Let ab and cd (Fig. 408) be given axes. Through c, draw fg parallel to.ab; from a and b draw af and bg at right angles to ab; divide fa, gb, ae, and eb, each into a like number of equal parts, as at 1, 2, 3, and o,o,o; from 1, 2, and 3, draw lines to c, through o, o, and o, draw lines from d, intersecting those drawn to c; then a curve, traced through the points i, i, i, will be that of an ellipsis.

Ellipse By Intersection Of Lines
Ellipse By Intersection Of Lines 585

Fig. 408.

Where neither trammel nor string is at hand, this, perhaps, is the most ready method of drawing an ellipsis. The divisions should be small, where accuracy is desirable. By this method an ellipsis may be traced without the axes, pro-vided that a diameter and its conjugate be given. Thus, ab and cd(Fig. 409) are conjugate diameters: fg is drawn parallel to ab, instead of being at right angles to cd; also, fa and gb are drawn parallel to cd, instead of being at right angles to a b.

Ellipse By Intersection Of Lines 586

Fig. 409.