POLYGONORVM RECTILINEORVM. 93 



qnod fic demonftratur : iunda A A' patct eflTe 

 ABA'ziiSo°-BAA'-BA'A= i8o-2BA'A ob 

 BA — BA', hinc AB A' — 1H0-2 BDA , ctt enim 

 BDA = BA'A. 



10. Problema 9. Datif lateribus a, b, c e$ 

 angulif A , B inuemre aiiguiujn C. 



Ex ae4Uiuiune tcrtia (latirn deducitiir 



fin. ( A ^ B H- C ) = - "Jia^^nihlLs^ll , 



qiine formula coirputo inflitucndo liuis corrmcda ett, 

 interim haec tr.insformatio adhibcri poflet. Ponatur 



7-nn.(A-l~B) — cof.Atan^'. E , critque 

 fin. (A -i B + C)=:-^-(rm. A +cof. A.tang.E)r-"-^|^. 



Valor angiili C cx formula propofita duplex prodif, 

 uam fi poiiatiir A-f-B+CriSo^-l-F, h.ibtbimus qiioque 

 ahum v.ilorcm pro C, per qucni fit A+B-iC— 360 -F, 

 anguli cnim ibo-i-F et 360*^— F cundem prorfus 

 hjbcnt finum. Hoc auieni cx confirudlione figurae 

 fiicile iUudratur , dudis enim redlis BC, A I) qu:ie Tab I. 

 cum d:ua 1 nca AE — ^ faciuiit ani^ulos «AB, ^BC ^'S- 7« 

 acquales datis A, B, caotaqne B C rr ^, fi centro C 

 ra.iio ziz c defcribatur circuhis , pro qi.arto puncflo 

 quadnlateri D accipi potcll: ahcrutra inttr[ed:io huius 

 circuli cum recla AD Sint iftac interledioncs D,D', 

 tumuut cfiedehebit IKf- fyC<;-— 2F— 180°. Duda 

 autem CK normali in AD, fiet 



DCt--D'C6-DCD'=2DoE, vnde DCErF-po^. 

 Eft aurem 



F:=^BC-i-flAB-f-i-CD-i8o'_::i8o"-CDE, 



iVl 3 hoc 



