142 mMONSTRATlO THEOREMJTIS 



determinatio putKfti g per formulas (§. aa ) iia fe ha- 

 beoit, ob p~g et ^~^. 



^ — i' ^/(bb-fj){bb-n ff) , ^ 5& — // . 



g b* nbbff f^ ^ bb-njf 



•\/(U U n.rr^— bb f ^ [bb - nf f)[bh — nbb) __hfyl (' — n) 

 V \00—gg) — i^ _ nbbjf — ^ibb-.aff) 



V(Ah ff<rir\ i>'^^bb-7ifn{bb-n bh)_ hb^/{t- n) 

 Y\t)0 — ngg)— b*-nbbff ~ — ^{bb-iiffy 



Vnde fi anguli , quos applicatae F/ et G^ cum cutaa 

 faciunt, in computum ducantur, crit 

 g- b fin A/F et f—b fin A^G. 

 Atque hinc fequiiur ilta conftrudio pro pundto g inue- 

 niendo : Ad pundtum / ducatur tangens f T, donec axi 

 CA produdo occurrat in T, tum in ea, fi opus eft, 

 produdla capiatur TV — CB — ^, et per V agatur redta 

 © G axi C A paraileJa , eritque pundum g qnaefitum , 

 ita \t arcuum A/ et B^ differentia fit geometrice 

 aflignabilis. Verum ex problemate praecedente, ob p-g 

 ct 4'^b , erit haec diflfefentia : 



Arc. A/- Arc. ^^-"4'= "S^^^WS- 

 Ad quam conftruendam notetur ^^zx 



■C f AF r^ hh— nff 



'^J—finAfP—J ^ bb^^ 



€t ex natura ellipfis: 



|-irp nh fc^Vfr — n} 



^ * ^{bb—ff) V(66— /J)« 



Hinc fi ex centro ellipfis C in tangentcm F/ demit. 

 tatur perpendiculum CS, ob ang. CTSzrang. A/F, 

 €iusque finum =:yf|^ et cofinum z::-^^:^}, eric 

 TSzzCTcofCTS — :;?|^'j^"^) hincque 



r f q- / 'p b^-rf*- bb)-i-rd}b f nf{b h-jf ) s^/ ih-jf 



*V — ^J •" *-y^i{bb~Jf){bb—nff) — •^{bb~fJ)\bh~nff) — »J ^ tb-nfr 



Pottio 



