1 7 * -Mif ceUanea Curio [a . 



being other Portion's of it, equally capable 

 of Quadrature. 



In order to which, I there fhCvv (De Motu, 

 Cap. 5. Prop. 20. A. p.802,803,804.) that not 

 only the Cycloid is Triple to the Circle Ge- 

 nerant, (which was known before) but that 

 the refpettive Parts of that are Triple to thofe 

 of this : Which is the Foundation on which 

 I build my whole Procefs concerning the Cy- 

 cloid in both Treatifes, (and which is not pre- 

 tended, that I know of, to have been obferv'd 

 or known by any Body before me :) That is, 

 b^ a A (Fig. 28. j Triple to the Se&or B*A 

 (taking h$ parallel to B where-ever, in 

 the Curve A t, we take the point b. 



I then fliew, that the Cycloid is a Figure 

 compounded of thefe two ; the Semicircle 

 A D «, and the Trilinear A D A r b A, lying 

 between the two Curves A D A and Ad r> 

 (and therefore, to Square any part of thefe, 

 is the fame as to Square the refpe&ive part 

 of the Cycloid. 



I mew farther (Ibidem, pag. 804.) that this 

 Trilinear is but a diftorted Figure (by rea- 

 fon of the Semicircle thruft in between it 

 and its Axis) which being reftored to its due 

 Pofition (by taking out the Semicircle into 

 a. different Figure, (as Fig. 29.) and thrufting 

 the Lines bB home to the Axis, fo as that 

 BVbz the fame point) is the fame with 

 At <t y (Fig. 30.; (the Parallelograms bp &B 

 being fet upright, which in the Cycloid ftand 

 (loping-, and the Circular Arches b 3, (Fig. 28. ) 

 becoming ftreight Lines (in Fig. 30.) and the 

 Lines b B being, in both, equal to the refpe- 



ftive 



