SP4;

 
 

 

_ 1’ ' :7“ ,, ,., .... ..
‘7 w. ,. W5 ,. ,-..mw.... -—

184; Of Excljmge. , ChafiXXIL
A Spanifb Merchant doth receive a Bill

of Exchange {mm Lmdan of 700 Ducket5,:
‘ 'and is for 196l.-——-15 s. delivered at La”.

don. I demand at what price the Docket
was delivered? ~

g

i
l
l
S
:j
a
a
o
‘
E
a
2

3
i
[I

deit 5 5. 3&5.

III. How to know at who? mte we makg
the Exchange, tmnfivorting [Money or P774715;

from one Confirm)! to‘another.

If a Bucket of Venice be worth £20 3. 5
33d at 1407261072 51.741. At what price is the}:

Exchange made for the Docket of I 12 5. if: '
tranfporting from Venice ,?
«110*:"5' Jo ~-—-—---7 d.

 

112

facit 5 s. 2 431mg. _

If a Pram}: Crown atiHmlzboraugb be {V

Worth 45:, Luéz’jh, and an Angel be worth

785, and at Lom’og a Freficb Crown isd

worth 6:. Sterling, and the Angel 1H.

Sterling. Whetherris it better to bring‘

Angels or French Crowns from Hambarm‘gb'
to London? " ' I

l \
8 ' '

“in

ling, and at frmkford it is worth ‘C all h
7 ‘ , charges

It is better to bring French Crowns by 3

If a piece of Searge be worth 28 so. Stet; ’
    

Chap.XXU. Of Excljmge; 18$

charges abated) I7. Florines at 60 [fireman
the Florine, at what price do I make the
Exchange for 66 Kremuw in carrying
Searges from London to F i’dflhfira’ .?

facir r 5.52%";

If a Mark at flamborozgh be worth 332 .r.
Lubifh, and at London 135. 7d. at What
price is the Exchange made for one pound
Sterling in bringing Marks from Hambu-
rm‘gb to London 5’

, facit 1 84 5. 3% Lubifh.

If a French Crown be worth 7 r. 2- Flem.
’at Antwerp, and 6:. at London, at what
price do I make the Exchange for one
pound Sterling in bringing French Crowns
from Antwerp to London ?

facit 25 5. § FlemiflL

If a Dollar at @anmick be worth 39
Grofs, and at London 45. 8 d. at what price
do I make the Exchange for one pound
Sterling, tranfporting Dollars from thence
to London .3

. facit 167 3% Grofs.

CHAR

 
 

 

I 8&2 I I. ~ Chap. XXIII. 1

 

— Hmmmw »

C H A P. XXIIK
Of Lnfsmz/i Gigi/’9‘.

' Need not go about to aajuaint you
E with the meaning of thisRule, becaufe-~
the words themfelves are fufiieient to in- '.
form you. And for its nature , I {hall'
fliew it you by many and various Qgef’ci.
ons; which indeed are fomething hard to ‘
apprehend, without the well-minding of
thefe four principél Heads, which being
' well underflood, will carry you through

the difficulties thereofe:

As, i,
Firfl, To know what is gained or 109:
per cent. “ ,

Secondly, Tel-{now how it {hall be fold _
for to gain or lofe’ to much per cent.

. Tbirdly, Having gained or-lol’c fo- much
per cent. to know/“Whit it (709:. .

Famrkly, There being {of much gain-ed ,
per cent; when fold for fnch a rate: To;
know What is gained per cent. when fold for
i more, or: what is loll: per cam. when fold for g

' 0f
  

Chap.XXIII. Laf: Md Gait/‘92. 187

Of theft: in order.
.Firfl,‘ To know what is gainad 01‘ I09:
gar Sent 1267 Peund, per Ei},perYard,@a.

E xz’m‘m’e.

If 3 155. of Tobacco (0?: 18 d. andis fold.
for 21 d. I demand how much is gained
per cam? Fz'rfl, [65 what the Gairz or Lofs 2:5»
by Subtrafifon. 21

18'

3

Then let the price it cofl be the fir]? number
in the Rule of Three, the gm or Laj} the
flacond, Md ICOI. the third.

18 gain ~-———-- 3 J’s-“W" \Vhat we?
facz't 16 L 13 5. 4d.

If a Leather-fella bay a parcel of Lear,
ther for 2:. 10d per fiéin, and felleth the
fame again for; s. 2 oi. what; doth he gain.
per cent?

3 5- 2d. if 346%} gain 40). what ICOE.

 

2-....-19 facit 21E. ”5-36-79;
3mm '4;
If

 

 
‘ . W mUCh the [91‘s is per cent? -

 

  

188 Lofi 422:1 Gaza Chap.XXlII. i;
If I buy an El] of Holland for 6:. 7d.
and fell it again for 5:. 9 d. I demand how

 

 

 

s. d.
6 7
5W9
, 10' V
If 6:. F7al. W‘Wiod. 1C0 l.

 

facit ml. 1:; s. 01 chi—g}

If I lb. col’t 10d. and is fold again for :

8 d. the qUel’cion is, whatxis lol’c per cent .9 ,
If 10d. lofe wad. what real.

facit 201. ;

If apiece of Cloth contain 24 Yards, '

/ Colt 42. s. and one Yard is fold for 2-5. 8d. ,7

the queflion is, how much is gained or loft

per cent? ' ‘

 

Gained 52. l. 7 5. 7d. 3- percent-
’ If a piece of Silk contain 36 Yards, coll:
91. and one Yard is fold for 95. 8d. Ide—_ ;
» rmd whether I win or lofe, and how much ‘ ‘
per cent. , , . ‘
facit 93 l._-———6 s.——8 d. gaina
A Draper hath a piece of Cloth contain-
ing 3Q Yards, cof’c him 145. the Yard, and ,
anorhsfr Cloth containing 19 Yards, colt 7 s.
, , the Yard, and he fella them one With and-
ther for I 3 s. the Yard, I demand wher‘hfir»
r / C

 
  

Chap.XXIII. Loj} m Gain; 189
he doth win or Iofe, and how much per
cm. *

. 4—1 7i faoit gains per Yardo
fflCIt I; 1.».03 5. 9d. fit;- gains in EU.

If one Yard wit 3 :2." ready money, and is
' fold again for g ihiL4d. for 8 men. I de-
mand how much is gained per cent. per 422-
mm, without Interefi upon Interefi ? ‘

facit I6 l.—-1 3 s. 4d.gains.‘

if one Yard COR 9 5. ready money,and is

fold for 85. the Yard, for 16 months, the

queftion is, how much is 101’: percent. per
“mm”, without lofs upon his?

facit 1 l. 2s.-—-~3 for 16 months:

‘3 Loft 8 l.-—-6 5.”; for 12. months.

if I buy Cloth for 6 s. 21 Yard for 8 mom

and fish the fame again for q 5. 6:]. ready

money, how much doI loi'e per cam. per
ammm .9

Quefiions of this’natnre are to be refol—

ved at two workings by the Rule of Three,

thus:

If 6 s. iofe-w 6d.-——-—'What 1001.

, facit zoood,‘

If 8 mo. lofe 2000 d.-—-— what 12 mo.

fact: 12!. 103.

       

 
 

 
 
  

59° Lofi 4’34 G427”. Chap.XXIII. ‘4

if I buy Cottons for 3 s. a yard for 5 v _,
months, and fell them again for-g 5. 2d.
readyinoney: The queflionis, how muchI ‘
gain per amt. allowing 6 percent. Interefi?
Fir/1", See what they coé’c in ready money,
Thus: '
mz.l.--—Io:. - . —-1001. 3(1.
" facit 25.11%;3?

 

 

 

 

Zia—114.15: adj-15‘ . 1001.
few 81. 3:. IO an; gam per cent,

A Grocer doth fell Gloves for 4.5. per
pound ready money : The quefiion is, how
hang time he mufl: demand, when he doth _
buy the fame Cloves at 3 5. 8 d. the pound,
to'xxgain x; Z. per cent. per/4722mm, without
gain upon gain, at '6 per cent; Interefi. ‘

Fir/f, bee what the gain is, if bought at
3 5. 8 6%. ,

Thus:
3 5.-8 d. >m—«M4sr—i‘ww 1001.
' facit 109 1-?

Here is gained but 91. g-f, but he mni’c
gain 131. that is g 1.5% more, which mufl:
be gained by time: Therefore fay,

If 61.:ZMT12m0rw- «M3 1. f3;

' * * ' ‘ facit 7 [110.7%

  
  

’

:5

Chap. XXIII. Lofi ma! Gain. 1 9 I

A Linnen Draper hath feveral forts of
Cloath, viz. 47o E115 at 2:. 10d. 1?” EH
ready money, 730 Ells at z 5. 6d. per Ell
ready money , and 179 Eils at 3 5. 1061.
per Ell ready money, and he ers the E11
one with another for 2 s. 24. to be paid i
at smoj atémo. and the refi at 9 mo.

Interef’: at 61. per 06m. I demand what is
loft per amt.

£125. 5, of. Z. .c. d.
470-at 2~~--~10 i5m65'W‘IIm~28
730mm 2w-~~~6 ism-”~91 m» osm-zo
I79mat 3-~— IO ISmr34‘MO6m-2'2

mm...” W W W’

I 379 EUS cofi ~-m~¢~>~w-m192m02m210

 

W
w a,- Yum...“

 

"1379 Ellsfnld at 2 5. 2&1 i3 1491. 7 5.104.
Which {um being to, be received as a-
bovefaid, wiii by Rebate at 6!. per mm.
come to no more than 144.1. 17 s- 4. d.
Then fay,
“19215.25. toimrcol. I44l. 173.4515
facit 24.1. :25. per cent. lofs.
V The fecront‘? Head.
To know 130%? (5 Conumdéty mzzfi” be fold to
gain 0;" [0/22 [a mach pm“ cent.
Example.
If one pouni’g of Nutmegs cofi: 95. 2 d.
how much mui’c it be foid fer to gain 61.
yer tam Let

 

 
' ~ e . - '~>‘v‘-w--
.., Iii—w: , ' ». , - " ’7 ,5 _____F 2:; ._. .‘

192 ' Lof} and Gdifl. ChapXXIIL
Let’IOOL betbefirfl mméber in the Rule

of Three,tl:7e price the ficond,and 1001. with s

.  the profizfiflak-{862'2 .or the 10f: fubtrdfied, the

. Yr third ZWLmber. ‘ .

‘ If 1001. be~—9 5. 2d; price, what'IOGI. _

' \ film 9 s. 8‘d.%

If a Barrel of Gum-powder cof’c 31. how
muff it be fold to Iofe 9 L per cm: .9
If 1‘00m~31.———~what91l. “

- facit 21. 14.5. 7 d. f

If one Gallon of Sack cof’c ; 5. 10 d. for‘
how much muPc’ it be fold for to Iofe 81.
percent .?

If looLm» ogs.~—xod.--——921. .

It mufi be fold for g s. 4. d. ;‘~

If 90 Eils of Cambrick coft 60 I. for how _
much mufl one yard be fold to gain 18!. '
percent? _

It muI‘t be fold for 125. 7 d. f?

Ifa Bag of Hops,weight 16 0.1 q. 12. HS.
coft 2.7 l. 65. 8d. for ho’w'much muff the ‘
C. weight be fold to lore 8. l. per cent .9

, facit €09: per C. I l. 13 :1 3d. *3-
' Sold‘to 105:? per C. 1!. 10 s. 8 d. fifi? k

A Sugar Baker hath 736 pound of Su-
gar that cofl 13d. a pound, and 137 113. j
3; d. a pound; I demand how he mufi fell '

- a ’ the

 
  

 
 

Chap. XXIII. LOfS dim; Gaizet 1 95
the pound one with another to gain 91 P37“

amt. Firf’c fee what one pound cofiE.
feat 13 d. i§§

   

It mul’t be fold for, to gain 91, per cm:
1:.1 d. Zi‘éif“ I g

If a pound of Mace cofl: 8 5. how muft it
_ be fold‘to gain 241. per cent. ’
facit 9:. ii-

If 3 yards :09: 5!. ready money,{or how
. long time mutt it be fold for 935 s. to lofe 20

per cent. without lofs upon )ofs?

If I lay out 100 Lil/refidy money, and
mu& receive butrrrng/fi/there is 5 per cent,
lofs; butI mutt loi'e 201. per cent. that is,
15!. more, f0 that I muPc fell my Goods,
as if I fold that which cof’c me 1031. for
80!. Therefoye fee in what time8ol. will
. amount to 951. at 6 per cam and that will'

anfwer the quei‘tion.
If 1001. lofe 61. in 12 monthS, in What
time {hall 95 [.lofe 151?
, - 0r thus :

If mo]. .._.._............6 l.~~ --80 !.

facitqu. ,16 5.,
4.1. “M1165. Mawlzw~ 151.

 

K _. If

 

 
1 94., Log/34ml Gain. ChapXXIII.
If one pound coi’c 23 d. ready money,
for how long time muff it be fold for 2 3‘ d.
to gain 11 per cent. per ammm, at 61. 3
per cent: ~ 3
Suppofe I feld for 12. mon. time, than I
gain in the price 81. 3%. .
As thus :
If 234. ~ 1001.

 

2"; d. =
. facit 1.08 3%.
ButI me: gain II 1. that is, 23% more;
thereforethis muflbe gained by Time,
' Thus: ' i /
61.—-+——-——12.mon. 2.1.213 .
facit 4 man. g§§ ,

 

 

 

This 4mm 3%? mufi'be fubflraé‘ted from
1 2. mm. and the remainder is the anfwer to
the quefiion.

  
 
  
  
 
 
  
 
 
       

faeit 7 mm. :gg-gi.

If one Yard (:09: 25. 9d. ready money,
at what race mui’c it be {old for 3 mon.”; to
lofe 8 l. per CWT. -

Eirfi,‘ fee what: rate it muff be fold for
in ready money to lofe 8 l. per cent.
Thus:

IOO l.—-—-——__.3 3d.———~.—92.l.3

'3 3 facit 30¢}?
if god. 539- be a ready money price, I;
,. . ’ mui’c '1

  
 
    

   

i ,
L

i

'0'

a:

~ r‘i'TFWi‘W" "N" ' 7m 6'

ChapXXIH.

§.

3 mo. *2 formy money. Therefore iet roof,

Lei/3‘ Moi um. 3:95
muit feii it for more, in regard I mufi ii

at!

be your firfl; number, and 100 with the
Interei’t for 3 mo. i be the fecond number
and the hit fact: your third number, thus 3,
1-OO-———-10!i.--——~—15 :.-——--30d.;%

- fm‘it 30 4- 735%?)

A Mercer buyeth Silk at 14:; a yard for
71110. at what rate mutt he fell it again for
ready money to gain 16 per cent. without:

gain upon gain?

Firf’t, fee what the yard is worth in ready

money, thus :,

10; l.-—-Io:.___mo[ ____._ 14,.
facit 13 5; 53—7?-

Then fay? if mob-13 5. $3.4 16 1,
facit 15:. fig.

The third Head.

When there is gained or [a]? pei‘ cent. to

know what the Commodity cofl.

Example.

If 10 yardsof Cloth be fold for 16: per
yard,and there be 61. IO 5. lofs per cent. the
quefiion is, how much the I 0 yards cofl?

Eirfi‘, fubfitaé't the lofs from the too I.

6—-—-10

~—

 

93*‘10
2.1x:

 
" _7 _ ., 5.35;“,

 

"* --\-§~».

1'95 Lofim Gm. Chap.XXIII.
t 2. Let the Remainder of 100 I. when i.
there is Iof‘S'7 and the gain added, to 100‘!”;
when there is gain, be the firft number ; let;
the price he the fecond number, and 1031, gf
thethird. ., j
i
i
a

 

If 93 l. 10:. 81. 190 1.
mi: 8 l. I I 5. 1%; -

_ If 20 TB. of Cloves be fold for 7 s. the
pound,and I“ gain 9 l, per cent.The quef’cion f
is how [pinch the whole 20 t5. wit me?

 

 
   
 

20
.7

 

’14lo

II-lh—unu—d
' »l

 

, r 7
I00 l.—--7l.-—-Ioo l. facit 6 l. riffia
IfI fell 28 E115 of Cloath {out 3. per. EU,
and thereby lofe 24 per rent. I demand what
the whole piece COPE?
76 l.-—-—I 12 s.~——100 1. fair; I. 7 5.31; '

If I 3 Ch; of Indieo be fold fox 361,.and.
E gain 13!. percent. I demand how much.»
the c. Weightcofti‘ *
I {gm—géu—Ioo ‘ fam 32 Is if?
It .276 Father of Lead, each 19 C i be
fish! for 256! at 5- months,I gain I x per amt}
Perl

  
  
   
  
   

 
    
 
   

Chap. XXIII. Lofc 472d Gain. I 97

per cm. the quefion is, how much the whole;

. cofi ready money ?

Ail—5."... . - >
1 ‘1' 256““ 100 fact: 24.4. :95 f

The fours}? Hey/16,5.
If Ware: [aid a; flick 4mm tlacrc is f0 mm};

. ‘ gained or 10]! per Cent. haw 10 @1012? what wczzlcf

be gained 07 lofl, cf/oéd at another Rate.
Exam-1c.

If Cloth {bid 3:85. the yard bc‘*zo per
cent profit, what gain or Iofs per cent. (hould
Ihave had, if fold at 7 5. per Yard P

In qucfl‘iam cf this nail/arc, lattbcffl' price"
be técfirfi‘ Wmécr 3 103 L which the prcfit‘ m?-
dcd, or lofs fnbtradl‘cd, the fecmcl immisrcr j.
and the other price the Third‘rmmbcr.

Example. .

H.815. ---» I 10!. -——~7 J. facit 96 if:

LOP: per cent. 3 1.?

If one Gallon of Wine be fold for 9 5..

and I lofe 8 per cent. what {hall Iwinor

lofe when 3 Galions are fold for 2.5 5. 10d.-

If mac—«4921. ~-~—2;.:. wow-IO
acit I I l. 33-”?- pcr cent. {of}.
If 10 yards be fold for 41. IO 5. I lofe 12
per cam. \Vllat {hall I win or lofc i“ fell the
fame for 9 5. 9 d. per yard? , >
9 5. W8 1.-——»~9 5. . .
facit 4'1. glofs per cent.

K3 CHA

 

 
 
  

Chapxfllva

    
     
    
    
   
    

' - x
{3 ii A P. XXlV.
Qf Alligdiim,

L L I G A T! ()N is {o named-,he‘

J: eauie it teacheth to knit or band i
togetl‘mr divers things; of unequal prices,
whereby to find how much of each muft be i

. taken attording to the quel’tion propounied. j

't‘ is‘eommonly divided into two parts, '

‘32,?“

Qwa
I

Adigerim Medial, and
Jélllslgetion Airemate.

ii. fl/[égztt’ian [Medial fimple in it felf is
no more than to difcover or find out a com- '
mot: Medium, Rate, Price, or Proportion in
the mixture of divers things together,
which is performed by reducing the feveral
prices topone Denomination.

Then multiply the qUanttity of each par—
cel by its price, and add all the Produfis
together; the» which total divide by the
number of all the parcels thatxare to be
mixed, and the QJotient is the Anfwer to
the Queflion demanded. ' For,

As the whole Quantity is to the whole
price, fo is 1 to its own price. , '
Ex-

.......
  

’ Chap.XXIV. ”Of A/zzgazm. V, 199 ,

y g ‘ Example. _
A Msahnan hath feveral forts of Meal
of Rivera! prices, and would mix them {0
that thcquantity mixed might be one coma
mon price, viz.

3 Bufhels atgg 5.4-; d; a Bufhd.

4 Buihels at 5:.-—-—6 d', a Bufhci.

6 Bufhels at,4 5.-———8 d. aBufhéi;

Now the queflzion is, what one? Bufhci of
this mixture is worth.

€725,117. 5, d. lmfla. syd, Mb. :5. (I. '

E \ MixtUre is worth 2”

i .

 

 

 

g at 3—5 4at gm6~ 6 at 4-—8 g ;C
3 ~ . 5 4 J. d. [mflm ‘ '
1"”‘5 ‘ 2...»- IO-—-—~23-—-—3’ ”
‘9 20 2.4 '22——:o--4.
‘ I 2 3 28-zo-——-6
0.....3 w I , M
g 22 J'. ----» 6]€:--—-3-——‘{3
10:. 3d. 28 . —-—----,-....._._...
‘ ’ L‘ 5‘. 01.31. 03. 3161'. ;

13~—-3_——'.0—-—:3 -—-- I

facit 4.5. 7 d, T?“ P” Bufly. , . "

‘ An Hoi’cler mixed Provender for Horfes,*
via 54. d. ‘ A
5 Bufhcls of Oatsat 3-——-6 per szfla.

3 Buihcls more at 44—8’per Bulb. ,

2 2 Bufliels of Malt at 2——-2 per Bafli.
4Bufl1e'lsof Beansat, 5--3 per BaflL, .
The quef‘cion is, what one Peck of thns \
«K 4. Bzffla. ’

_f\;{- __

 

  

 

   
  

”22212.2 21. 2242 2. 22.1222. 2 .2 22422 2. 21
sat 3-6, 3224 8, 2a2222,4,a23-2

Reduce each quantity into Pecks, each
222i2einm 43222222, audmuitipiy 6222: by thc
when T322222 iay as 2265022, 3

. mammal-um... 'v‘A-saflubmv 27.2.2» .. «2 . 2.. .2.

.ng to prove .A/ligmz'on erdz'al.1
Campare the total value of the'fevcral
3 mixturcsmith the value of the whoie mix-
. , wre, andifthey come bom alike, the W021:
is true; as in the farmer BMW?!” may.

3 appean 3 _
d. ’2 5. d.

> (
Buihtis at?
I... \

“8 2...... OWI4MO .
-—-Z, —-- Ow'o 3 04—2-4.
W3~““““‘” IWOl'fl-Q

(pm

7222 2222:2222.
U1 ~43”;

 

22—2—26220.

#200 Cf 2411262222022. ChapXXIV '

      

if 56 peeks. 682 d. 2 peckfizcz‘t 12d 3% ‘ R

i
2

 

L—éwcw—i'ym6 2 , 3

     
  

‘ mfg a poun

:’ Chap. XXIV. ofA/lzgatz'm. , ’25:"

An Alehoufe-keeper mixeth 3 forts of '

Ale togetherflzizn I 5 Gill. at 4d. *2 per Gal.

2,2:7Gal. at g d. per Gal. 20 Galzat 6 oi. ‘per‘
Gal. The quef’chn is,.what one Galldn of \
this mixture is worth? , '
facit 5'1d.-——cqr5.-§97- ,
A ,Refincr’ having 10‘ fls. ofSilver’ Bullion-
of 8‘ ounces finez, Izpound of 6 ounces fine,

' and 11 pound ofg ounces finefiis defirous to I -

:élt all together, and to know what finc-
d weight of this Mafs {hall be ?'
I. :

 

 

 

l .
».IO---~I.2, II’II: ~ -80 ,,
8‘ ,6 t 9 12,“ 72,: '
-—----—--—- ---- 10 - 99
so. 72" 99 . -—-.--—- ~—~-——-
‘ > t 33' , 2.3L
3""3u-231m1fdcit 7 ozéf- fine.
' ’ Or thus
V'EC»l‘I€2.4l-'II::33’1’ ,
to: x '8 :89, I Note that a --l~« fling,
1‘2 x 61:72: doth fign‘ifie Addition,»
[m x 9 :99 and two lines thnsn—«z
' ~ M 7 #Equalityor Equation,f
(Thenfay if A but a x thus, Multipli—

    

33—251—m— I ‘Cation.
facitv oz. fifine. , ,

J . o
4H: It will be necefi‘éry hcrgxto acquamt

  

 

    
 

 

2.02 Of ligation. Chap.XX1V . .
you, that as Silver isellimated 12. ounces
to the pound, and 20 penny weight to the
ounce ;. fo an ounce of Gold is divided in to
, 24 parts called Careé‘ts. Now, Refiners,
Goldfiniths, and Mint-mafiers, do (liltin-
guilh the differing finenefs of either, ac-

3'

cording as it endureth the fire. As for ex-
ample, an ounce of Gold being tried lofeth /

3 Carefis, it is efiimafted‘zhl Carec‘is fine;
if it lofeth IO penny'weight, it is efieem-
ed 11 ounces and ID. penny weight fine,
81c. .
A Goldfmith is to ”melt 9‘ TB. 45 it of
Gold Bullion of" 16 Careéls fine, with 7 IE.
6% of 22- Carefls fine; the quefiion is,how
' many Careé‘cs fine a pound of this mixture
is worth ? . .

Reduce theminto 3‘; ounces, and work as
before.

flcit 18 Careéts 5%,? fine.

Oirthus, ‘
22; x 15:3600 22314l—41,,8c:4c5
180 x 2223960.

 

 

" f Then fay, -
\ If 405*756‘0—1 facit 18 Car. 3:; fine,

A Mint-mailer hath 60 lbweightofGOld‘ .

of
  

> ,1 : r‘WR—rfiwfi W 2?”)? , .. A...» ': - -;{,- l 777?.fl F .T:‘:2"Vy,_ V . —
1. 7H1, , ,'- :'-‘~" 4:;:.£' 4’

ChapXXlV. 7 OfAZXZgar‘im. 20;
of 23‘ Calreas fine, and 893125. weight of
r 19 Carefis fine; “the quefiiou is, whether
there ought any Alloy » '

to be mixed with it, A,” 4’10“"; 4*Mix’m
to make a pound of this (21053535? 1:15:33;
Mgtuffi to be 2 I C3“ rate the: fincnefs of it.
re s.

 

23 19 1380 60
6o 80 I e2: 80
1380 . 132.0 2900 1.1.0
140 2900 -——-- 1 fdcit 20 71 Carefls

fine; but it {houlcl be 21 Careéts fine.

Wherefore I conclude this Mixture is
not fine enough by :— of 20 Carefis fine;
therefore no Alloy is to be ufed, but more
Gold to be put in..

The ficond p‘art‘of’ the Ride of
Alligatim.

I. The former Rule required only a
common rate or'price from the'whole of fe-
veral; quantities mixed together, but this
requires a price and quantity in general,
compofed of {webs particulars as the MK—
ture is to‘be made of, and the parts to beta;
kenproportionably aezording to the price,
"quantity, or quality of. each other.

Ex‘

 

 
 
 

 

Example.
j ‘A Tobacconifi having feveral forts of
Tobaccoes, as fome atz; :. apound, others
at 3 5. a Pound,oth“ers .at.6-s. 9. Pound, and:
{hebef’c at 74. aPound, and is defirousto
mix I 12,; pound together, {'0 that he might ;
‘ A fell the whole mixture for 4.r.,apound-,_y j
the quefiion is, what quantity of each, muff
be. taken to make up this mixture.

In order to the working of this Quefiion, R
and others following ;

" Firf’t fet down the common; number (or
price.)propounded (towards the—left hand)
which is 4.5. and likewife the prices given,
viz. 2.5. 3:. 6.5., 75. thus orderly one.
under another, as. youhave learned: in

- Addition...
‘ 32%
q.

3
“6
(y.
, '2» Obferve What-fums are greater and-é:

. what are leiTer than the common number, .n o
and coupler; greater and a l-eli‘er together,.
by‘ making. at Semicirclenfrom one to: the ;
other : for twogreater or twotlefl‘e’r can-not t ,
.bei‘mixt together, becaufettwo‘lefi‘er being; 2
. g‘hystaken, [can never-.gmake fomany as the
' come--

 
   
      
   
  
    
 

' ChépXXIV; amalgam "205,:
Common number, and twogrcafet will be'
: » too many.. 3 '. ,

 

 

3; Having thus linked them-7; ob’fe’tve-
what the difference is between each’of the
i greater Sums, and the common price; the
which difference is fet di‘realy againf’chis
fellow, which is linked with him,

*“ ‘2 -. ----- 3

' Thfi likewil’e mark the difference be:
:1 tween the-leflkr numbers, and the commgn y.
* number, andl‘et each difference Vthexeotag,
" -. gainfirathat whichislinked with it;

ZYM—i-K
41 r i l » “'7

 

   
 

 

' 5'05. ' ofmzzgm'm; Chap.XXIV;'
‘ Lafily, addall the differences into one
Sum, which Ought to be the Exit number ‘
in the-Rule of Three; and the whole quan-

tity to be mixed the fecond, and each par.» '
titular Difference the third. ~ \ a

2 ““7"""5';
(-7\\____2

gl

 

 

Then work thefe according to the Rule
of Three, and the fourth number will cle-
_ Clare the emit proportion of the mixture.

For as the whole difference is to the
whole quantity, fo is each particular diffev
rente toveach particular mixed.

8~112—3 facit 42 for the 621’: furt'.
_ 8—«112—2 fim't 28 of the fecondh

8,—IIZ—I facit 14, of the third.

‘Sx—I 12—2 fucit 28 of thefourtht

. 1L2

To prove this and the like quefiious,
multiply the Whole quantity mixed by the 15
common price, asuhere 112, by}, facit 4+8. ‘_

‘ 2. Mull-

 
       

Of Allig‘agz'mQ 207
2. Multiply all the particular quantities ' , ‘

‘ found by its own price, as4zbyz. 28 by,
4 Bic?" and/ if the total of all the Produété
agree with the former Sum (448) Yong
work is well done. i - l ,

i A Vintner bath 4 forts of Wine of ngf
’ veral prices, viz; fome of 13d. a Gallon; ’
17 d, a Gallon, 19% a Gallon, and 2301,
a Gallon ; of which he is minded-to mix.
the quantity of 32 Gallons. The quefiion '
i5, how many Gallons. he. mull: take of each

\fo‘r‘t, to make the Gallonfworth,but 18 d. j

, léhapXXIV.

um— 4:,er .u—m MTW‘J‘JXMVW, W ‘ 3‘“? u v

   
   
   

   

 

ll * . 105
E ‘ l , *Gall. \
1:)ng an»; facit 3%
10-QZW~5 fdcit 16 ,
10:...“ arms fan”: 9??
_,m-—-~—»32~m1 facit 3—?

   
v .
M. d~fl¢lhilflilAfifM$§flWWI
nun-m— ~
.3 3 ,1 17”.”,:~‘-,;,,V:,~,1 ‘ 1-H ‘ J" ' m";

3
I
I
3
3

3
3

.3 Mm—wwgwaz

 

  
  
 

258 [Of 3111341350”. Chap,XXIV.¢-_

A Druggifl: had 3 forts of Drugs, one Q“
was valued at4t. the pound, another fort
at 7:. the pound,- the third fort at 1 1 5. a
poundront of thefe forts he made two:-

parcels, either of them to be 30 pound

weight, whereofone of them thus - mixed to
be fold for 9.5. the pound,and the- other for
IO 5.- the pound. How many pound mni’c be»
taken of either fortto make each mixture?

The price propounded in thefirfi prOpo-
fitiOn is 9 ,5. and in the Otheriogr. Likewife
the prices given are 4 5. 7:. and I 1‘5. but"
fee’ing two of thefe given prices are lefi‘e’r
than the common price, I cannot proceed

‘ to the former example: Therefore I cou-

ple the two lefi‘er with the greater, and
their differences I fet againfi the greater,
and the difference of‘the greater againfi the '
two iefl'er, then Work as before. ‘

For as I I-the whole difference, is to 203.
the whole quantity, {0. is zithefirfi diffes
retire unto 3, and {tier its quantityt .

  
 
 

.. Chap .XXIV Of Az’lzgm‘zon 309%

. ‘Pr0p0fition I.P10p0fiti0fl 2..

" .; 2 :- -------- 2 ---22
9 7%. ..... 2 ' £08.? \t
II “HZ-J; «S12. (4/ 2 I"

1] II
”~3sz 192-3 II 11-—-'-3,<32-2--9192-245?2
Hugo-«2 fat-5 2f"? II-~30--1f2’- 27%
11*30‘"7f2 197% “—42—“ 1’22 22%

30
Early at 7 Greats the Buihel, \Vheat at
I I GrOats the BufheI, Rye at 5 Groats the
A BthcI, and Oats at 10 Groats the Bufhel,
_ are f0 to be mixed asa IOO BufheIs of the:
u mixtUrc may be fold for 8 Groats the BthcI;
f the quefiion is how much mufi; be taken Of
each foxt. a .

 

 

  

Iv?

)~‘-‘--~l

_ IO 1 — - -- - L— - 32
9::——-~’Ioo W3 faczt, 33' i9 BarIey;‘

 

 

 

:2 CQM-Iooj 2, facit 22 ; Wheat-7.
l2 9—~—--Iloo ' Ifzzcit 1‘1 5— Rye.
9~----2100 m3 fizcz't 33 a} 03“-

 

 

 

 

How" :2

  
 

 

 

210 Of A/lz'gatz'm. ChapXXIV.

How much Alloy mul’tI mix with Bulli-
on of I 1 ounces £- fine, to abate theBullton
to 6 ounces ; fine P -

Ounces Ounces
6i 1’! g of
0 . 5%

By this Alligation there mutt be taken
5 ounces and; of Alloy, toimix with the
6 oz. fiof Bullion.

A Goldfinith hathq, forts of Gold: one
finer than another, whereof one is 18 Ca-
reéts fine, 20 Careft’s; 16Care£ts fine, and
the fourth 22 Carefis fine. All thefe he
would mix with fuch an Alloy, as that the
Whole'mi‘xture of 150 oz. {hould be 15 Ca-
reas fine; the q'uel’cion is, how much muf’c
be taken of each fort ?‘

To anfwer this, and others of "this na-
ture, fer clovvn as before the Rate demand-
ed a-t the left hand, and the particulars un-
der one another, and fubfcribe a Cypher
under all for the Alloy unknown, to fer the
Alloys difference, which is 15, againf’c all
the “Other Sums, according to the Exam:
ple. Then work as before, faying, 35 76
the whole difFerence is to 150 the ,WhOlC
quantity, for is each _-particular difference to
the. quantity fought.
    
  

é EChaRXXIV; of A/lzgatz’m. ' 211

1?:

 
  
  
   
  
 
 
 
   
    
    
  

76 --—150—-—:—-—- 15 facit; 29

 

 

 

76wlso—-—~13facit 29 32‘s;
'76; :50 ‘ Iéchit’ 31% A
few 150

A Refiner hath feveral forts of Bullion,
2121.30 TE. 0% oz. fine, 6'of80z.fine, 12 Th. '
i of‘9 ozafine; and he would to mix them
together, thata pound thereof ihould bear ’ _;
“6 ounces fine. The demand is, whether any
E Alley ought to be mixed with it, and how , f
a; much 3- ~ , x . “
3i Firft, “fee by Alligati‘on Medial what,
t; finenefs an ounce of this mixture will bear
when mixed together, then work as in the
laf’c quei’cion fave one. , . , '

 

‘ \
     
    
    
    
         
      

i ‘21,; Of Aflzgooiom ' Chap..XXV.,
V - ~ V ‘ 1 180 30_§
’30 16 1125 1 2:93 ‘ 15

18o°128 108 V 41:6 53

 
 

 

 
  
 
 
  
  
   
    
   

Therefo1e it is manifefi that Alloy muff-9;"
be mixed to Alloy from 7 oz. g {06 oz.
. j whichis to be done thus, and you willfind‘ -
for every 6 ounces of Bullion hc mui’r take

, 1 oz. ;5- of Alloy to mix with 1t.. '

6 E779)”6g

 

 

CHAP. XXV.

Qflnfirozfiz'omfor the moafzz‘ring of any Sizper-*
fioios, Board HGlzzj} Hoa-ngizogs, Pavements,&c.

I. Bfervc that Board and Glafs are
1 ’ ufuall'y meafured by the Foot,
and theFoot contiaineth144lnches. ‘ 9
There
  
    

jr Chap XXV. OfMeafitrmg , 213
There is aTable 24— footin length, and
3 foot wide. Idemand how many foot 15
contained therein? ‘
The Ruleis.
_ Multiply the length bythe bredth, and
_ the Product giveth the content of the
1 , Whole ‘

‘24-

fact: 72 “fiffoot
There is a. Table of 20 foot 9 Inches
:leng, and 3 foot 8 Inch‘esBroad; how many
51301: doth it contain ?
' Reduce them into Inches, and multiply
as before. '

 
  
   
  
 
 
 
 
 
 
   
    
     

 

facz't 76 feotfi

, Hanna mmfme Glaf. ‘ ‘
There is a houfe hath 2.6 panes of Glafs
in the Window, each pane being 2 foot 3 ,
inches long, and 18 inches wide: The
gueltibn is, how many fsotof Glafs1s cone.
tained in all ?

 

facit87 foot 3
g . Pavements and Hangings are ufually
' ~ mcafured by the Yard.

1 1 One Yard 1n length 15 3 foot.

' One Yard [quare upon the Superficiesis
‘ , 9f00t.
,1 How ‘ L
v e " v.1"-

214 -. Z 0f eafwmg .\ C ha'p.XXV;

Haw to mmfure Pavement”;

, There is a piece of Ground to be paved,
eontaining 49 yards in length , and 3 I
yards in breadth; how many yards is con-
tained therein? ' - _
_' facit I 5' 19 yards.
A Gentleman had his Door paved, being
37 yards 2.,foot one way, and 7 yards I foot
the other way; I demand how many‘yards
are there in all ? '
facit 2.76 yards 3.
A Suit of Hangings 45 yards;— long, and
, 2 yards: broad; how many yards are there
in all P y .
_Divide by 16, becaufe 16 quarters is one
yard fquare. '

 

  
 
  
  
   
 

facit Ioz yardsg.

Inflrufiiam for the meafuring of Solidx,
tee Timber and S zone, @"0.

t ’1 2 Inches is one foot in length.
144. Inches is one foot fquare fuperficies:
' 1 72.8 Inches is one foot folid.
There isa Stone of 4 foot long, 3- foot
broad, and 2 footdeep; Iiideménd how ma—
, ny {quare footis contained therein? -
' - , The _I

  
m m ”w" m..— _.. "uw www.—
l

on

  

  

Of Medfarz'fig.

The Role is :
Multiply the threeDitnenfions one into

another, and the Produé’c is the Anfwer.

facit 24. foot.

A fione of 5 foot 9 Inches long, 4. foot
7 Inches broad, 2 foot 8 Inches deep 5 I de—
mand how many foot there is contained in '
the faid fione? A
Reduce all the Dimenfions into Inches,‘
and divide by 1728.
facit 70 foot 3%,

How to meal/”are Timber;

A piece of Timber 20 foot 8 inches in
length, 2 foot 5 inches broad, andzfoot
thick; how many foot doth it contain?

facir 99 foot 5.

A Countrey' man borrowed of his Neighu
bouraStack of Hay, the content whereof
Was 40 foot fquare.~-~ VJhen the time of
payment came, he told his Neighbour he
he could not pay him all together2 but he
would pay him 20 foot: {quart-z at that time,
and 20 foot fquare more at another time
afterwards, which he performed. The que-
[tion is, whether he paid the foil quantity
borrowed, or what was wanting thereof?

. 40

(re

a) ‘ 1:,“ ‘ 1"“ .W , , a". . ._¢
W _ w ”a“ ,.., ‘ ‘"‘
. R 7.» v. .5 -

“\,_:.........-,_h .. “ow..." 7’

  

 
 

I;6 OfMeaflrwg ChapXXV

20
2.0

w,“

40
40

1600 ' 400
4.0 2.0

54000 borrowed 8000
8000

W

W

16000 paida

So that he paid, but one quarter of the
quantity he borrowed. ’ ,
, - There are many things of this nature,
that -might be brought in under theie two
heads,Wh'ich are more difficuft; as the mea-
fitting of Land of feveral forms, and the
.me-afhring of Timber, Stonezor other things
_-hot equally {quiet}; the weli managing
thereof would requiteaTreatife of it felf,
, whichI omit, in regarditdoth not f0 much ‘
concern my pr‘aé’ciee, nor my intention in
, this Trad}; butI judge this fofficient for the

prefent.

1,1403 131:9.
,«FINIS. '

 
(11:54:?

{Flak} 1b.! iv 4.9.4.11}an '4‘! 1