C r 4* ] 
CoroL 2.' 
Therefore, if the greateft Amplitude be given 
(from Experiment) the Amplitude answering to any 
propofed Elevation, above, or below, 45 Degrees, 
may from hence be found: For it will be as the Ra- 
dius, to the Sine of double the given Elevation, fo is 
the greateft, to the required. Amplitude. 
CoroL 3. 
Hence, al fo, the Altitude of the Projection may 
be known ; for when the Angle JgjPT is half 
a Right Angle, will be = and therefore HE 
(i ^ Q) = ■? ‘PSj alfo, * n f his Cafe, S 2 = ~r 2 $ 
whence our Proportion S z : s 2 : : HE : he will here 
become ~r 2 : s 1 : : yTSj. he $ from whence it ap- 
pears, that, as the Square of the Radius is to the Square 
of the Sine of any given Elevation, fo is half the 
greateft horizontal Amplitude, to the Altitude of 
the Projection. Hence it alfo follows, that the 
Height to which the Ball would afeend, if projected 
direCtly upwards, is juft half the greateft Ampli- 
tude. 
CoroL 4. 
Therefore, fince it is well known, that a Body 
in vacuo afeends and defeends with the fame Velo* 
city 5 and that the Diftances defeended are as the 
Squares of the Velocities 5 it follows, that the Am- 
plitudes, at the fame Elevation, with different Ve- 
locities, will alfo be to one another as the Squares 
of the Velocities ; bccaufe they are as the greateft 
Amplitudes, with the fame Velocities (by CoroL 2.) 
T 2 and 
