A View of Sir Isaac Newton's PhilosophyPemberton, Henry
Science
A View of Sir Isaac Newton's Philosophy
Pemberton, Henry
Newton, Isaac, 1642-1727. Principia
wherewith the centripetal force exerts it self, during the passage of
the body from B to H. After the same manner the inclinations at I and K
depend entirely on the degree of strength, wherewith the centripetal
force acts on the body in its passage from H to K: if the centripetal
force be weak enough, the lines A H and A I drawn from the center A to
the body at H and at I shall be more obliquely inclined to the curve,
than the line A B is inclined towards B G. The centripetal force may
be of that strength as to render all these inclinations equal, or if
stronger, the inclinations at I and K will be less oblique than at
B. Sir ~ISAAC NEWTON~ has particularly shewn, that if the
centripetal power decreases after a certain manner with the increase
of distance, a body may describe such a curve line, that all the
lines drawn from the center to the body shall be equally inclined to
that curve line.[82] But I do not here enter into any particulars, my
present intention being only to shew, that it is possible for a body to
be acted upon by a force continually drawing it down towards a center,
and yet that the body shall continue to recede from that center; for
here as long as the lines A H, A I, &c drawn from the center A to the
body do not become less oblique to the curve, in which the body moves;
so long shall those lines perpetually increase, and consequently the
body shall more and more recede from the center.
7. BUT we may observe farther, that if the centripetal power, while
the body increases its distance from the center, retain sufficient
strength to make the lines drawn from the center to the body to become
at length less oblique to the curve; then if this diminution of the
obliquity continue, till at last the line drawn from the center to
the body shall cease to be obliquely inclined to the curve, and shall
become perpendicular thereto; from this instant the body shall no
longer recede from the center, but in its following motion it shall
again descend, and shall describe a curve line in all respects like to
that, which it has described already; provided the centripetal power,
every where at the same distance from the center, acts with the same
strength. So we observed in the preceding chapter, that, when the
motion of a projectile became parallel to the horizon, the projectile
no longer ascended, but forthwith directed its course downwards,
descending in a line altogether like that, wherein it had before
ascended[83].
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