%io Mifcellanea Curiofa. 



This follows, for that the Action of Gravity 

 being continual, in every Space of Time, the fal- 

 ling Body receives a new lmpulfe, equal to what 

 it had before, in the fame Space of Time, recei- 

 ved from the fame Power : For Inftance, in the 

 firft Second of Time, the falling Body has ac- 

 quired a Velocity, which in that time would car- 

 ry it to a certain DJftance, fuppofe $1 Foot, 

 and were there no new Force, would defcend at 

 that rate with an equable Motion \ But in the next 

 Second of Time, the fame Power of Gravity con- 

 tinually a£ting thereon, fuperadds a new Velocity 

 equal to the former ; fo that at the end of two 

 Seconds, the Velocity is double to what it was at 

 the end of the firft, aiad after the fame manner 

 may it be proved to be triple, at the end of the 

 third Second, and fo on. Wherefore the Velcci' 

 tics of falling Bodies, are proportionate to the 

 Time of their Falls, £. £. D. 



Prop. II. The Spaces defcribed by the Fall of 

 a Body, are as the Squares of the Times, from 

 the beginning of the Fall. 



Demonflration. Let A B {Fig, 9. Tab. 4.) re- 

 prefent the Time of the Fall of a Body, B C per- 

 pendicular to A B, the Velocity acquired at the 

 end of the Fall, and draw the Line A C \ then 

 divide the Line A B reprefenting the Time, in- 

 to 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 ma- 

 nifeft that the feveral Lines, be, repreient the 

 ieveral Velocities of the falling Body, in fuch 

 Parts of the lime as A b is of A B, by the for- 

 mer Propofition. It is evident likewife, that the 

 11 Area 



