f **'• 1 
///is the greatefl: poflible, AB will alfo be the greatefl: 
poiiibkj in which Circumftance^C(ifthe Angle FAE 
be given) will likewife be the greatefl: poflible: And 
k is evident > muft bc > when ///coincides with 
A/G, or when the Angles HEA and HAE are 
equal (as in Fig. j and 8)5 at which time the Point 
n coincides with H } becaufe AD and EH are 
always equal to each other. Therefore, flnee, in 
this Cafe, HAE ( HEA ) is — N AH, it follows, 
that the Amplitude, on any inclined Plane AE , will 
be the greatefl: pofllble., when the Line of Direction 
AH bife&s the Angle made by the Plane and 
Zenith. 
Coro/. 4 
Hence the greatefl: Amplitude on any inclined 
Plane may alfo be known j for the rkht-anHed 
Triangles AOG and HOB , having AO — HO and 
the Angle O common, are equal in all refpe&s; and 
therefore, as fang, of AHG ( BAH the Angle of 
Elevation): Tang, of CHG ( CAB the Plane's In- 
clination) ; : AG.GC ; whence AC—AG^-GC is 
alfo known. 
Coro/. 5 . 
Hence, alfo, if the greatefl: Amplitude on an in- 
clin’d Plane be given, the greatefl: horizontal Ampli- 
tude may be determined : for, Radius : S. BAG : 1 
AC:BC—CG= the Difference of the given, and 
the required, Amplitudes. 
Coro/. 6. 
But if, inflead of the Plane s Inclination, the per- 
pendicular Height, or Depreflion, of the Objea: be 
given 5 then, AC ( AG+BC ) being to BC, as Radius 
to 
