SmAERlCIS, si5 



hemma 2. 



Si arcus BOL femicirculi BLA, in (ua elementa "Lm 

 diftributus intelUgatur , erit fumma omnium EL.Lw, 

 quam fummam iam ufitato more,pcr/BL. hm defignabo, 

 eritinquam/BL. L7;dAB. BP, fada nempe AP=:AL. F/^.4» 

 Fig. 4. 



Nam triangula fimilia ABL & mhn prsebent AB : 

 BL :: Lw : L« •, ergo BL.Lw— AB. L« , ergo /BL. 

 Ltw— /AB.Lw •, atqui/\B.L«— AB in omnesLw, o- 

 mnes vero L« funt =AB-AL (conftr, =AB — APjzr 

 BP, ergo/BL. L^«z=AB. BP, Quoderat &c. 



Theorema. 



Pars Epicycloidis Sphaericae EL defcripta a pundo 

 defcribente L provolutione circuli generatoris HL fuper 

 immobili EB cx E ad B , eft ad 2BP , fiAa AP=:iAL, 

 ut V{aa—2bab-\-bb) ad ^ , fi nempe radius circuli BE, 

 hoc eft BC fit rr^, radius BG circuli HL znb , ac cofi- 

 nus inclinationis circuli huius ad circulum immobilem 

 Tizhj ad radium in l . 



Per B ducatur tangens BV circuli immobiiis BE , 

 & haec tanget etiam circ. generatorem HL in eodem 

 pundloB. Intelligantur in circ. generatore & in circu- 

 lo immobili duo arculi indefinite parvi & aequales B|3 & 

 Bb, dudlaque ex b in BV normali be^ iungatur (3^, erit- 

 que angulus fieb menfura inclinationis plani HL ad pla- 

 numBEC circuli immobilis. His pofitis 



Si circdus generator HL promoveatur, lineola B(3 

 rotabitur circa pundum B usque dum cadat fuper BZ^^in- 

 terea vero defcribet BL feAorem LB/ fimilem fedori 

 Bp^ , in quo fedore arculus L/ eft elementum Epicy- 



cloi- 



