Coefficiens ipfius b eft 



rzfBC(C-r-D)— a(CC-f-DD)=r2AB(A-B) 



— 2«(AAH-BB), 

 coefficiens autem produfti B C eft — a (C -f- D) rr 2 A a? 

 Quare fi integrae aequationis quadratum fumatur, prodibit 

 4A 2 B 2 ab(C 2 -Ca-Cb-4-ab)z=b 2 [ABC-a(A 2 - B 2 )] 2 

 -+-2ABCab[ABC-a(A 2 +B 2 )]+-A 2 B 2 C 2 a 2 . 

 Eft autem ABC-a(A 2 + B 2 )~^|l^ (j. = .), unde 

 pofito breuitatis gratia C 2 + ABzr m, vt fit a = ABC (J. 2.), 

 et integra aequatione in A3 ™ 2 C2 du&a, nancifcimur 



4b[Cw-ABC-(m-AB)b]=ABbb-2ABCb + ABCC 5 

 five ob m — AB~CC, 



4 bCC(C — b)=_AB(C- b) 2 . 



Vnde fponte patet , aequationis huius quadraticae binas 

 effe radices 



i.)b = C, et^Obzz:^^, feu 



b = a - b(a - b) . a e. 1. - 



4 ( A2 -f- B2 ) — .7 A B ^- 



5. 5. Hinc iam clarius perfpicitur lex, iuxta quam 

 radii a , b , etc. progrediuntur. Prior nempe radix dat ra- 

 dium circuli C , altera radium circuli b , quorum uterque 

 circulos A, B, a, tangit, quemadmodum m Problemate re- 

 quiritur. Quum itaque feries circulorum tangentium, quae 

 in infinitum continuari poteft, incipiat a circulo a, erit pro 

 circulo a, index n~ 1, adeoque pro circulo b, n~ 2, pro 

 circulo vero C, n~o, quibuscum formula generalis fupra 

 affumta (J. 3.) perfefte convenit, in qua li ponatur n ~ o, 

 \ fit 



