202 DE RES0LVTI0NE 



IV. tffin.a-t-£fin.(a+-(3) — cGn.Szzo , 

 quae ex priori elicitur loco fin. (a +- (3 -4- y) adhi- 

 bendo — fin. <T, ob <T — 360° — (a +- 13 +- y). Qua 

 autem ratione ope harum quatuor aequationum 

 omnes quaeftiones ad refolutionem quadrilateri re- 

 fpectu angulorum et laterum quibus includitur, per- 

 tinentes , refolui debeant ; iam fufius oftendere prae- 

 termittimus, qnia nondum oftendimus quot et quae- 

 nam huiusmodi quaeftiones refoluendae occurrunt, de 

 quo infra ex inftituto agemus. 



11. Pro Peatagono fequentes binas adipifcimur 

 aequationes : 



a fin.ct-f-6fin.(a+(3) T 4-f fin.(fl6-t-j3-f-Y)+^ fin -( a +P-t-Y+^) =° ( A ) 

 a cof.a+-£ cof.fa-h {3)-W cof.(a-f-(3+ y)+^cof (a+ p+y4-cTJ+ e~o , 



quarum pofterior vel ita exprimatur 



-fizrtfcof a+&co^a+(3)+-4-cof.(a+(3+Y)+^cof.(a-J p+ y+cT) (B) 

 vel fic 

 — £— </cof.e:z=dcofa+&con(a+(3)+ccof.(a+j3+Y) (C), 



Ex priore autem dum pro fin.(a-+{3-f- y + <T) fub- 

 ftituitur — fin. e , confequimur 



</fm.s — tffin.a + £fin.(a + f3) + ffin.(a+ , |3 + y) (D). 



Suir.tis iam quadratis aequationum (B), (C) , nec 

 non aequationum (A) (D) addkisque quadraiis ex 

 (B), (A) et (C;, (D) has obtinebimus aequationes: 



I. ^3a I +&*+c 2 +/+2tf£cof.f3+2tfccof('j3+Y)-f 2dtfcof.({3+Y+c?) 



+ 2^coI.Y+aWcof.(Y + cT) + 2^col.cT 



II. ^+/+2^cofez/+^+6 ,, +2^cof(3+2^txof.((3+Y)+2^cofY, 



Giiae 



