ARITHMETIC. 
if r 
B advife him that ha can draw for them direftly on Eng¬ 
land at 5od. fterling per ruble, or on Holland at 45 (livers, 
or 9od. banco, per ruble; which method will be the mod 
advantageous to A, fnppofing the exchange between Hol¬ 
land and England at that-time to be 36s. 4d. per pound 
fterling t 
As 5od. fterling : 9od. Flemifti :: 240ft. fterling : 433d. 
—36s. Flemifti, the arbitrated price between Holland and 
England, according to the other exchange from Peterl- 
burgh. Then, as 1 ruble : ^od. :: 5000 rubles : 250oood. 
— to4il. 13s. 4d. fterling, the amount if drawn for directly 
on England. 
As 1 ruble : 90ft. :: 5000 rubles : 450000ft. — 1S75I. 
Flemifh. As 36^. Flemiflt : 1875L Flemifh :: 20s. fter¬ 
ling : 1032I. 2s. 2-|-d. nearly. Laftly, 1041I. 13s. 4d.— 
1032I. 2s. 2i-d. — 9I. its. ii-d. fterling, faved by this ne- 
gociation. coming through Holland. 
If Amfterdam draw's on Hamburgh to remit to-.Cadiz 
at 12od. Flemiflt per ducat of 375 marvidies, and to draw 
for the value-on London at 33s. 4d. per pound fterling, 
what price muft the exchange between Amfterdam and 
Cadiz be, fnppofing the courfe between London and Am¬ 
fterdam at 34s. 6d. per pound fterling? 
As 33s. 4-d. : 1 zod. :: 34s. 6d. : 124-id. Flemifh per du¬ 
cat. the anfwer. 
Compound Arbitration, has refpedl to the ex¬ 
changes of four or more different places, and its utility 
conftfts in .difcovering the belt and moil advantageous me¬ 
thod of negotiating exchanges with different countries or 
cities. Or when feveral different forts of things are com¬ 
pared together, as to their value, to find how many of one 
fort are equal to a given number of another fort. 
Rule. Place the terms in two perpendicular columns, 
the antecedents to the left,and the confequents to the right, 
with the fign 222 between; fo that there may not be found, 
in either column, two terms of one kind. Then the num¬ 
bers in the lefs column muft be multiplied together for a 
divifor, and the number in the greater column, where the 
odd term Hands, for a dividend, the quotient thence ari- 
fing will he the anfwer. To abridge the work, throw out 
any common numbers that are found in both columns, by 
the fecond rule in Compound Proportion. 
London having to remit 500I. to Spain, how many piaftres 
of 272 marvidies will it amount to there, exclufive of 
charges, fnppofing the faid fum be remitted to Holland at 
34s. per pound; from thence to France at 56ft. Flemifh 
per crown ; from France to Venice at 160 ecus per 84 du¬ 
cats banco ; and from Venice to Spain at 320 marvidies 
per ducat banco ? 
Thus, if il. fterling — 34s. or 4o8d. Flemifh 
56d. Flemifh 2= 1 ecu of France 
160 Ecus of France — 84 ducats Venice 
1 Ducat Venice 2= 320 marvidies Spain 
372 Marvidies — 1 piaflre 
How many piaftres 222 500I. fterling? 
408 X iX&4X3 2 °X i>< 5 °^ 
1X56X 160 x I X 272 
51X 12X1 X 125 
1X34 
5 jX 1X84X2X1X125 __ 
1X7X1X1X68 ~ 
=-3X6X 125=2250 piaftres, the anfwer. 
A merchant of Amfterdam, owing 1200I. Flemifh to 
London, remits the fame firft to France, at 54d. Flemifh 
per crown; from thence he orders it to be remitted to Ve¬ 
nice at 100 crowns for 83 ducats, from thence to Ham¬ 
burgh at 99d. Flemifh per ducat, from thence to Lifbon at 
4 - 8d. per crufade of 400 reas, and laftly from Lifbon to 
England at 5s. 5ft. per milrea; now the queftion is, how 
much will the fame amount to in fterling money, and how 
much will be faved, fnppofing the exchange from Holland 
diredlly to England at 3-6S. 42.1I. perl, fterlingat that time? 
If 54d. Flemifh — 1 crown of France 
100 Crowns of France — 63 ducats of Venice 
1 Diicat of Venice — 9gd. Hamburgh 
43d. of Hamburgh 222 400 reas of Portugal 
Veu. 11. No-65. 
1000 Reas of Portugal 2= 65a. fterling 
How many pence fterling — 1200b Flemifh — 2&8ocod. 
Flemifh ? 
1X 63X99X400X65X1200 __ 7 X 99 Xf_X 65 X__u ' _ 
54X100X1X48X1000 ~ 6x1X48X10 
7 X 3 3 X 6 c 
--- — 750I. 15s. now 363. 4-l-d. 222 291 and nociz: 
2X10 
192000 three-halfpences. 
As 291 : 1 1 . :: 192000 : 959I. 15s. iod. 2-^5-qrs. amount 
in fterling money, if the remittance had been made direct- 
ly to England. Laftly, 750I. 15s. — 659I. 15s. io-?,-d. — 
90I. 19s. 14-d. gained by this negociation. 
If A of Hamburgh orders B his correfponderit in Eng¬ 
land to buy 441 ells of cloth, and advifes him he muft 
have five yards for 4I. fterling, and, though he does not 
know exactly the proportion between their ell and the yard 
of England, he advifes him that i-U of their ells make one 
ell in Holland, and that feven ells in Holland make four 
of France, and laftly that feven ells of France make five 
yards of England ; now the queftion is, how much cloth 
muft B fend, and how much will it come to? Anfwer, 
150 yards, and comes to, 120I. 
Of DUODECIMALS. 
Duodecimals are fo called becaufe every fuperior place, 
or denomination, is twelve times its next inferior in that 
fcale of notation ; that is, the foot is divided into twelve 
equal parts, called primes (or inches), each being one inch 
broad and twelve inches long; the prime into'twelve equal 
parts, called feconds; the fecond into twelve equal parts, 
called thirds ; and fo on, each inferior denomination being 
twelve inches long, and juft one-twelfth part in breadth 
of the next fuperior denomination ; therefore any lower 
denomination, being divided by twelve, will reduce it to 
the next higher. 
Rulefor multiplying duodecimatly. Under the multiplicand 
write the correfponding denominations of the multiplier; 
multiply each term of the miitliplicand by each term of 
the multiplier, and obferve, that feet into feet give feet; 
feet into primes, give primes; feet into feconds, give fe¬ 
conds ; primes into primes, give feconds; primes into fe¬ 
conds, give thirds ; primes by thirds, give fourths, &c. 
and in general let feet be marked with (°), primes with 
(*), feconds with (‘ 1 ), thirds with C 111 ), fourths with 
( 1V ), &c. which are called indices of the faftors ; and the 
name of the product of any two factors will be exprefted 
by the fum of their two indices. In multiplying feet, 
incites, and parts,-the operation may often be abbreviated, 
by taking aliquot parts as in Pratiice. 
Ex. What is the product of 24 feet, 7 inches, 5 feconds., 
into 8 feet, 6 inches, y feconds t 
Multiply 
O 
24 
1 
7 
1 1 
5 
222a 
By 
s 
6 
9 
z=.b 
O 
196 
1 1 1 
1 V 
«X 8 2= 
I I 
4 
O 
0 ~C 
ax6 =2 
1 2 
3 
8 
6 
0 22 zd 
1 1 
flX 9 — 
I 
6 
5 
6 
9 22:e 
af-b-\-c — 
210 
9 
6 
0 
9 22: the produdl. 
Or .thus, 
by the rule of Practice : 
O 
1 
1 i 
24 
7 
5 
z=xz 
8 
6 
9 
22 -.b 
196 
111 
IV 0 
i 
i S 
«X8 2= 
II 
4 
0 
0 222 c for S 
O 
O 
a-^-i — 
I 2 
3 
8 
6 
0 222 d 0 
6 
O 
d-^r 8 22: 
I 
6 
5 
6 
9 r e 0 
O 
9 
210 
9 
6 
O 
9 anfwer for 8 
6 
9 
Ex. 2. How many fquare feet in a pavement whole 
length is i7feet 10 inches, and breadth 15 feet 7 inches ? 
O 1 01 Oil! 
I bus 17 10 X 15 7 222 377 ic 10 the anfwer. 
3 A ALLIGATION 
