EXAM. 9.

As .9 on B: 1 on A:: 1.62 on B: 1.8 on A.

EXAM. 10.

As 32.8 on A: 1 on B:: 2122.16 on A: 64.7 on B.

Ex. 11.

As 125 on B: 1 on A:: 35 on B: 28 on A.

EXAM. 12.

As 632 on A: 1 on B:: 15 on A: .0237 on B.

PROBLEM III.

To find a fourth proportional to three numbers; or to perform the Rule of Three by the lines A and B.

gal.

As 44 on B: 55 on A:: 8 on B; to 10 on A.

As 24 on A; 1 on B:: 1200 on A ; 150 on B.

EXAM. 4.

As 12 on B: 24 on A :: 36 on B : 72 on A.

bu.

EXAM. 5.

S.

bu.

S.

As 3.25 on A: 28.5 on B :: 8.75 on A: 76.73

gal.

S.

As 1 on B: 19.75 on A:: 45.5 on B: 898.6

on A.

As 16 on B 8 on A:: 20 on B: 10 on A.

men.

EXAM. 3.

da.

men.

da.

As 48 on A 18 on B: 8 on A: 3 on B.

offi.

As 6 on B 12 on A:: 2 on B: 4 on A.

PROBLEM V.

To reduce a vulgar fraction to a decimal, by the

Unity. Num.

Dec.

As 2 on B 1 on A:: 1 on B: .5 on A.

Den.

EXAM. 3.

Unity. Num.

Dec.

As 4 on A 1 on B:: 3 on A: .75 on B.

Den.

EXAM. 4.

Unity. Num.

Dec.

As 96 on B: 1 on A:: 24 on B: .25 on A.

PROBLEM VI.

Having a divisor given, to find, by the lines A and B, a factor that shall perform the same by Multiplication as the Divisor would do by Division.

EXAM. 2.

As 282 on A : 1 on B :: 1 on A : .003546 on B.

EXAM. 3.

As 231 on B 1 on A:: 1 on B. :.004329 on A.

EXAM. 4.

As 2150.42 on A : 1 on B. ;; 1 on A ; .000465 on B.

PROBLEM VII.

Having a Factor given to find a divisor by the lines A and B.

EXAM. 2.

As .0003546 on B: 1 on A. :: 1 on B: 282 on A.

EXAM. 3.

As .004329 on A: 1 on B:: 1 on A: 231 on B.

EXAM. 4.

As .000465 on B: 1 on A :: 1 on B: 2150.42

on A.

PROBLEM VIII.

To square any number, by the lines C and D.

EXAM. 2.

Set 1 on D to 1 on C, then against 12 on D is 144 on C.

EXAM. 3.

Set 1 on D to 1 on C, then against 17.5 on D is 306.25 on C.

EXAM. 4.

Set 1 on D to 1 on C, then against 125.8 on Dis 15825.64 on C.

PROBLEM IX.

To extract the Square Root of any number by the lines. C and D.

EXAM. 2.

Set 1 on C to 1 on D, then against 144 on C is 12 on D.

EXAM. 3.

Set 1 on C to 1 on D, then against 306.25 on C is 17.5 on D.

EXAM. 4.

Set 1 on C to 1 on D, then against 15825.64 on C is 125.8 on D.

PROBLEM X.

To find a mean proportional between two numbers, or to extract the Square Root of their product by the lines C and D.

EXAM. 2.

Set 48 on C to 48 on D, then against 243 on C, is 108 on D.

EXAM. 3.

Set 18 on C to 18 on D, then against 32 on C, is 24 on D.

EXAM. 4.

Set 96 on C to 96 on D, then against 486 on C, is 216 on D.

PROBLEM XI.

To cube any number by the lines C and D.

EXAM. 2.

Set 1 on D to 12 on C, then against 12 on D is 1728 on C.

EXAM. 3.

Set 1 on D to 18 on C, then against 18 on D is 5832 on C.

EXAM 4.

Set 1 on D to 35 on C, then against 35 on D is 42875 on C.

PROBLEM XII.

To extract the Cube Root of any number by the lines C and D.

EXAM. 2.

Find 64 on the line C, then move the slide until 1 on D, 64 on C, and 10 on D, cut the same number on the opposite lines, which you will find to be 4, the root required.

EXAM. 3.

Having found 120 on the line C, move the slide until 1 on D, 120 on C, and 10 on D, stand against the same number on the opposite lines, which in this case is 4.93 the root required.