MifceUanea Curio fa. 311 



Area ABC is the Sum of all the Lines be be" 

 ing taken, according to the Method of JW k .•/- 

 jfN^j, infinitely many ; fo that the Area A B C 

 reprefents the Sum of all the Velocities, between 

 none and B C fuppofed infinitely many ; which 

 Sum is as the Space defended in the Time re- 

 prefented by AB. And by the fame Reafon the 

 Areas A b c, will reprefent the Spaces delcended 

 in the Times A b ; i'o then the Spaces defcend- 

 ed in the Times AB, A b, are as the Areas of 

 the Triangles A B C, Abe, which by the xoth 

 of the 6 of Euclid, are as the Squares of their 

 Homologous Sides A B, A b, that is to fay, of the 

 Times: Wherefore the Defceots of falling Bodits 9 

 are as the Squares of the Times of their Fall, 



Prop. III. The Velocity which a falling Body 

 acquires in any Space of time , is double to that, 

 wherewith it would have moved the Space, de- 

 fended by an equable Motion, in the fame 

 time. 



Domonftration. Draw the Line E C parallel 

 to A B, and A E parallel to B C in the fame 

 Fig. 9. and compleat the Parallelogram A B C E, 

 it is evident that the Area thereof may reprefent 

 the Space, a Body moved equably with the Ve- 

 locity B C Would defcribe in the Time A B, and 

 the Triangle ABC reprefents the Space defcrib'd 

 by the Fall of a Body, in the fame Time A P 5 

 by the fecond Proportion. Now the Triangle 

 A B C is half of the Parallelogram A BCE; 

 and confequemly the Space defcribed by the 

 Fall, is half what would have been defcrihed by 

 an equable Motion with the Velocity B C, in the 

 X 4 fame 



