198 DEMONSTR. IHEOREM, BERNOVILUANL 



■vnde fli: • 



Pro alteio ergo tennino cuiuae B , vbi fit amplitudo 

 i;"Cp,et «"jzr^.ent CV,-j~, ita Yt fit AC: 

 B C — I : n. Hrt V£ro C centrum circuli immobilis , 

 CB eius nidius , et AC-BCrr7^„ diameter circuli 

 Hiobilis pro dcfcriptione epicycloidiSj vel hypocycloidis. 



XLIV. 



Cum fit AN=:Ar-4-'^=:A-+5g:^, erit 



AN=^^rT;r(i-7mr^) ^^ CNz=r^:rTr- j!n.v 



ideoque, ob CE — .".^^^ , erit 

 • CNiCBnilin.wi;: fin.i;. 

 -Qiiaro fi centro C radio CB defcribatur circulus re- 

 dlam MN fecans in L, ducaturque CLr=:CB , ob 

 •angulum A N M — i? et C N : C L :r: fin. C L N : fin, v , 

 ■er.it flngtihis CLN — nv , et arguius ACL-(i-?j)c. 



XLV. 



1-1 n ■nii-K.i y d z y n c r /• ■HcoJ vjin.nv\ 



Porro eft MN -Vx- 'sih- ,-r^(cor«.'y- -7^- ) 

 twm vero ex triangulo CNL reperitur 



_ »T nnc fin.{ 1 — i^v nnc . f. co[,v jin.nvx 



LN-7:^7nr- jm.v ■ = riinnr ( cof « i; jt^r) 



vndc concluditur L M :r: ~^nn cof 7i -v — ~rn cof. n v* 



At ra^ius ofculi curuae in M eft rzj^—nx:coC.}W , 



qui cum cidat in rcclam JVIL, erit 



radius ofculi ad ML vt i-\-n sd i,hoc eft in ratione 



confianti , quae funt proprietates epicydoidum et hy- 



pocycloidum. 



DEMON- 



