3 14 MifceBanea Cur to fa. 



from S to T, from R to V, from L to X, and 

 from F to B, and draw the Lines TH, VD, 

 XY, BC parallel to G F ; I fay, the Points 

 T, V, X, B, are Points in the Curve described 

 by the Project, and that that Curve is a Parabola. 

 By the (econd Axiom, they are Points in the 

 Curve ; and the Parts of the Defcent GH, GD, 

 G Y, GC, ts to ST, R V, LX, F B, being 

 as the Squares of the Times (by the Second Pro- 

 pojitioy) that is, as the Squares of the Ordinates^ 

 HT, D U, Y X, BC, equal to G S, G R, G L, 

 G F, the Spaces meafured in thofe Times; and 

 there being no other Curve but the Parabola 

 whofe Parts of the Diameter are as the Squares 

 of the Ordinate*, it follows that the Curve de- 

 fcrib'd by a Projetl, can be no other than a Pa- 

 rabola : And faying, as R U the Defcent in any 

 time, to G R or UD the direH Motion in the 

 lame time, fo is U D to a third proportional ; 

 that third will be the Line calPd by all Writers 

 of Conickj, the Parameter of the Parabola to the 

 Diameter GC, which is always the fame in 

 Prcjetts caft with the fame Velocity : And the Ve- 

 locity being defined by the Number of Feet mo- 

 ved in a Second of Time, the Parameter will be 

 found by dividing the Square of the Velocity, 

 by 1 6 Feet, i Inch, "the Fall of a Body in the fame 

 Time, 



Lemma. 



The Sine of the double of any Arch, is equal 

 to twice the Sine of that Arch into its Co-fine, di- 

 vided by Radius', and the -z^r/ed of the 

 double or any is equal to twice the Square of 

 the Sine thereof divided by Radius, 



