C«8] 
\Angle KGD {ball be the depreffion betow the Horizon : Now 
this Conftruftion fb naturally follows froni tlie EfiMimy that 
I fhall need fay no more about it. 
Prop. XL To determine the force or Velacity of a Proje^y 
in every point of t]\Q Curve it defcribes. 
To do this we need no other pracogmtdy but only the third 
Propofitionj, Viz. that the Velocity of falling Bodies, is double 
to that which in the fame time, would have defcribed'the 
fpace fallen by an equable motion : For the Velocity of a Pro- 
jeO:, is compounded of the conftant equal Velocity of the im- 
preffed motion, and the Velocity of the fdly under a given An-- 
gle, viz. the complement of the Elevation : For inttance, in 
Fig, 2, in the time wherein a projefl: would move from G to 
L, it deftends from L to X, and by the third Propofition has 
acquired a F^^wV/, which in that time would have carried it 
by an equable motion from L to Z or twice the defcent L X; 
and drawing the line G I fay the Velocity in the point X, 
compounded of the Velocities G L and L 2 under the Angle 
G L Z, IS to the Velocity imprefl in the point G, as G Z is to 
G L ; this follows from our fecond A> iome ; and by the 20 
and 21. Prop, /iki^ conic, Midorgii^ XO parallel and equal to G 
Z fhall touch the Parabola in the point X^ So that the Veloci- 
ties m the feveral points, are as the lengths of the Tangents to 
the Parabola in thofe points, intercepted between an^^ two 
Diameters : And thefe again are as tte Secants of the Angles^ 
which thofe Tangents continued make with the Horizontal 
line G B. From what is here laid down, may the compa- 
rative force ofa in any two points of the C^rx/<?, -be ei- 
ther Geometrically or Arithmetically difeovered. 
Corollary. 
' From hence it follaws, that the force of a Shot is alwaies 
leaft at U, or the V^'r^^fjc of the P^^r^ W^, and ^^t^^ 
diftances therefrom, as at T andX, G and B its force is al- 
waies equal, and that the leaft force in U is to thatin G^and 
as 
