CONIC SECTIONS.

OF THE PARABOLA.

DEFINITION.

1. If a thread equal in length to B C be fixed at C, the end of a square, A B C, and the other end fixed at F; and if the side A B, of the square be moved along the right line A D, and if the point E be always kept close to the edge B C of the square, keeping the string tight, the point or pin E, will describe a curve E G I H, called a parabolo.

2. Focus is the fixed point F, about which the string revolves.

3. Directrix is the line A D, which the side of the square moves along.

4. Aris is the line L K, drawn through the focus F, perpendicular to the directrix.

5. Vertex is the point I, where the line L K cuts the

curve.

6. Latus rectum or parameter, is the line G H, passing through the focus F, at right angles to the axis I K, and terminated by the curve.

7. Diameter is any line M N drawn parallel to the axis IK.

8. Double ordinate is a right line R S, drawn parallel to a tangent at M, the extreme of the diameter M N, terminated by the curve.

9. Abscissa is that part of a diameter contained between the curve and its ordinate, as M N.

VOL. I.

F

PROBLEM

PROBLEM I.

To describe a parabola by finding points in the curve, the axis A B, or any diameter being given, and a double ordinate C D.

1. Through A, draw E F parallel to C D.

2. Through C and D, draw D F and C E parallel to A B, cutting E Fat E and F.

3. Divide B C and B D, each into any number of equal parts, as four.

4. Likewise divide C E and D F into the same number of equal parts, viz. four.

5. Through the points 1, 2, 3, &c. in C D, draw the lines 1 a, 2 b, 3 c, &c. parallel to C D.

6. Also through the points 1, 2, 3, in C E and D F, draw the lines 1A, 2 A, 3 A, cutting the parallel lines at the points a, b, c, then the points a, b, c, are in the curve of the parabola.

FIG. II. Another Method.

1. Join A C and A D; from A make A E equal to B C. or B D.

2. Through A and E, draw H I, and F G, parallel to C D, cutting A C and A D in the points F and G.

3. Through F and G, draw F H and G I parallel to A B, cutting HI at the points H and I.

4. From the points H and I, take any number of equal divisions on the lines H F and I G, from these points draw lines to A.

5. From B, set the same divisions towards C and D, draw the parallel lines 1 a, 2b, 3 c, &c. intersecting the former at the points a, b, c, they will be in the curve of the parabola.