Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/49

Book I. to the force of its gravity, and the velocity of its motion. The les its gravity is, for the quantity of its matter, or the greater the velocity with which it is projected, the les will it deviate from a rectilinear coure, and the farther it will go. If a leaden ball, projected from the top of a mountain by the force of gunpowder, with a given velocity, and in a direction parallel to the horizon, is carried in a curved line to the ditance of two miles before it falls to the ground; the ame, if the reitance of the Air were taken away, with a double or decuple velocity, would fly twice or ten times as far. And by increaing the velocity, we may at pleaure increae the distance to which it might be projected, and diminih the curvature of the line which it might decribe, till at last it should fall at the ditance of 10, 30, or 90 degrees, or even might go quite round the whole Earth before it falls; or latly, o that it might never fall to the Earth, but go forwards into the Celetial Spaces, and proceed in its motion in infinitum. And after the ame manner that a projectile, by the force of gravity, may be made to revolve in an orbit, and go round the whole Earth, the Moon alo, either by the force of gravity, if it is endued with gravity, or by any other force, that impells it towards the Earth, may be continually drawn aide towards the Earth, out of the rectilinear way, which by its innate force it would purue; and be made to revolve in the orbit which it now decribes; nor could the Moon without ome uch force, be retain'd in its orbit. If this force was too mall, it would not ufficiently turn the Moon out of a rectilinear course: if it was too great, it would turn it too much, and draw down the Moon from its orbit towards the Earth. It is neceary, that the force be of a jut quantity, and it belongs to the Mathematicians to find the force, Rh