CORPORVM RlGlDOaVM. 255 



peruenerint in pun&a a, b, c et m-cuum A B, a b ; 

 AC, nc; B C, bc inierje&ioncs fmt in punCtis y, p, a; 

 erit an-us B b — ang. Apar^C[3c; Aa-Bab-Cac; 

 Cc^Ayaz^zByb. 



, Demonflratlo. 



Ducantur arcus B(3, ^p et ob nrcus ABrBC-po", 

 erit quoque B(3zi9o'' er ang. B(3 A — 90°, tum vcro 

 ob baz:ibc — ()Oy erit item b^-^o^ et ang.^(3Ar9o, 

 \nde deducitur Bp A^^j^^rt et B<^b-^.^a-^ atqui ob 

 BPirr^P — 90°, mcnfuia anguli B(3^ eft arcus Bi^; 

 liinc idem arcas aequabitur angulo A(3^, Simili 

 plane ratione oftenditur effe A a = ang. B a ^ et: 

 Q c ~ ang. A y «. 



L e m m a IIF. 



14.. In Tetragono ACcb, quod componitur ex 

 areubus circulorwn maximorum in Juperficie Jpbaerica^ 

 Ji, fuerit A C'— b c — 90° , erit'. 



cof AZ^^rin.ACf. fin.^<7C-cof.C^.CQr.AC^.cof.i»^C. 



Demonflratio.. 



Ducatur arcus ^C, eritque 

 cof A^z:fin,^C.cof. AC^, hincque ob ACfcACr-^Ctf", 

 zo{.kb — fin. ^C(cof.A C^.cof. ^Cf+fin. AC<;. fin.^Cf)* 

 lam notctur efle : 



fin. b C. fin. bQc^{\^.b cQ et 



cot. ^ C c = — coC C f . cot. b cC^ hincquc etiam 



fin. C ^. cof. ^ C f — — cof. C <r cof ^ <• C , 



his 



