» 7 » 
A R IT H 
Ex. If 2 yards of Irifh cloth cod 5 diiUings,, what will 
6 yards cod ? Here it is evident that a greater number of 
yards will require a greater fum of money ; therefore, ac¬ 
cording to the rule, 
2yds. : 5S. :: ,6 yds. 
6 
2)30(15 (hillings the anfwer. 
But if a greater number requires a lefs, or a lefs a great¬ 
er, it is called the Rule of Three Inverfe, or Reciprocal 
Proportion. 
Rule. State and reduce the terms as before. Then mul¬ 
tiply the fird and fecond terms together, and divide their 
produdt by the third, and the quotient will be the anfwer 
in the fame denomination as the middle term. 
Ex. If 6 men do a piece of work in 24 days, how long 
would 9 men be doing the fame ? Here it is plain that 
more men require lefs time to do the fame work, therefore 
the dating and operation will dand thus: 
6 men : 24 days :: 9 men 
6 
9)144(16 days the anfwer. 
For contracting fome operations. When the divifor and 
either of the other two terms can be divided by a common 
meafure, or divifor, divide them by fuch common mealure, 
fetting down the quotients, together with the undivided 
term, direftly under their fird refpedtive places. And, if 
the new divifor and either of the other two terms can be 
again divided by any number, proceed as before, and fo 
often as may be convenient; and work with the lad three 
terms as you would have done with the fird. 
Ex. 1. If i 61 b. of coffee cod 4I. 5s. 4d. what will 
1281b. cod at the fame rate ? 
i6lb. : 4I. 5s. 4d. :: i28lb. 
Or 4 .-454 :: 32 the id and 3d - 4 -ed by 4 
Or 1 1454 :: 8 do. do. H-edbyq 
_8_ 
1)34 2 8(341. 2S. 8d. the anfwer. 
Ex. 2. If I lend my friend 168I. for 7 months, ho w 
long ought he to lend me 144I. to requite me? 
Reciprocally. If 1 681 . : 7m. :: 144I. 
Or 21 : 7 :: 18 id & 3d -t-edby 8 
Or 7 : 7 :: 6 do. by 3 
7 _ 
6) 49 (8-J- months the anfwer. 
Compound Proportion, or the Double Rule of 
Three, is when five numbers are given to find a fixth, and 
is commonly performed by two operations in the Single 
Rule of Three, either direct or inverfe, as the quedion 
requires. The three fird terms contain a fuppolition, and 
the two lad a demand. 
Rule. As in the Single Rule of Three, put that term in 
the middle, or fecond place, which is of the fame kind and 
denomination with the anfwer, or term fought; and all the 
terms of fuppofition, one under another, in the fird place; 
alfo the terms of demand in the fame order, one under 
another, in the third place; but note, the fird and third 
term of every row mud be of the fame denomination. 
Take the three terms in each row feparateiy, and fay, If 
the fird term give or require the fecond, does the third re¬ 
quire more or lefs ? if more, mark the lefs extreme for a 
divifor; if lefs, mark the greater extreme for a divifor. 
Multiply all thefe divifors together for a divifor, and all 
the red of the terms, or numbers, together for a dividend, 
and their quotient will be the anfwer in the fame denomi¬ 
nation as the fecond term. When the fame numbers are 
found in the divifor as in the dividend, they, may be ex¬ 
punged. Or any number may be divided by their greated 
common divifor, and the quotients ufed infiead of them. 
Ex. If the wages of 4 men for 3 months be 20I. what 
will be the wages of 6 men for the fame time ? 
4 men : 20I. :: 6 men 
■— 3 months : — ;; 12 months 
M E T I C. 
In both datements more requires more, therefore, 
12 : 20 :: 72 or dividing idand 3d by 12 
1 : 20 :: 6 : 6 X 202=1201. the anfwer. 
Sometimes a quedion may mod eafily be folved by two 
operations; thus, in the above example, conlidering the 
time to be the fame, the datement is 
1 , 12X30 , 
4 men : 20I. :: 6 men : -— =301. 
4 
And now, confidering the number of men to be the fame, 
the quedion is reduced to this: 
, , 12X50 
3 men : 30I. :: i2inonths : -~=ii2ol. the anlwer 
as before. 
PRACTICE. 
By rules of Rraftice are meant certain expeditious me¬ 
thods of cading up accounts, or finding the value of any 
fort of goods or merchandize, by taking fome aliquot part 
or parts of the thing propol'ed ; and is evidently nothing 
more than a compendious method of working the Rule of 
Three. An aliquot part is that which is contained a pre- 
cife number of times in another; as 4 is an aliquot part of 
8, 12, 16, 20, &c. 
Tables of Aliquot Parts. 
Of a 
Of a 
Of. a 
lb. 
A- 
Of 
a Ton. 
I 
O U N 
D. 
Shi 
L LI N 
G. 
VO 
IRD 
u- 
cwt. 
is 
ton. 
POISE 
. 
20. 
I 
s. 
d. 
d. 
oz. 
lb. 
io v 
is 
x 
[O 
6 
5 
0 is a 
8 a 
0 a 
half 
3 d 
4 
6 is a half 
4 a 3d 
16 
12 
8 
is 
is 
is 
I 
3 
4 
1 
5 
4 
2 f 
is 
is 
is 
4 
t 
8 
4 
3 
2 
0 
4 
6 
a 
a 
a 
5 
6 
8 
3 
2 
if 
a 
a 
a 
4 
6 
8 ' 
4 
2 
1 
is 
is 
is 
1 
4 
1 
8 
-J- 
2 
I £ 
I 
is 
is 
is 
To 1 
1 
1 (T 
2V 
2 
O 
a 
I 0 
I 
a 
I 2 
1 
is 
1 6 
1 
A 
is 
To 
I 
I 
I 
8 
4 
3 
a 
a 
a 
I 2 
15 
16 
°4 
of 
0 * 
a 
a 
a 
16 
2 4 
48 
i 
4 
is 
"3 2 
1 
64 
4 
Of 
IS Wo 
Time. 
I 
O 
a 
20 
Of a 
II U N- 
month. 
A. 
year. 
0 
10 
a 
2 4 
D 
RED 
2 
1 
0 
8 
a 
30 
Of 
We 
IGH 
T. 
4 
3 
O 
7f 
a 
3 2 
a lb. 
3 
4 
0 
6 
a 
4° 
lb. 
cwt. 
2 
is 
i 
O 
5 
a 
45 
i Roy 
I I 2 
is 
I 
if 
is 
1 
8 
O 
O 
4 
J 4 
a 
a 
60 
64 
oz. 
lb. 
56 
28 
is 
is 
1 
2 
4 
1 
is 
1 2 
0 
3 
a 
80 
I 2 
is 
I 
l6 
is 
■f 
Ota Month. 
0 
2 2 
a 
96 
9 
is 
3 
4 
14 
is 
1 
8 
days. 
month. 
0 
2 
a 
20 
8 
is 
3 
8 
is 
14 
30 
IS 
I 
0 
if 
a 1 
60 
6 
is 
i. 
2 
7 
is 
_JU 
1 6 
1 5 
is 
f 
0 
if 
a 1 
92 
4 
is 
3 
4 
is 
1 
Z3 
IO 
is 
1 
3 
0 
I 
a 2 
4° 
3 
is 
3 f 
is 
-JL 
32 
5 
is 
1 
0 
<§ 
a 3 
20 
2 
is 
6 
2 
is 
J 
5 6 
3 
is 
1 O 
0 
of 
a 480 
if 
is 
i 
i| 
is 
1 
64 
2 
is 
__1 
1 5 
0 
of 
a 960 
I 
is 
12 
I 
IS ^ 
1 
’1 2 
I 
is 
30 
Ru le. FirfTmultiply integers by integers, in order to 
find their value; and for the inferior denominations take 
what aliquot parts you can get, and for what is wanting 
take parts of that part, and fo on ; then add up the whole. 
Ex. What is the value of 58 cv. t. 3 qrs. 17 Jlb>. at 9I. 
iis. 4d. per cwt 
1. 
s. 
d. 
Cwt. 
qr. 
lb. 
1. 
s. 
d. 
5 ^ 
X 9 = 
522 
0 
O 
38 
O 
b 
at 
9 
0 
0 
58 
- 2 — 
29 
0 
O 
38 
0 
0 
at 
O 
IO 
0 
29 
-10“ 
2 
18 
O 
58 
0 
0 
at 
O 
I 
0 
218 
- 3— 
0 
19 
4 
58 
0 
0 
at 
O 
0 
4 
’554 
17 
4the 
price of 58 
0 
0 
at 
9 
11 
4 
9 11 
4 - 
- 2— 
4 
15 
8 
O 
2 
a 
4 13 
S- 
- 2“ 
2 
7 
JO 
O 
I 
0 
2 7 
IO- 
- 2 — 
1 
3 
I I 
O 
O 
14 
1 3 
I I - 
— 4“ 
0 
5 
11-I 
0? 
O 
3 f 
Therefo re 563 10 Sj is price of 58 3 iy£at9 11 4 
1 W hen 
