Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/283

 VBP, when EB is radius) as 2 CE to CB, and therefore in a given ratio.

And the length of the emi-perimeter of the cycloid AS will be equal to a right line which is to the diameter of the wheel BV as 2 CE to CB.

To caue a pendulous body to ocillate in a given cycloid.

Let there be given within the globe QVS, (Pl. 19. Fig. 3.) decribed with the centre C, the cycloid QRS, biected in R, and meeting the uperficies of the globe with its extreme points Q and S on either hand. Let there be drawn CR biecting the arc QS in O, and let it be produced to A in uch ort that CA may be to CO as CO to CR. About the centre C, with the interval CA, let there be decribed an exterior globe DAF, and within this globe; by a wheel whoe diameter is AO, let there be decribed two emi-cycloids AQ, AS, touching the interior globe in Q and S, and meeting the exterior globe in A. From that point A, with a thread APT in length equal to the line AR, let the body T depend, and ocillate in uch manner between the two emi-cycloids AQ, AS that as often as the pendulum parts from the perpendicular AR, the upper part of the thread AP may be applied to that emi-cycloid APS towards which the motion tends, and fold it elf round that curve line, as if it were ome olid obtacle;