1 76 Mifcelianea Curiofa. 



COROL II. 



If the Semidiameter of the Bafe is fuppofed 

 infinite, the Epicycloid then being the com- 

 mon Cycloid, the Area of the faid Triangle 

 will be equal to the Square of the Radius of 

 the Generant, and fo it falls in with that 

 Theorem which Ldovera found, and calls 

 Jldirabile* 



Though I do not think the abovefaid Qua- 

 drature can eafriy be deduced from what has 

 been yet publiflied of the Epicycloid, I have 

 not added the Demonftration ; but think it 

 enough to name a general Propolition from 

 whence I deduced it, viz.. The Segments of 

 the Generant Circle are to the Correfpondent 

 Segments of the Epicycloid, as C B to 2CE 



C B. For Example, fuppofe FmG the 

 Pofition of part of the Generant when the 

 point F of the exterior Cycloid was defign'd, 

 then the Segment Fm G n is to the Segment 

 DFnG : : as CB to 2 CE-\~CB. 



And confequently the whole Epicycloid to 

 the whole Generant in the fame Proportion : 

 Which is the only Cafe demonftrated by 

 Moufieur Be la Hire. 



It follows alfo that in the Vulgar Cycloid, 

 its Segments are triple of the Correfpon- 

 dent Sectors of the Generant, which was 

 firft fhewn by Dr. Wallis. 



A General 



