JMifcellanea Curio fa. I 8 I 



Square of KE, to the difference of the 

 Squares of KL and KB, or as RR+ 2Rr + rr 9 

 to 2Rr +• 2rr, that is, as R -V r, to 2r, or 

 KE to BV. And confcquently the Rectan- 

 gle BE x CE or rm is equal to the Space 

 XyNB. But the Space VZB is equal to the 

 Rectangle t ar + i sr, am} fo according to 

 our Profofition it will be as a to 2w, fa ~ ar 



, mar+msr . , . - _ . v % 



i~ i sr, to equal to the Curvilmeal 



a 



Space QUZLBNQ From hence fubftraft 

 the Space XyNB = nn, and there remains 



the- Space QUZXy = And fince the 



Spaces ZXL, Q_y T, are equal, the Space 



QULTCL mall alfo be equal to — . There- 



- ~» ' ■' ■ ■ a ° v 



fore when a to m\ or the Circular Motion 

 is to the Progreflive Motion of the Center^ 

 in a given Katio, there will be a perfect 

 Quadrature of the Curvilineal Spaces 

 QULTCL. And the whole Space UPL, will 

 be to the Square of the Radius BE, in the 

 fame Ratio (m to a) of the Motions, that 

 is in every Primary Epicycloid," in the Pro- 

 portion of the Radii, KE, KB, which is 

 Mr. Cafwelfs Proportion. 



But the lefTer Spaces QULTQ will be to 

 one another, as the Sines of the Arches UZ 5 

 and the Triangular Spaces QTP, by the fame 

 Argument, will be as the verfed Sines of the 

 Arches QT or ZL, and confequently are al- 

 fo fquar'd. After the fame manner it will 

 be prov'd, that the Spaces pat, pLu, p*r, 

 are ever to the Square of the Radius BE 



N 3 (jta 



