C *4° 3 
by TT, and the Confequents by pt\ we have TT. 
pt\\S\s 5 from which it appears, that the Times of 
flight are dircdly as the Sines of Elevation. 
Again, the Times of deferibing ZsJ^and eq (which 
are the Halves of the Wholes) being alfo to one an- 
other as S : s, and the Didances EH , eh defeended 
in them, as the Squares of the Times, it likewife 
follows, that S 2 :s z ;:EH:ehs or that the greateft 
Altitudes are as the Squares of the Sines of Eleva- 
tion. 
Moreover, becaufe (by Trigonometry) TT= 
an( j pf — and it has been already proved, 
C r ‘ 
that, S: s : ; TT :pt, it follows, that S: s : : 
r -*P ? 5 whence, by multiplying the Antecedents by 
c 
9 and the Confequents by it will be 2 19 : — 
r r r r 
(: 2 ,pq) ; :Tgjpq. But 2 I£ is known to be 
the Sine of double the Angle whofe Sine is S, and 
Co-line C, &c. Therefore the horizontal Ampli- 
tudes are to one another, as the Sines of the double 
Elevations. 
Corol. i. 
Hence it follows, that the greateft Amplitude pof- 
fible will be, when the Elevation is half a Right 
Angle, or 45 Degrees (becaufe the Sine of ^o° is 
the greateft of all others). 
Carol* 
