3 1 6 Mijcellanea Curiofi. 



ble Angle, whereof s is the Sine ? Wherefore 

 'twill be as Radius to Sine of double the Angle 

 FGB, (b is half the Parameter, to the Horizon- 

 tal ^ange or Diftance fought \ and at the leveral 

 'Elevations*) the Ranges are as the of the 



double Angles of Elevation^ gi £. £>. 



Corollary. 



Hence it follows, that half the Parameter is the 

 greateft \andon, and that that happens at the 

 Elevation of 45 Degrees, the '5s»e of whofe dou- 

 ble is Radius. Likewife that the Ranges equally 

 diftant above and below 45 are equal, as are the 

 Sines of all double Arches, to the Sines of their 

 doubled Complements. 



Prop. VII. The Altitudes of Projections made 

 with the fame Velocity, at (everal Elevations, 

 are as the wfr/e^ Sines of the doubled ^^/ fJ of 



Elevation : As c is to s ; lb is -^^=:GB to 



£jLf=BF: andUK- RU=?ii the Al- 



4 



of the Projection Now by the 



foregoing Lemma rr to the verfed Sine of 



the double Angle, and therefore it will be as Ra- 

 dius, to verfed Sine of double the Angle FGB, 

 fb an 8 th of the Parameter to the height of 

 the Projection V K ; and (b thefe heights at fe- 

 deral Elevations, are as the faid verfed Sines 9 



C&ro tikft. 



