C"3) 
By Ryl underftand the Radius of the Circle Generant • 
and by s, the Right Sine of the Arch B Ay whoft Verfed 
Sine is FA. 
And, where ever in my whole Difcourfe of the Cy- 
cloid, or the Reftored TriKnear (which is a Figure of 
Archs, and a Figure of Verfed Sines) the Arch a is no 
Ingredient in the defignation ; fuch part or portion of 
them is capable of being Geometrically fquared. But 
when I exclude I do therein exclude P ( for that is 
an Arch alfo) and /==^ + 5, and e^a — j, becaufe a 
is therein included. 
Mr. C a/well, ( not being aware that I had fquared thefe 
Figures ) had done the fame by a Method of his own, 
( which he ftiewed me lately ) which I would have in- 
ferred here, but that he thought it not neceflary ; and 
inftead thereof, hath given me the Quadrature of a 
Portion of the Epicycloid (which you will receive with 
this) and, I think, it is purely new. 
i V. The Quadrature of a Portion of the Epi^ 
cycloid. By Mr. Cafwel. 
SUppofe D?F to be half of an exterior Epicycloid^ 
FB lis Axis, Kthe Vertex, FLB half of the ge- 
nerant Circle, E its Center ; D B the Bafe, C its Center : 
Bifed the Arc of the Semicircle FB in i, and on the 
Center^ through L draw aXircle cubing the Epicy- 
cloid \nP : Then I fay the Curvilinear Triangle FL P 
CE 
will ht^BEqm-^r^^ ^h^^ is, the Square of the Se- 
midiameter of the generant Circle will be to the Cur- 
vilinear Triangk FLP, as Cfi the Semidiameter of the 
B^ft, toC£ ; which C£ in the exterior Epicycloid is 
the. 
