[lo] 
the Area ABC rcprefents the fum of all the FelocUiesyhetvi/Qca 
none and B C fuppofed infinitely many ; which fum is the 
fpace defended in the time reprefented by A B. And by the 
fame reafori the Jreds Abe, will reprefent the fpaces defend- 
ed in the times A b ; fo then the fpaces defeended in the times 
AB, Ab, are as the Jreas of the Triangles A B G, A b c, which 
by the 20 th of the 6 of Euclid are as the Sqmres of their jFfc: 
wologous [tdes A B, A b, that is to fay, of the Times : where- ' ' 
fore the pefcents falling Bodies ^ are as the Scjuares of the times 
oftheirM^E.a 
Frop. III. The {Velocity which a falling Body acquires in a- 
ny Ipace of time, is double ^ that, wherewith it would 
have moved the j[pace,defcendcd by an equable motion, in the 
fame time, 
Demonflrationy Draw the line E C parallel to A B and A E 
parallel to B C in the fame i. and compleatthe F ar allele- 
gram ABC E, it is evident that the Area thereof may repre- 
fent the fpace, a Body moved equably with the Velocity B C, 
would deferibe in the time A B, and the Triangle ABC repre- 
ftnts the fpace defcribed by thtfall of a Body^ in the fame time 
A B, by the fecond propofition. Now the Triangle A B C is 
half of the Parallelogram A B C E, and confequently the fpace 
defcribed by the is half what would have been defcribed 
by an ecjuahle Motion with the Velocity B C,in the fame time > 
wherefore the Velocity B C at the end of the fall^ is double to 
'that Velocity which in the time A B, would have defcribed 
thtff ace fallen^ reprefcnted by t\\Q Triangle A B Cy with an 
equatle Motion, ^E. D. 
Prop. IV. AH Bt?^wonor nearthe furfaceofthe£/«r/yE^, in 
their/^//, defceud ib, as at the end of the firfl fecond of time, 
they have defcribed 16 feet one inch London Meafure^ and ac- 
quire d the Velocity of ^ 2feet two inches in a fecond. 
Th is is made out from the 2 5th propofition of the fecond 
part o f that Excellent Treatice of ySx. Hugenitis de Horologio 
Ofcillatorio v^\\(^i'<^in he demonfl:rates the time of the leaft 
] Orations of a Pendidnmyto to the time of the faUoH a Body^ 
from 
