The Sections of Solids.

OF A SPHEROID.

DEFINITIONS.

1. A spheroid is a solid, generated by the rotation of a semiellipsis about the transverse or conjugate axis, and the centre of the ellipsis is the centre of the spheroid.

2. The line about which the ellipsis revolves, is called the axis.

3. If the spheroid is generated about the conjugate axis of the semiellipsis, then it is called a prolate spheroid.

4. If the spheroid is generated by the semiellipsis about the transverse axis, then it is called an oblong spheroid.

PROPOSITION I.

Every section of a spheroid is an ellipsis, except when it is perpendicular to that axis about which it is generated, in which case it is a circle.

All sections of a spheriod parallel to each other, are similar figures.

PROPOSITION III.

If a semispheroid is cut by a plane at right angles to the base, then the section is a semiellipsis, and the intersection with the base will be one of its axes; and if a line is drawn perpendicular from the middle of that intersection to the base of the spheroid, to cut its surface, that line will be half the other axis, whether transverse or conjugate.

PROBLEM

It is here meant that the base is a section made by a plane, passing through the centre of the spheroid at right angles to the transverse or conjugate axis of the spheroid.

SECTIONS of SOLIDS.

A Cylinder and its Sections

page

41.

A Cone and its lections page 45.

A Sphervid &c. page 50 A Sphere or Globe,

Engraved by WLowry.

Pl. 46.

page 47.