l9l 
Proportions concerning the Defcentof hea^vy Bodies^ 
and the Motion of Pr ojeds. 
PropL The Velocities o? falling Bodies, are proportionate 
to the times from the beginning of their falls. 
This follows, for that the aftioii of Gravity being contimid^ 
in every (pace of time, the falling Body receives a new im- 
pulfe, equal to what it had before, in the fame fpace of time, 
_ received from the fame power : For inftance, in the firft fe- 
cond of time, the falling Body has acquired a Velocity., which 
in that time would carry it to a certain diftance, fuppoft j 2 
foot, and were there no new force, would defcend at that 
rate with an equable Motion \ but in the next fecond of time, 
the lame power of Gravity continually afting thereon, fu- 
peradds a new Velofity equal to the former ; fo that at the end 
of two feconds, the Velocity is double to what it was at the 
end of the firft, and after the fame manner may it be proved 
to be triple, at the end of the third fecond, and fo on. Where- 
fore the Velocities of falling Bodiesy are proportionate to the 
times oftheir/^Z/j, J^E, D. 
Prof. II. The Spaces defcribed by the fall of a Body, are 
as the Sqt^ares of the times, from the beginning of the FalL 
D^fmnfiration. Let A B {Fig.i. TaLi.) reprefent the time 
of the fall of 3. Body y B C perpendicular to A B the Velofity ac- 
quired at the end of the fall, and draw the Hne A C, then di- 
vide the line A B reprefenting the time into as many equal 
parts as you pleafe, as b, b, b, b, &c. and through thefe 
points draw the lines be, be, be, be, &:c. parallel to B C, 'tis 
manifeft that the feveral lines, bc,reprefent the feveral Veloci- 
ties of the falling Body, in fuch parts of the time as A b is of 
A B, by the former propofition. It is evident likewife that 
the Area A B C is the fum of all the lines be being taken, ac- 
cording to the method of Jndivifihles^ infinitely many ; fo that 
