L 14 3 J 
again by Equality, AT : AB : : AB :AN y therefore, 
by Divifion, AT:BT::AB:BN j and, confe— 
quently ATxBN = BTx AB. 
Let AT be now bife&ed in O; then BTxAB 
being = AQ Z — - OB 2 (in the fir ft Cafe) and =OB x 
~—A0 2 ' (in the fecond Cafe), we fhall therefore 
have 0B Z =A0 7 ^ APxBN— AOx AO + 2 BH. 
whence the Diftance AB is like wife known. fhEJ. 
- ' , * r 
Corollary . 
Hence, if the Elevation, and the greateft Ampli- 
tude, together with the Diftance AB of the Objeft 
be given, the Height or Depreflion of the Ball in 
the Perpendicular BCD will be known : For it is 
proved, that AT : BT : :BA: BN ; whence BN is 
known : But, as the Radius to the Tangent of BNC 
(BAD)AoisBN to BC. 
Troblem III. 
The greateft horizontal Amplitudes of the Tiece, 
together with the 'Diftance and Height ( or De- 
prejfton ) of the ObjeCl being given, to find the 
Direction or Angle of Elevation . 
Let BC {Fig. 4 and f.) be the perpendicular 
Height or Depreflion of the Object, AB its giver} 
horizontal Diftance, and AH the required Direction; 
Alfo let Tftf {Fig. 6.) be the greateft Amplitude 
(anfwering to 45 0 of Elevation) ; draw AC, in which 
produced (if need be) take AG=T£j make MGO per- 
pendicular to AG, meeting AB produced (if need be) 
in 0 i and from the Centre 0 , with the Interval OA , 
let 
