[ *39 3 
Flighty of thoir great eft Altitude s, and of their 
horizontal Amplitudes . 
Let Fq {Fig. i.) reprefent the Plane of the Ho- 
rizon, FEQ and peq the Paths of the Projediles, 
defcnbed inthe Flight; moreover let QFT and qpt 
be the given Angles of Elevation, and let ^Pj^and 
pq be bifeded in H and h ; drawing HE, he 
and qt, all perpendicular to Fq\ and making the 
Sine of 6ftPT=zS, its Co-fine =C, the Sine qpt=s , 
its Co-fine =c, and Radius =r. 
Therefore, fince the Diftances defeended by heavy 
Bodies (whether from a Point at Reft, or from the 
right Lines in which they would move, if not aded 
upon by Gravity) are known to be as the Squares of 
the Times, £)T will be to qt, as the Square of the 
Time of deferibing FEftf (or of that wherein the 
Bali would move uniformly over the Space FT with 
its firft Velocity at F) is to the Square of the Time 
of deferibing peq (or of that wherein the other Bali 
would move uniformly thro’ the Length pt). But 
the Celerities at F and p. being equal, by Hypothe- 
cs, the Times in which the faid Lines FT and pt 
would be uniformly deferibed, are manifeftly, as the 
Lines themfelves: Whence the Squares of thofe 
Lines muft, aifo, be as the Squares of the Times, 
and, confequently, as the Diftances defeended: that 
is, Pt 2 :pt 2 ’. * Tgj.tq. 
Now, by Plane Trigonometry TQ==z Sy - PT and 
tq= S 1P1 j therefore TT* -.pt 1 ( : : S JL El ■ 12 p) : : S 
xFT'.sxpt i whence, by dividing the Antecedents 
T by 
