POLYGONORVM RECTILINEORVM. 187 



quomodo ope harum aequationum , omnes folutio- 

 num cafus facile expediri pofiunt. 



3. Theoremata igitur ifta fundamenti loco 

 fubfternenda , ita habentur expreffa : 



Si polygoni reBillnei anguli exierni dicantur a, (3, 

 y, £, e . A et latera ipfis interiacentia refpe&iue de- 

 Jignentur per a, b> c, d, e . . . 1 erit : 



I. flfin.a-f^fin.(a+(3j+^fin.(a-f(3-hY)+^fin.(ct+j34-V+^).... 



+-/fin.(a+(3+Y... + X)=o 

 II.tfcoCa+3cof.(tt+(3)+<'Cof(ct+(3+v)+</cof.(tt+p+Y+^)... 



+/cof(a+(3+v..+A;~o. 



Demonftratio. 



Repraefentet figura redilinea A B C D E F G Tab. I. 

 Heptagonum et prociudis lateribus C B, D C, D E, Fig. 2. 

 E F dum lateri A G producto occurrant in H, I, 

 M, O ; liquet eflfe angulum 



BAHzza; HBA~(3; ICH-y; LDI-£; MEO=e; 



OFG = £; FGO— >j, 

 tumque ktera 



A B, B C, C D, D E, E F, FG refpeftiue indigitari 

 litteris a t b, c, d, e, /, g. Tum vero habebitur : 

 ang. CHK:=BAH+-HBA — a + (3 



DlK-CHK+lCH = a + (3 + Y 

 35o°-DMN — LDI + DIK — a + p + v + ^ 

 3tfo - EOM — 36o°-DMN4-OEM— a+(3+Y+^4-e 

 360 -FGO~3<Jo -EOM + OFGz=:a+(3+Y+£+e-HJ 



36"o°:=:a+(3-+Y + £ + e + <! + '>1- 



A a 2 Iam 



