C 147 ] 
to the Sine of BAC, and Radius : Cotang. BAC 
: : BC\AB 5 the greateft: Didance AB , at which the 
Ball can pofiibly hit the Objed, will from hence be 
given: which Pitta nce (be caufe AC=AG+BC, and 
AB 2 =AC +CB X AC — BC) will alfo be exprelfed 
by y ' ag xAG+iBC' Hence the greateft horizon- 
tal Amplitude of a Ball, projeded from a given 
Height above the Plane of the Horizon is known : 
For ST {Fig. 8.) may here be fuppofed to reprefent 
the Plane of the Horizon, and SA the given Height > 
and then SC, bcins; equal to AB, is given from 
above AGxAG\ 2 BG. 
Corol 7. 
But, if the horizontal Diftance AB be given, and 
it be required to find the greateft Height the Ball 
can pofiibly reach in the Perpendicular BC\ T) j we 
fhall have HG ( AB ) : AG : : Radius : Tang, of the Ele- 
vation ( BAH or AHG) ; and Radius : Tang. BAC 
{iBAH^ 5>o°) : : AB : BC ; which therefore is known. 
But (becaufe ACFBC—AG, and AC ~\ CB x 
TiC — CB — AB Z ) the fame will alfo be truly exhi- 
, . .. AG Z ^AB Z 
biced by- 
2 AG 
Corol. 8 . 
Laftly, let the Height, or Depreftion, of the Objed 
be given, together with its Diftance AB, to deter- 
mine the Diredion, and the leaft Impetus poftible, 
to hit the Objed: Then AB'.BC : -.Radius: Tang. 
BaC whence the Elevation BAH is known: And 
as Radius : Tang. AHG (BAH ) : : MG ( AB):AG ; 
whence the Impetus is alfo known. 
- U 
111 . 
