MifceUanea Curioja. 3 1 j 



Corollary, 



From hence it is plain, that the greateft Alti- 

 tude of the perpendicular Projeaion is a 4th of Pa- 

 rameter, or half the greateft Horizontal I{ange j 

 the verfed Sine of 1 So Degrees being = 2 r . 



Prop. VIII. The Lines G F, or Times of the 

 Flight of a ProjeB call with the fame Degree of 

 Velocity at different Elevations, are as the Sines of 

 the Elevations. 



As c is to fo is p ~ — GB by the 6 



Prop, to — G F ; that is, as to Sim 



of Elevation, fo the Parameter to the L/»* G F ; 

 lb the Lines G F are as the Sines of Elevation, 

 and the TjW; are proportional to thofe Lines ; 

 wherefore the Time* are as the Sines of Elevation : 

 conftat propofitio. 



Prop. IX. Problem. A Projection being made 

 as you pleafe, having the Diftance and Altitude, 

 or Defcent, of an Object, through which the 

 Project paffes, together with the Angle of Eleva- 

 tion o£ the Line of Direction ; to find the Para* 

 meter and Velocity, that is (in Fig, 1.) having the 

 ^/e FGB, GM, and MX. 



Solution. As 2<«/iiu to Secawf of FG B, fo G M 

 the Diftance given to GL; and as Radius to 



of FGB, fo G M to LM. Then LM 

 ■— M X in Heights, or 4MX in Defcent s j or 

 elfe M X — M L, if the Direction be below the 

 Horizontal Line, is the F*// in the Time that the 

 direct Jmpulfe given in G would have carried 



the 



