De La Hire's Construction of an Ellipse
One of many ways to construct an ellipse using only a ruler and compass is due to de La Hire . Proceed as follows:[more]
1. Draw two circles with radii and , equal to the semimajor and semiminor axes of the ellipse.
2. Draw a radial line from the center, at an angle from the horizontal, that intersects the two circles at points and .
3. Drop a line from to the horizontal axis (shown in blue).
4. Draw a line from the vertical axis through point to intersect this line (shown in green).
5. The intersection represents a point on the ellipse. To trace the ellipse, repeat steps 2 to 4 for different angles .
This construction reproduces the standard parametric trigonometric representation of an ellipse: .[less]
 Wikipedia. "Ellipse." (Sep 25, 2019) en.wikipedia.org/wiki/Ellipse. De la Hire construction taken from K. Strubecker: Vorlesungen über Darstellende Geometrie, Göttingen: Vandenhoeck & Ruprecht, 1967 p. 26.