Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Plural form of epicycloid.
Etymologies
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Examples

Thereupon followed the epicycloids, curves which  as the cycloid is generated by a point upon the circumference of a circle rolled along a straight line  are generated by a similar point when the path of the circle becomes any curve whatever.

This circle ought strictly to roll upon the true elliptical curve; and assuming, as usual, the tracingpoint upon the circumference, the generated curves would vary slightly from true epicycloids, and no two of those used in the same quadrant of the ellipse would be exactly alike.

The convenience of the constructions given in Figure 252 is nowhere more apparent than in the drawing of the epicycloids, when, as in the case in hand the base and generating circles may be of incommensurable diameters; for which reason we have, in Figure 254, shown its application in connection with the most rapid and accurate mode yet known of describing those curves.

“caustic curves” — which are epicycloids, as is now well known.
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