C 71 ) 
ready Theorems; the one to find the greateft Horizon- 
tal Range at 45° Elevation, by any Shot made upon 
any inclined Plane, with any Elevation of the Piece 
wbatfoever: And the other to find the Elevations pro- 
per to ftrike a given Objed, uith any force greater th^n 
what fuffices to reach it with the aforefaid middle Ele- 
vation. Both which being performed by ona fingle 
Proportion, may be very (erviceable to fuch as are con- 
cerned in the Practice of Gunnery, but are unwilling to 
trouble themfelves with tedious and di5icult Rules. The 
two Propofitions are thefe. 
P R 0 P. L ^ 
A Shot being made on an Inclined Plane, having the 
Horizontal Diftance of the Objed it ftrikes, vAth the 
Elevation of the Piece, and the Angle at the Gun be- 
tween the Objeft and the Perpendicular : to find the 
greateft Horizontal Range of that Piece, laden with the 
fame Charge ; that is, half the Latus return of all the 
ParaloliB made with the fame impetus, 
RVLE. 
Take half the Diftance of the Objed from the l^adir^ 
and take the difference of the given Elevation from that 
half,- the Verfed Sine of that difference fubftrad from 
the Verfed Sine of the Diftance of the Objeft from the 
Zenith: Thenlliall the difference of thofe Verfed Sines 
be to the Sine of the Diftance of the Obkct from the 
Zenith, as the Horizontal Diftance of the Objedt ftrook, 
to the greateft Horizontal Range at 4f- 
M 2 
PROP. IL 
