EXAM. 2.

.7854)254.5000(324 quotient.
235 62

18 880

15708

31720

31416

304 rem.

324(18 inches, Ans.

1

28)224
224

PROBLEM IV.

To find the hypothenuse of a right angled triangle, when the base and perpendicular are given.

EXAM. 1.

Here 105 x 105 11025, the square of the base; and 56 × 563136, the square of the perpendicular; then √11025 +3136 = √14161 = 119 inches, the hypothenuse.

EXAM. 2.

Here 112 x 112=12544, the square of the length; and 84 × 847056, the square of the breadth; then ✓12544 +7056 = √19600 =140 inches, the dia gonal required.

EXAM. 3.

Here 72.5 x 72.5 × 2 = 5256.25 × 2 = 10512.5, twice the square of the side; and ✔10512.5 = 102.53 inches, the diagonal required.

D

PROBLEM V.

Given the hypothenuse of a right angled triangle, and either of the legs, to find the other leg.

Here 1532

EXAM. 1.

135223409-182255184; and

✓5184 72 inches, the perpendicular required.

Here 602

EXAM. 2.

362 = 3600 - 1296 = 2304; and ✔2304 48 inches, the perpendicular depth required.

Given the head and bung diameters and length of a cask, to find the diagonal or distance between the centre of the bung hole, and that point where the middle of the opposite staff and head of the cask intersect each other.

2

then 212152 = 441 +225 666; and ✔ 666 = 25.8 inches, the diagonal required.

40

meters; and

2

20, half the length of the cask; then

282 + 202=784 + 400 1184; and 1184 = 34.4 inches, the diagonal required.

PROBLEM VII.

Given the diagonal and diameters of a cask, to find

its length.

meters; then 25.82

212665.64 441224.64;

and ✔224.64 × 2 = 14.98 × 2 = 29.96 inches, the length of the cask.

meters; then 40%

3221600 1024 576; and

✓576 x 2 = 24 x 2 48 inches, the length of the

cask.

D 2

CUBE ROOT.

To extract the Cube Root of any number.

ЕХАМ. 2.

63044792(398 Ans.

27

36044 resolvend.

9 triple of 3.

27 triple square of 3.
279 divisor.

729 cube of 9.

729 square of 9 × by the triple of 3. 243 triple of 9 x by the square of 3. 32319 subtrahend.

3725792 second resolvend.

117 triple of 39.

4563 triple square of 39.

45747 second divisor.

512 cube of 8.

7488 square of 8 x by the triple of 39. triple of 8 x by the square of 39.

36504

3725792 second subtrahend.

PROOF.

Here 398 × 398 x 398 = 158404 x 398 =

63044792, the same as the given number.

10584 square of 6 x by the triple 98. 172872 triple of 6 x by the square of 98. 17393256 second subtrahend.

PROOF.

Here 986 × 986 × 986 = 972196 × 986 = 958585256, the same as the given number.

D 3