16 Review of OQ. Gregory’s Treatise on’ Mechanics. 
If F be put for the force, M the mass, or number of parti- — 
cles in a body, and V its velocity, then is Fa MV, and 
Vo. If V be constant, then is F proportional to M, the 
mass; but why is it so, unless it be by the inertia, or the 
greater force of a greater mass? If M be indefinitely small, 
and F be constant, then is V indefinitely great, or if the 
mass or inertia be nothing, the velocity would be indefinite- 
ly great, so that if there were not in matter a force of iner- 
tia proportional to its mass, the least force would cause ® 
body on which it acts. to move with an infinite velocity; 
but that it is not infinite, and that the velocity is modified to 
a definite quantity in the inverse ratio of the mass, is wholly 
the effect of the force of inertia. 
After delivering Newton’s three Jaws of motion, the au- 
thor goes into long arguments @ priori, and @ posteriori, to 
prove their validity. Now nothing can be more obvious, 
mental principle is advanced, that the resultant of two equal 
forces, acting at a point, bisects the angle, which the direc- 
tions of the forces make with one another. No proof is 
given of this, but the Leibnitzean, and metaphysical one of 
the sufficient reason. It ought either to be proved directly, 
or by the reductio ad absurdum, or assumed as an axiom 
or intuitive truth, not susceptible of demonstration. 
same objection lies against another fundamental proposition, 
in oe 
- a 
m Art. 38, which is not attempted to be proved, though it 
is made the basis of the succeeding proposition, intended 
to demonstrate the parallelogram of forces 
. This demonstration, if it may so be called, appears to be 
compounded, of what had been done by D’Alembert and 
others, by the analytical and far-fetched method of the 
moderns, which, however valuable in itself, is certainly de- 
