POLYGONORVM RECTILINEORVM. i 90 



a, (3, y et latera AB, B C, CA litteris a, b, c 

 exprimantur , noftra Theoremata binas has fuppedi- 

 tant aequationes : 



aCm a-f-&fin.(a4-p)— o; acoCoL-\-bcot.(oi-\-p)-\-czzo, 

 Quum ex pofteriori harurn aequationum deducatur 



c zz — a cof. a — b cof. (a -V- p) 

 fumendo vtrinque quadrata obtinebimus: 



^—«'cof; a 2 +-£*cof.('a+-p) 2 -f- 2#&cof acof. (tt+-p) 

 eft vero per priorem aequationem 



d lin. a 2 -r~ £ 2 fin. (a +-' p/-+- 2 tf & fin. a fin. (a+P) = o 

 hincque fiet : 



fr * =: flVora 2 + 2 fl ^cof.acor(a-l-(3)+^cof(a+P) 2 _ * , ,« . t fS 

 H-11'fin.a +atf*fin,ttfiD.(a+P)+^fin.(ft+p/-"' 1 **" ^ 2 *" tol P 



quia nimirum eft 



ccf. « cof. (ct +- p) +• fin. a fin. (a +- p) zr cof. p. 



Prima igitur aequatio refolutioni trianguli inferuiens 

 ifthaec erit : 



I. c c — a a -+- b b -+• 2 # & cof p. 

 Reliquae duae fequentes habentur : 



II. flfin.a+-&fin.(a+-P)— o; III. tf fin.a-Min.y— o, 



quarum fecunda per ipfum Theorema rioftrum pri- 

 mum exprimitur , tertia vero ex noc Theoremate 

 deducitur in locum ipfius fin. (ct-Hp) fubftituendo 

 — fin. y , quippe quum fit y zz 360° — tt — p". 

 Patet autem has tres aequationes fufficere ad omnes 

 quaeftiones refoluendas > quibus ex datis tribus parti- 



bus 



