( 2 rf _ ,) A B, quae abit in A 2 -4- B 2 — A B = C 2 -f- A B , 

 pofito »,= -ij| ut itaque n fit ipfe ille fa&or vel exponens* 

 de quo in Theoremate J. i. fermo fuit, 



Problema. 



§. 4. Invenire radium Mb circuli b, qui tres circu- 

 los A, B, a tangat. 



Solutio. 

 Quuffi circulus C problemati aeque fatisfaciat ac cir- 

 culus b , praevidere iam licet , aequationem inventum iri 

 quadraticam, cuius una radix praebebit radium Q~K—B 9 

 altera radium M b , quem ponamus — b. Eft autem iu 

 Triangulis bBa, bBA, aBA, 



r- 1 -r» n B a a H- B b* — a b z B(BH-a -4- b)_~ a b 



COl 15 a zTa~Tb B[B-^a-t-b)-hab * 



r> 7 t> A B A* H- B £2 — A &* A6 — B(A — B — &) 



COl £> A 2B A.B6 """" A&-(-B(A — B - 6 ) * 



cofaB A = 



B A* ■-+- B a2 — A a2 Aa — B ( A — B — a) 



2BA.Ba Aa-+-BIA— » JJ -— a) 



Ex iisdem Triangulis habetur 



finbBA = '^;;z; -=|p.et 



fln a B A 



2 . / [ A B a ( A — B — a)] 



Aa + B[A — B — a) " 



Ponatur compendii cau£a 



A — B — C, A + B = D, B + a = E, B — o = F. 

 Vnde ob b£ft = bBA — oBA, reperitur 



Ci t> „ (Da — BC)(D& — BC)H-4ABi/[a&(C — a)(C — &)•] 



cof 6 B a — — _— J-J-J3 . 



At fupra inveneramus cof b Bfl = - ^MlJLjL &) , quibus vala- 

 xibus aequatis adipifcimur; 



4 ABj/ob(C-— o)(C— b)=b(CCF-hBCD-— DDa) 



-+-BC(CE4-Da — BC). 

 K. 3 Coeffi- 



