is a Parabola . By the second Axiom , they are Points in the Curve ; and the Parts of the Descent GH, GD, GY, GC, = to ST, RV, LX, FB, being as the Squares of the Times (by the Second Proposition ) that is, as the Squares of the Ordinates , HT, DU, YX, BC, equal to GS, GR, GL, GF, the Spaces measured in those Times; and there being no other Curve but the Parabola , whose Parts of the Diameter are as the Squares of the Ordinates , it follows that the Curve describ'd by a Project , can be no other than a Parabola : And saying, as RU the Descent in any time , to GR or UD the direct Motion in the same time , so is UD to a third proportional; that third will be the Line call'd by all Writers of Conicks , the Parameter of the Parabola to the Diameter GC, which is always the same in Projects cast with the same Velocity : And the Velocity being defined by the Number of Feet moved in a Second of Time, the Parameter will be found by dividing the Square of the Velocity , by 16 Feet , 1 Inch , the Fall of a Body in the same Time .
Lemma.
The Sine of the double of any Arch, is equal to twice the Sine of that Arch into its Co-sine, divided by Radius; and the versed Sine of the double of any Arch is equal to twice the Square of the Sine thereof divided by Radius.
Let the Arch BC (in Fig. 2. Tab. 5. ) be double the Arch BF, and A the Center ; draw the Radii AB, AF, AC, and the Chord BDC, and let fall BE perpendicular to AC, and the Angle EBC, will be equal to the Angle ABD, and the Triangle BCE, will be like to the Triangle BDA; wherefore it will be as AB to AD, so BC