RULE. 
duce it to the next denomination, and then 
divide. Go on thus to the lowest denomi- 
-nation, where, if there is a remainder, it 
must be applied fraction-wise to the divi- 
sor; and thus you will have the complete 
answer in a simple or mixed number. 
Note. If any of the dividends is less than 
the divisor, reduce it to the next denomina- 
tion, and to the next again, till it be greater 
than, or equal to, the divisor. 
EXAMPLES. 
Quest. 1. If 3 yards of cloth cost 8s. what 
is the price of 15 yards? Answ. 40s. or 21, 
Work. 
yds. s. yds. 
3 — 8 — 15 
' — r 
3)120(40s. 
Explanation. 3 yards and 8s. contain the 
supposition, and 8s. is like the thing sought; 
therefore 8s. is the middle term, and yards 
on the left : then the demand arises upon 
15 yards, and therefore it is on the right. 
Again, from the nature of the question it is 
plain, that 15 yards require more than 3 
yards, t. e. the answer must be greater than 
the middle term; wherefore 8s. is to be 
multiplied by 15 yards ; the product is 120s. 
which divided by 3 yards, quotes 40s. with- 
out a remainder; so 40s. or 21. is the num- 
ber sought 
Quest. 2. If 416. of sugar cost 2s. 9d. 
what is the value of 1816.? Answer, 12s. 
4|d. 
Work. 
Ib. s. d. Ib. 
4—2 : 9 — 18 
12 
33 d. 
18 
264 
33 
4)594(148 d. 
2 
4 
4)8(2 jfarf6ing-». 
Explanation. The supposition is in 416. 
and 2s. 9d, this last term being like the 
' thing sought, which is connected with 18 16, 
wherefore the terms are stated according to 
the rule: then the middle term being mixed, 
it is to be reduced to pence; and then 
argue thus; if416. cost 3Sd,, 1816. mustcost 
more ; therefore multiply 33d. by 1816. and 
divide their product by 4; the quotient is 
148d. and 2 remains, which is to be reduced 
to farthings, and the product divided by the 
former quotient, gives 2 ; so the answer is 
148d. 2 farthings, or 12s. 4|d. because 148d. 
is by reduction, 12s. 4d. 
Quest. 3. Wliat time will 7 men be boarded 
for 251. when 3 men paid 251. for 6 months ? 
Answ. 2 months, 16 days, reckoning 28 
days to 1 mouth. 
Work. 
men. mnths. men. 
3 6 7 
7)18(2 
. 14 
Rem. 4 
28 
7)112(16 days. 
Explanation. The 251. is a superfluous 
number ; then the supposition is in the 3 
men and 6 months, and the demand regards 
the 7 men : tlie terms being all simple, you 
are to argue thus ; if 3 men are boarded 6 
months for 251. (or any sum), 7 men will 
be boarded for the same a shorter time : 
therefore multiply 6 months by S» and di- 
vide the product 18 l)y 7, whereby the 
answer is found to be 2 months and 16 
days. 
Note. The first two questions are what 
is called the rule of three direct, that is, 
where the third term, being greater or less 
than the first, requires that the answer also 
be greater or lesser than the second term. 
The last, of the rule of three indirect, or 
reverse ; where the third term being greater 
or lesser than the first, requires the fourth 
contrarily lesser or greater than the second. 
But we have comprehended both in one ge- 
neral rule. And from this observation may be 
learned what questions are of either kind. 
Rule, or Ruler, an instrument of wood 
or metal, with several lines delineated on 
it, of great use in practical mensuration. 
When a ruler has the lines of chords, 
tangents, sines, &c. it is called a plane 
scale. 
The carpenter’s joint-rule is an instru- 
ment usually of box, &c. twenty-four inches 
long, and one and a half broad ; each inch 
being subdivided into eight parts. On the 
same side with these divisions is usually 
added Gunter’s line of numbers. On the 
other side are the lines of timber and board 
measure ; the first beginning at 82, and 
continued to 36, near the other end ; the 
