Mi [cell anea Cur to fa . |# J 



ftive Arches B A % every where j) which there- 

 fore I call Trilineum Reftitutum (the Trilinear 

 reftored to its due Pofition, which Figure I 

 do not find that any before me has confi- 

 der'd : ) So that to Square any part of this, 

 is the fame as to Square the refpe&ive part 

 of the Cycloid, (or of the Trilinear in the 

 Cycloid: ) That which in the Cycloid lies be- 

 tween two Aiches of the Circle Generant 

 in different Pofitions, anfwering to that 

 which, in the reftored Figure, lies between 

 the refpective ftreight Lines. 



And therefore AdD A,~ T d£ T ,( Fig.iS.) 

 = Ad D A— T df T ,(Fig. 30.; —R\ And 

 AbkdA, rbk^T, (Fig. 28.J ~AbkdA y 

 t K <^ t, (Fig.$Q ) — s R. And b\d (Fig.2%.) 

 = bkd, (Fig. 30J ~R*~-sR, Ibid. Cap. 17. 

 B. pag. 75(5. Where, if b be taken above 

 ~dkD C, (pafling through the Center C) thefe 

 Figures are within the Cycloid, and within 

 the reftored Figure but without them, if 

 b be taken below that Line, and adjacent to 

 the Curve A b t ? in both Cafes. 



By R, 1 underftand the Radius of the Cir- 

 cle Generant , and by s, the Right Sine of 

 the Arch B A, whofe verfed Sine is V A. 



And, where-ever in my whole Difcourfe 

 of the Cycloid, or the reftored Trilinear 

 (which is a Figure of Arches, and a Figure 

 of verfed Sines) the Arch a is no Ingredient 

 in the designation ; fuch part or portion of 

 them is capable of being Geometrically 

 iquared. But when I exclude a, I do there- 

 in exclude P (for that is an Arch alfo) and 

 f = a s, and e = ^ - — ' s 7 becaufe a is there* 

 in included. 



