Demonjlr. Per Theor. XV. eft 



tang;. r — V =zi£^-X 



et per Theor. XVIII. 



tan r' =z "^- cor.S c of.^S -A) cor.(S -B^ co f. (S - Q 

 3 col. i A co(. ^ B cof. i C " ' 



vnde liquet propoiTtum. Simili quoqtie ratione colligitar 

 cffe 



tang. f' __ fin, (s — a) fin. (/ — ^) fin, (i — f) . 



tang. »• a fin. ^ a fni. ; ^ fin, ^ f * 



tang. / _ c of. (S-A)cor. ( S - B) cof. (S-C) 



tang-. r z cof. ; A cof. i B cof. ^ C 



f. 2S. Hac occafione non praeter rem erit vt 

 oflendamus, quomodo hae proprietatcs inuentae analogae 

 ^int illrs, qnae pro triangulis planis locum obtinent. Sic 

 fi A A B D fupponatur efle planum, habebitur loco Theo- Tab. lU, 

 rematis XI, hoc Theorema: 2BL — ^^4^: loco Theor, ^'S- ^v 



XII. \ero iftud : 



<^ 



g J^ *ys(s - a) fi — h)(s - e1 , 



Theorem. vero XIII. iti ifthoc mutatur; 



BC:=: 



060 



4 V t (s - o) (s - &) (s - c; ' 



vbi area triangnli 



A B D = ^, B L . A D - Vi (i- tf) (J-^) [s-^c), 

 vnde 



4BC.AABDc=^^f. 



Thenremat. XIV et XV. adplicatio ad triangola plana fi- 

 cri quidem non poteft, interim tamen obferuare coauenit,. 



qnia 



