body H arrives at L, to the ſemi-periphery HKM, the time in which the body H will come to M. And the velocity of the pendulous body in the place T is to its velocity in the loweſt place R, that is, the velocity of the body H in the plane L to its velocity in the place G, or the momentary increment of the line HL to the momentary increment of the line HG. (the arcs HI, HK increaſing with an equable flux) as the ordinate LI to the radius GK or as, to SR. Hence ſince in unequal oſcillations there are deſcribed in equal times arcs proportional to the entire arcs of the oſcillations; there are obtained from the times given, both the velocities and the arcs deſcribed in all the oſcillations univerſally. Which was firſt required.
Let now any pendulous bodies oſcillate in different cycloids deſcribed within different globes, whoſe abſolute forces are alſo different; and if the abſolute force of any globe QOS be called V, the accelerative force with which the pendulum is acted on in the circumference of this globe, when it begins to move directly towards its centre, will be as the diſtance of the pendulous body from that centre and the abſolute force of the globe conjunctly, that is, as CO x V. Therefore the lineola HT which is as this accelerative force CO x V will be deſcribed in a given time; and if there be erected the perpendicular TZ meeting the circumference in Z, the naſcent arc HZ will denote that given time. But that nafcent arc HZ is in the ſubduplicate ratio of the rectangle GHT, and therefore as . Whence the time of an entire oſcillation in the cycloid QRS (it being
