(147) = 



F fld piint^^a eiiis cxtrema duciiiitur lincne F\f, FN, ratfo 



ipfius NM ad FM — FN llntuitur datn, ir.odo niniirum an- 



gului qucm N M cum axc A B conflituit ruppoiiituc datus. 



Hoc vcro vt dcmonltrctur ("upponamus produclam cflc cordam 



M N vsquc dum ordinatac CF pcr focum F duclac iii K oc- Tab. 17. 



currat, tum<.juc cx K in lincam FO, quac angulum NFM ^'S- :> 



bifariam fecat, ducatur rormalis K r, quac rccTias FM et FN 



in m . n intcrlccat, ct dcniquc cx pundis !M, N in CF du- 



cantur pcrpcndicularcs MP, N Q. lam vti dcrnonftraui y/c- 



torum Acadcviiae pro Awio 1780, pag. 3<52, crit Fw — F«zz: 



FE, tumque cx ibidcm demonftratis liquct eflc Q N : N n zn 



P M : M //7 in rationc data, fcu vt CA:CF, hinc altcrnan- 



do erit Q N : P M = N « : M n/, idcoque etiam K N : K M 



= N « : M ;;/ , hincquc K N : N M — N // : F M — F N , ob 



M w — N « = F M — F N, tumquc dcnuo altcrnando NM:FM 



— FN = KN:Nf;; atqui K N : Q N z= i : fm. Q K N et 



Q N : N ;/ z:z C A : C F, quare pcr compofitionem rationum 



crit N M: FM — FNr::C A: CF.fin. QK N. Introdudis 



\cro dcnominationibus pro fig. 3. adhibitis, fit 



FM-FN:NM::FCcof.QTC:CA-CF.cofFCO:CA. 



At in triangulo F C D eft F D : C F r= fin. F C O : fin. F D C , 

 at fupra J.emm. II. vidimus cfl*e fin. F D C : i =r C H : C O, 

 fiet igitur fin. FCO:izz:FD.CH:CF.CO. Hinc au- 

 tem colligitur 



cof FCO' : I — CF'. CO'— DF^ CH' : CF*. CO*; 



ideoque 



CF'cof FCO* : CA^ — CF' . CO* -DF' . CH^ : CA^ . CO' 



rrCO»— CH-CO-i quia 

 (A C— F C) C 0=— (AC^— FD') CH*— HC CO', 

 ideoquc A C (C O^ — C H') = C F* . C O* — D F^ . C H'/ 



T a Hinp 



