If a body be projected in free space, either parallel to the horizon, or in an oblique direction, by the force of gunpowder, or any other impulse: it will, by this motion, in conjunction with the action of gravity, describe the curve line of a parabola.

A parabola is the section formed by cutting a cone, with a plane, parallel to the side of the cone.

Gravity (vide [page 316]) is a force of such a nature that all bodies, whether light or heavy, fall perpendicularly through equal spaces in the same time, abstracting the resistance of the air; as lead, and a feather, which, in an exhausted receiver, fall from the top to the bottom in the same time. The velocities acquired by descending, are in the exact proportion of the times of descent, and the spaces descended are proportional to the squares of the times, and, therefore, to the squares of the velocities. Hence, then, it follows that the weights, or gravities of bodies near the surface of the earth are proportional to the quantities of matter contained in them; and that the spaces, times, and velocities generated by gravity, have the relations contained in the three general proportions before laid down.

A body in the latitude of London falls nearly 16-1/12 feet in the first second of time, and consequently, at the end of that time, it has acquired a velocity double, or of 32⅙ feet.

The times being as the velocities, and the spaces as the squares of either; therefore,

if the times be as the Nos.
1,2,3,4,5,6,7,8,9,10;
the velocities will also be as
1,2,3,4,5,6,7,8,9,10;
and the spaces as their squares
1,4,9,16,25,36,49,64,81,100;
and the spaces for each time,
1,3,5,7,9,11,13,15,17,19.

Namely, as the series of the odd numbers, which are the differences of the squares denoting the whole spaces. So that if the first series of natural numbers be seconds of time,

namely: the times in seconds1234&c.
the velocities in feet will be32⅙64⅓96½128⅔,&c.
the spaces in the whole times16 1 12 64⅓144¾257⅓,&c.
and the space for each second16 1 12 48¼80 5 12 112 7 12 ,&c.

of which spaces the common difference is 32⅙ feet, the natural and obvious measure of the force of gravity.