L, A, S3, B, (Fig. 3.) erect the perpendicualrs Ll, Aa, Ss, Bb, of which ſuppoſe Ss equal to SI;
and through the point s, to the aſymptotes Ll,
LB, deſcribe the hyperbola asb meeting the perpendiculars
Aa, Bb, in a and b; and the rectangle
2ASIſubducted from the hyperbola AasbB,
will leave ANB the area ſought.
Example 3. If the centripetal force tending to
the ſeveral particles of the ſpheres decreaſe in a
quadruplicate ratio of the diſtance from the particles;
write for V, then for PE, and
DN will become as
Theſe three parts drawn into the length AB, produce
ſo many areas, viz. into ; into ; and into . And theſe after due reduction come forth , and . And
theſe by ſubducting the laſt from the firſt become
. Therefore the entire force with which
the corpuſcle P is attracted towards the centre of
the ſphere is as , that us reciprocally as . Q. E. I.