320 Mifcellatiea Curiofa. 



or ^.bb —^ph in defcents, do exceed pp, the Ob- 

 jett is without the reach of a Projett caft with that 

 Velocity, and fo the thing impoiiible. 



From this Equation ^bb ^ ^ph := pp are de- 

 termined the utrnoft limits of the reach of any 

 Projctf, and the Figure afligned, wherein are 

 all the heights upon each Horizontal diftance 

 beyond which it cannot pafs ; for by reduction 

 of that Equation, h will be found =£: | p — 



- — in heights, and j p in dcfccnts \ tram 



P P 



whence it follows, that all the Points h are in 

 the Curve of the Parabola, whofe Focus is the 

 Point from whence the Project is caft, and 

 whole Latus re&nm, or Parameter ad Axem 

 is rrr. p. Likewife from the fame Equation may 

 the leaft Parameter or Velocity be found capa- 

 ble to reach the ObjcB propofed ; for bb -| 

 ■p p j£. p h being reduced , k p will be — 



Vbb H- bb ±h {in £fent S l which is the 



hh^ontal \ange at 45; degrees, of a Project caft with 

 the leaft Velocity that would juft reach the Ob- 

 jcB, and the£/^rf^\mrequifite will be eafily had ; 

 for dividing the fo found Semi-parameter by the 

 Horizontal diftance given b, the Quote into Radius 

 will be the Tangent of the Elevation (ought. This 

 Rule may be of good life to all Bombardiers and 

 Gunners, not only that they may ufe no more 

 Powder than is neceffary, to caft their Bombs in- 

 to the place affigned, but that they may {hoot 

 with much more certainty, for that a (mall Error 

 committed in the Elevation of the Piece, will 

 produce no fenlible Difference in the fall of the 



Shot : 



