§ii MifceUanea Curtofo. 



D L s= £ ; + Vfc />/> + ;jb — 1?. And as D G ; 

 D K and D L : : Radius : Tangents fought, 

 which coincides with our Algebraical Expreiiion 

 thereof. 



Prof. XI. To determine the Force or Velocity 

 of a Prejc8, in every Point of the Cjtrve it de« 

 fcribes. 



To do this we need no other Pracognita* but 

 only the third Proportion, That the Velo- 



tity of f Ailing Bodies, is double to that which in 

 the lame time, would have defcribed the Space 

 fallen by an equable Motion : For the Velocity of 

 a Project, is compounded of the conftant equal 

 Velocity of the impreffed Motion, and the Velocity 

 of the Fall* under a given Angle* vif the Com- 

 plement of the Elevation I For inftance, in ffc z. 

 in the time wherein a Project would move from 

 G to L, it defcends from L to X, and by the 

 third Propcfition ha3 acquired a Velocity* 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 Z, I fay, the Velocity 

 m the Point X, compounded of the Velocities 

 G L and L Z under the Angle G L Z, is to the 

 Velocity imprefs'd in the Point G, as G Z is to 

 G L this follows from our fecond Axiom* arid 

 by the 20 and ^I Prop. lib. I. conk. Midorgit* 

 X O parallel and equal to G Z (hall touch the 

 Parabola in the Point X. So that the Velocities 

 in the fcveral Points, are as the lengths of the 

 Tangents to the Parabola in thofe Points, inter- 

 cepted between any two Diameters : And thefe 

 again are as the Secants of the Angles* which 

 thole Tangents continued make with the Horizon- 

 tal Line GB, From what is here laid down, 



may 



