## evolutes

Noun

- plural form of
*evolute*

- The fifth book contains properties of normals and their envelopes, thus embracing the germs of the theory of
**evolutes**, and also maxima and minima problems, such as to draw the longest and shortest lines from a given point to a conic; the sixth book is concerned with the similarity of conics; the seventh with complementary chords and conjugate diameters; the eighth book, according to the restoration of Edmund Halley, continues the subject of the preceding book. - Again, the normal, qua line at right angles to the tangent, is connected with the circular points, and these accordingly present themselves in the before-mentioned theories of
**evolutes**and parallel curves. - His enquiries into
**evolutes**enabled him to prove that the evolute of a cycloid was an equal cycloid, and by utilizing this property he constructed the isochronal pendulum generally known as the cycloidal pendulum. - The determination of the true relation between the length of a pendulum and the time of its oscillation; the invention of the theory of
**evolutes**; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly isochronous; the ingenious although practically inoperative idea of correcting the "circular error" of the pendulum by applying cycloidal cheeks to clocks - were all contained in this remarkable treatise.

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