2i5 SOLVTIO PROBLEMATIS GEOMETRICI 



quibus reperitur 2 bp ( B* — P ! - Q_ J ) -f- 2 B P ( b* -p z - 5* ) 



= a (B'-*) fty_flF)_~_-^>_--KJ = 



__ .(.P-twf^- ^ H -o+t^ Deinde erit ( B , _ p _ 



Q.')(^-^-f- + B/5Pp = ^E^- , --(B'-^)^-4 



Tj/n, fB*P* — £>'_>*)*_ (B z — £. a )* — *BfrP_?( B a — 5 a ) a 



DOrp — pj*__& 7 'p . — 



[( B P -+-& _> J 2 -+- (B 2 — & 2 ) a J r(BP — 6_>) 2 — (B a _£*)*] 



[b 2- — & 2 ) 2 ~ ' 



§. 18. His ergo valoribus in expreflione inuenta 

 fubftitutis prodibit tangens anguli A2#— : 



2 (_____-& a )(B P — 6 _)[(B P-4-&j Q__-f- _____-_____] ___B__5__(b P — 6 _> ) 



fTBT - ■'6_>) 2 -+TB a ~-— 6 2 ) 2 ][(BP— i>p) 2 — (B 2 — 6 a j*] ■ ,(BP— 6_))*-(B«_"fc* ] a «- 



Ex qua expreflione intelligitur tangentem kmiftis anguli 

 ad 2 fore zz-ItE^. Cum vero fit BV(0-B 2 )-BP 

 =__£V (c z -b z )-bp, erit tang. ang. .2_: BV{C , J^ ^r_p 

 ex qua expreflione intelligitur quantitatem anguli 2 per 

 foias quantitates C, <;, B, £ determinari, neque a litteris 

 variabilibus P,£, Q., ct q ptndcre. 



§. 19. Ponatur angulus ____ro, quo rectae A£ et 

 <*B partes aequales a lunulis abfcindentes fiant inter fe 

 parallelae, qui eft cafus, quem Celeb. Daniel Bernoulli 

 folum dedit folutum; Hoc ergo pofito fiet tang. |2 

 _z_o, ideoque erit B 2 -^ 2 = o et Bz_:_*. Cum autem 

 fit B__^ ex aequatione RQjzzbq fequitur fore Q=#; 

 atque aequatio P 2 + B 2 4-Q : _:_) 2 + ^+. 2 fuppeuitabit 

 P 2 ___0 2 ; ex qua fequitur fore vel P zzzp vel P=:— p. 

 Aequalitas autem P=__0 a_ inftitutum noftrum eft inuti- 

 iis _ ex ea enim fequeretur fore C__</, adeoque circuli forent 

 aequales, qui calus in problema non cauit. Quod autem 



fatii- 



