Six philosophical dissertations on the mechanical powers, elastic bodies, falling bodies, the cycloid, the parabola, the rain-bow / By Dr. Morgan, late master of Clare Hall. Published by Dr. Samuel Clarke, in his notes upon Rohault's Physics. Done into English by Dr. John Clarke.

  • Charles Morgan
Date:
1770
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Licence: Public Domain Mark

Credit: Six philosophical dissertations on the mechanical powers, elastic bodies, falling bodies, the cycloid, the parabola, the rain-bow / By Dr. Morgan, late master of Clare Hall. Published by Dr. Samuel Clarke, in his notes upon Rohault's Physics. Done into English by Dr. John Clarke. Source: Wellcome Collection.

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    be CD, CI, and their vertexes A,N. Let A N be joined, which will be parallel and equal to DI, and will therefore be the bafe of a whole cycloid, defcribed by the fame generating circle as CBA, . CN. Let this cycloid be AFN. Nowifa heavy body be hanged © in F, upon athread CF or any fuch thing which will bend, and fo ofcillate upon the center C, between the femicycloids CBA, C N, that whenever it moves from the perpendicular, the upper part of _ the thread may bend upon that cycloid towards which the motion is made, and the remaining part, which is not applied to the cycloid, be ftretched out in a ftraight line; I fay, the heavy body will always be found inthe cycloid A FN. Demonft. Let the generating circle of the cycloid AFN be de- fcribed on the axis GF; and from the point E, where the heavy body is when removed from the perpendicular, let EL be drawn parallel to AG, meeting that circle in L, and let GL be joined, From the point B, (in which the thread EB touches the cycloid CBA, the remaining part being bent upon the arch CB) let BH be drawn parallel to A G alfo, meeting the generating circle AHD in H; and let AH be joined. The whole length of the thread CBE is equal to twice AD; (by conftruction) therefore it is equal to the femicycloid C B A; (by the nature of the cycloid)-and the part of the thread C B is equal to the arch C B, to which it is applied. Therefore the remaining part of it BE is equal to the remaining arch B A, and is therefore equal to twice the ftraight line A H, (by the nature of the cycloid.) It alfo touches the cycloid in B; therefore (by the nature of the cycloid) itis likewife parallel to A H ; therefore AH and BK are equal, and therefore BK and K E are equal alfo ; therefore the pa- rallels EL, and BH are equally diftant from AG; therefore they eut off equal arches of the generating circles, viz. G L equalto AH, and LF equal to HD; therefore GL and AH are parallel, and therefore GL, and KE are parallel, and therefore E L. js equal to KG. But KG (becaufe of the parallels HA,K B, and by the na- ture of the cycloid) is equal to the arch HD, that is, to the arch | Br’;
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