104 



P/+At4-/i_ 



quibiis valoribus substitutis iieqnalitas identica ^^ m 

 indiict hanc rormam : ^a-f-juj "r ce ^ » qnae est ipsa 

 aequalitas dcmonstranda. 



Tab. I. g. i5. Ilaec insignis propiietas etiam soinpcr locnm 



° ' habct, ubicnnquc piinciuni O extra tvian:j,nlnm accipialur, 

 vehui in fimui 3 , diinimodo dcnominationes per literas 

 An, B5, Ce rite staluantur. Ita in hac figura pio recta 

 A a eiit A Or: A, Ou-a, at pro rccla B6, posito BO = B, 

 erit 05r=: — 6, atqiie pro recta Ce poni débet COnC et 

 Oc:::!: — c. Ilinc ergo erit AanzA-f-a; Bb:=zB-f-/;; 

 C c:r= — (C-i-c). Cum iiîitur semper sit — — -i- r — + -^ ,,ri^ l. 

 erit pro iineis in ii^tua ductis ^ — ^ rz i. 



§. i6. Ilac autem proprielate stabilita satis commo- 

 de area totins trianguli ABC invcniri poterit. Cum enim 

 sit area triangiili AO B =:= î AB sin.r, ob sin.rzzCR ista 

 area erit AOB zr: i, A BC. R. Simili modo area A OC rc- 

 perietur — ïABC.Q, et area BOCzn ^ ABC .P, sicque 

 tota triangiili area erit rz: i ABC (P + Q -|_ K). 



^. 17. Postmodum vero porro posuimns P r=: -^ ; 

 a— "".f- Rm"/. Erat autôm F — --: G— ^-^ ; H — ;,- 

 {§. 9); unde fict area trianguli =i ABCA(^-^--t-p^_,-^^^-). 



Demonstra\'imus autem esse -~] h,,-' — t-r-'r— ^^ '? quani- 



obrcm area nostri tiianguli erit zz: i ABC A. Praetciea 



