334 Review of the Principia of Newton. 
We come now to the rectilinear motion of bodies, urged 
by the only remaining law of force, previously investigated 
for orbicular motion, which is that of the distance directly, 
which would cause a body to revolve in an ellipsis whereof 
the center is the seat of force. A rectilinear descent of a 
body according to this law, will be found by the same prin- 
ciples as before laid down, to be in a point of the rectangular 
co-ordinate, but the time and velocity are represented ina 
and the space passed over by its versed sine, As all elliptical 
or curvilmear motion, under the influence of such a force, 
will be performed in the same time, it follows, that rectilinear 
descents from all distances, under this law, will be performed 
in the same or equal times. It may seem to be a subject of 
mere curiosity, ora work of supererogation in our author, 
to have investigated the motion of bodies acted on by forces, 
which are not found to exist in the material creation by them- - 
selves ; but every one well versed in these subjects, knows, 
that mixed or complicated forces, produced actions of 
different bodies in the natural world, may be the points of 
investigation in physico-mathematical researches, and that 
resultant or joint effect of these forces may constitute a 
law of force very different from that of the simple forces ; 
hence the importance of investigating movements according 
to any law of force. _ Sensible of the practical results depend- 
ent on these apparently speculative problems, and of the con- 
nection there ever must be between the movements of bodies 
tant, but is rendered much more so by its intimate connec- 
tion with those which follow in the next section. In this pro- 
position we have, not for first time, a complete exempli- 
fication of the fluxional or differential calculus, independent 
of its forms, or before it was reduced to any forms or rules as 
a science : indeed, the investigations of the Principia could 
never have been made but by one, whatever his genius might 
have been, who was a perfect master of its principles as well 
‘as of all its refinements. We have, also, in this proposition, 
am instance of a pure analytical solution, which consists in 
€ assumption of the thing to be proved, and proceeds, by 
9m the complex or compound proposition to the 
