Page:Cyclopaedia, Chambers - Volume 1.djvu/521

Rh CYCLOID, in Geometry, one of the Mechanical, or, as others term 'em, the Tranſcendental Curves; called also the Trachoid. See Curve, and Trochoid.

It is describ'd by the Motion of a Point A, (Tab. Analysis, Fig. 55.) in the Periphery of a Circle, while the Circle makes a Revolution along the right Line A P.

Hence, the Properties of this Curve, viz. that the right Line A E is equal to the Periphery of the Circle A B C D ; and A C to the Semi-periphery; and in any Situation of the generating Circle, the right Line Ad is equal to the Arch D d.—Again, a d being parallel to A C; A D is equal to the Arch of the generating Circle d F.—Further, the whole length of the Cycloid is four times that of the Diameter of the generating Circle; and the Cycloidal Space comprehended between the Curve and the Subtense A E, triple the Area of the generating Circle.—Lastly, any Part estimated from the Vertex, as F I, is every where dou- ble the Chord of the Circle F; and the Tangent thereof GI, perpetually parallel to the same Chord F b.

The Genesis of the Cycloid, may be conceiv'd by imagining a Nail in the Circumference of a Wheel; the Line which the Nail describes in the Area, while the Wheel revolves in a right Line, is the Cycloid.

The Cycloid is reputed a modern Curve, and its Invention ascrib'd by some to Mersenne; by others to Galileo: but Dr. Wallis shews it of an older standing, and to have been known to Bovillus, about the Year 1500; and even consider'd by Cardinal Cusanus much earlier, viz. before the Year 1451.

M. Huygens has demonstrated, that from whatever Point, or Height, a heavy Body, oscillating on a fix'd Centre, (v.g. a Pendulum) begins to descend; while it continues to move in a Cycloid, the Times of its Falls, or Oscillations, will be equal to each other.

This Property M. Fontenelle states thus: The Nature of the Cycloid is such, that, if a Body which describes it, fall from a greater height, and by that means acquire a certain Augmentation of Velocity, as in Galileo's Theory, the greater Cycloidal Arch which it describes, takes up precisely that Excess of Velocity. So that the Body does not describe it, either sooner for its being accelerated, or later for having a greater Space to move: And hence arises an Equality in Time, notwithstanding the Inequality of Arches. On this Foundation it is, that the Pendulum-Clock is built on the Subject whereof, the same M. Huygens has wrote a large Volume, under the Title of Horologium Oscillatorium. See Pendulum; see also Oscillation.

CYCLOIDAL Space, the Space contained between the Cycloid, and the Subtense thereof. See CYCLOID.

CYCLOMETRY, the Art of measuring Cycles, or Circles. See CYCLE, and CIRCLE.

CYCLOPÆDIA, the Circle, or Compafs of Arts and Sciences; more ordinarily call'd Encyclopedia. See ENCYCLOPEDIA.

CYGNUS, the Swan, in Astronomy, a Constellation of the Northern Hemisphere. See CONSTELLATION.

Stars in the Constellation Cygnus, in Ptolemy's Catalogue ate 17; in Tycho's 19; in the Britannic Catalogue 107. The Order, Names, Longitudes, Latitudes, Magnitudes, &c. whereof, are as follow.

Stars in the Constellation CYGNUS.