if 3 85 ) 
A Body, with any the leaf l ajjignable Force, will move 
through infinite Space , if it meets with no Reftftence, 
in an infinite Time . And in Spaces where there is an uni - 
form Reftftence to Motion, the Space defcribed before 
the Motion ceafe?,muft needs be as the Force and as the 
Time together: Becaufe a double Force will carry a 
Body twice as far in the fame Time , and will alfo 
caufe the Motion to be twice as long Time in defray- 
ing by an uniform Reftftence. The Space defcribed 
therefore before the Motion ceafes, is in this Cafe de- 
monftrably as the Square of the Force. A Body 
thrown upwards with double Force , will be carried 
four Times as high, before its Motion be flopp’d by 
the uniform Reftftence of Gravity ; becaufe the double 
Force will carry it twice as high in the fame Time , 
and moreover require twice the Time for the uniform 
Reftftence to deftroy the Motion. The Cafe is the 
fame in accelerated Motion, in Bodies acceleratedby 
a Succeflion of elaftick Impreflions, or falling with a 
Motion accelerated by the uniform Power of Gravity, 
or by any other uniform Power whatfoever. The 
Space defcribed muft needs be as the Force , and as the 
Time wherein the Force operates. 
What 1 have thus demonftrated concerning any Force , 
conftdered as the Caufe producing an Effed-, and con- 
cerning the Time , during which the Force operates; 
is on all Hands acknowledged to be true concerning 
Velocity . And therefore V elocity and Force , in this 
Cafe, are one and the fame Thing. So that to affirm 
Force to be as the Square of the Velocity , is to affirm 
that the Force is equal to the Square of it felf. 
Now from hence appears very clearly the Ground 
of the Errour thefe Gentlemen have fallen into, and 
F f f of 
