$. 5. Ducantur ad pundta P. Q in quibus Dia- 

 meter circulo occurrit, lineae rectae BP, BQ, et habe- 

 bimus: 



i-cof^ cot< D pc ; '-=^? — cot. B P C et 



cfin. n ' bjm. m 1* 



'-'-,*'».-» — cot. B Q C , 



bjin.m ^- ' 



hinc ifta fraftio: 



1 _ c cof. n (1 — & cof. m) . (1 -4- 5 c o/. rc) (1 — c cof. n) _ ._ 



c/in. « " Jin. m ' b c Jin. m jin.n ' 



ita Geomeuice exprimetur: 



cot D P C - cot. B P C : cot. BQC. cot. DPC-i; 

 fiue ob 



nnp f npp- Jw.fBPC — D P C) — fln. D P B pt 



COf. L/ r U- COl. D r ^ _ ^ mJ pc Jw Dpc ~fin.BPC.ftn.DFC 



cot. b q c . cot. dpc-i =%:°&±m, 



hinc erit ifta fraclio propofita quoque 



fm. D P B . ftn. B Q.C 



/wi. B P C . coj". (D P C + BQC)' 



Si dufra concipiatur Q O, quia eft 



QOB — jch-POB et BQO ~ <)0-D PC -BQC, 

 confcquemur ex triangulo Q O B : 



BQ: OB zr fin.QOB : fin. BQO = cof.BOP : cof. (DPC+BQC), 

 tum vevo quum ____.' 



P B : B Q ___: fin. B Q C : fin. BPC et 



O B : B P _=_ fin. D P B . fiq. F O B , 

 fiet coinponendo has rationes : 



_.of. POB. fm. B Q C. fin. D P B 



== fin. P O B. fin. B P C. eofi (DPC + BQC), 

 ideoque 



^anp- P O B — fin - B Q- c • /"aJLILP . 



atqui 



