Chap. 6. 



point A, draw the line A D 

 perpendicular to the line B C, 

 & let it be divided into three 

 equall parts by the lines E F 

 and G H, in the points I and 

 K. And I fay that becaufe the 

 line A K is twice as long as 

 the line AT, therefore the tra- 

 pezium E F H G, is thrice as 

 big as the triangle A E F: for 

 as A K is to A J,fo is G H to 

 E F. But the triangle A G H 

 is to the triangle A E F, in a double proportion of the lineG H 

 to the line E F: which being double the proportion of one tri- 

 an^leto rhe other muft befourefold: fo that fubtrafting the tri- 

 angle AEF, the trapezium E F HG remaineth thrice as big as ic. 

 And thus the whole triangle getteth an encreafe of three, whiles 

 the perpendicular is encreafed but one, te make his length two. 

 Which when it cometh to thrce,the trapezium GHCBthat con- 

 taineth the third divifion of the perpendicular, becometh five 

 times as big as the triangle AEF ; for fince the line A D is three 

 times as -long as the line A I; and thelineB C is three times as 

 ion< as E F; it followerh that the triangle ABC is nine times as 

 big as the triangle AEF;but AGH is foure times as big as AEF; 

 therefore fubtraiting it from the whole triangle ABC.u Icaveth 

 the trapezium GHCB five times as big as thefirft triangle AEF 

 Which proposition is very ingenioufly fet down by the learned 

 Monficur GafTcndi in his firft Epiftle de motu imprejfo a moto- 

 retraflatff, to the fame purpofe for which we bring it. Thorg!t 

 we do not here make ufeofhis fcheme and way of demonftrac;- 

 on; becaufe we had fallen upon this before his book came a- 

 broad: and therefore we onely note his to dire the Reader un- 

 to it } who pcradventtire may like his better then ours. Hcnvbcit 

 we do not conceive that he hath in his di(cour(e thcre,arrived to 

 the true reafon of the effect we fcarch inco; as may appear by 

 what we have already delivered. 



But we muft not imagine, that the velocity of motion willi 

 alwayes cncreafcthus for as long as we can fancy any motion:^ 1 

 btu when it is arrived unto theutmoft period that fuch a move- ^ 

 able with fuch caules is capable of, then it keepcch 



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