CONIC SECTIONS.

OF THE ELLIPSIS.

DEFINITIONS.

1. If two pins are fixed at the points E and F, a string being put about them, and the ends tied together at C; the point C being moved round, keeping the string stretched, it will describe a curve called an Ellipsis.

2. Foci, are the two points E and F, about which, the string is made to revolve.

3. Transverse axis, is the line A B, passing through the foci, and terminated by the curve at A and B.

4. Centre, is the point G, bisecting the transverse axis A B. 5. Conjugate axis, is the line C D, bisecting the transverse axis at right angles, and terminated by the curve.

6. Latus rectum, is a right line passing through the focus. F, at right angles to the transverse axis terminated by the curve; this is also called the Parameter.

7. Diameter is any line passing through the centre G, terminated by the curve.

S. Conjugate diameter, is a right line drawn through the centre, parallel to a tangent at the extreme of the other diameter, and terminated by the curve.

9. Double ordinate, is a line drawn through any diameter, parallel to a tangent at the extreme of that diameter, terminated by the curve.

PROBLEM

The transverse and conjugate axes A B, and CD, of an ellipsis being given, to find the two foci, from thence to describe an ellipsis.

1. Take the semi transverse A E, or E B, and from C, as a centre, describe an arc, cutting A B, at F and G, which are the foci.

2. Fix pins in these points, a string being stretched about the points FC G, then move the point C round the fixed points F and G, keeping the string tight it will describe the ellipsis, as in the first definition.

PROBLEM II.

The same being given, as in the last problem, to describe an ellipsis, by an instrument called a trammel.

The trammel, as is used by artificers, is two rules, with a grove in each, fixed together, so that the groves will be at right angles to each other; to this, there is a rod, with two moveable nuts, and another fixed at the end, with a hole through it to hold a pencil; on the under side of the sliding nuts are two round pins, made to fill the grove of the trammel, and is used as follows.

OPERATION.

Set the distance of the first pin at B, from the pencil at A, to half the shortest axis, and the distance of the second pin at C, from A, to half the longest axis, the pins being put in the groves, as is shown by the figure, then move the pencil at A, it will describe the ellipsis required.