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20

1443.65625

142.656250

1350
1443.65625)1492.65625 (1.03047

1443.65625
49.0080000 20.60940 Ans.
433096875

690312500
577462500
112850000

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Ex. 2. Let the transverse be 80, the conjugate 60, the ordi. nate 10, and the abfciffa 2.1637, required the length of the arch GB.

Anf. 19.3 Ex. 3. The tranfverse is 120, the conjugate 72, the ordinate 48, and the abscisla 49, required the length of the arch.

Anf. 62.6496.

PROBLEM XVIII.

To find the area of an hyperbolu, the transverse, conjugate, and

abscisa being given.

RULE.

To the product of the tranfverse and abfciffa add of the square of the abscisla, and multiply the square root of the sum by 21.

To this product add 4 times the square root of the product of the transverse and abfciffa, and divide this sum by 75.

Divide 4 times the product of the conjugate and abscissa by the transverse.

Multiply this last quotient by the former, and the product will give the area of the hyperbola.

EXAMPLE I.

In the hyperbola GBH, the transverse is 60, the conjugate 36, and the abscifia 20, required the area.

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Ex. 2. The transverse diameter is 50, the conjugate 30, and the abscifla 25, required the area.

Anf. 805.09. Ex. 3. The transverse 30, the conjugate 18, and the abscissa 10, required the area.

Anf. 151,668.

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Multiply the square of the revolving axis by the fixed axis, and multiply the product by.5236 for the solidity.

EXAMPLE, I.

Required the folidity of the prolate spheroid ABCD, the transverse or fixed axis AC is 45, the revolving axis DB 35.

35

35

175 105

1225 sq. of the revoly, aris.

45 fixed axis.

6125 4900

55125
.5236

330750
165375
10250
275625
28863.4500 Anf.

Ex. 2. Required the folidity of the oblate spheroid, whose fixed axis is 60, and revolving axis 1oo. Anf. 314160.

Ex. 3. Required the solidity of a prolate spheroid, whose fixed axis is 9, and revolving axis ?, Anf. 230.9076.

Ex. 4. What is the content of an oblate spheroid, whose axis are so and 30 ?

Ans. 39270.

PROBLEM XX.

To find the folidity of the segment of a spheroid.

RULE.

CASE I. When the base is parallel to the revolving axis, multiply the difference between triple the fixed axis and double the height of the segment, by the square of the height, and the prodve again by.5236. Then,

As

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