20 CAROLI JOHANNIS MATTHES, iienr. fil. 



b^ + c^ — a'^ 2/ 



( form. 1 et Tlieor. I. Coroll. 3.) 

 = ^?^>^' (3) 



4/ 



Eodem modo : BG = ^(fili^i=±) et CG = ''(-'+ ^'; - ^'^ 

 quibus per se invicem muliiplicandis, hatebimus i 



AG X BG X CG = - -(^' +;; - "' ) X '^"' +;; - ^^ x ^^"' +/; - ^'^ 



4/ 4/ 4/ 



- «^'^ X 6475 



4RIN > 



= - ^, „ ■ (Theor. I. Coroll- 1. et form, a) 



^RN ^6I^Ria'- + ,^ + c'--8RO ^ ,„ ^, 



ibl- 16/* '^ 



idem quod invenimus in Theor. XV. Coroll. 2. 



Reliquarum perpcndiculorum partium EG , FG, DG, valor ut innotescat , consi- 

 derauda nobis sunt iriangula inier se similia GEC et BDC , quae dabunt. 



r„ BD X CE a' + c' — b' a'' + b^ — c- 2/ 



i-G = -,— := X . • — 



CD 2c 2a c 



(a° + c- — b^) (a^ + &^ — c^) a* ~b* — c* + ib^C 



W ' — 8a/ ^> 



Eadem ratione : FG = ^'' '^ "^ ~ "gjf :^ "' " ^-^ = ^' ~ "' ^j' ^ '"''' 



et- DG — C^" + ^»^ — g') (c» + fl° — &') _ c" — a'^ — M + 2a''& '' 



8c/ — 8c/ 



Factum continunm erit ; 



EG X FG X DG = (^' + «^^ - ^°)° (c + a' - ^^')' C«° + &' - c^Y 



5i2abcl^ 



- ^^rf = ^^mr* ^^°''"- "•> 



_ {a'' + b^ + c^ — ZR^Y 

 ~ 8R 



idem in quod incidimus Theor. XVI. Coroll. 

 AG si per EG multiplicetur , efficitar . 



AG X EG = <l>^ + e^-a:) X i-'-^c'-^'Ua^ + b^-c') ^f,,^. 5 «t 4,) 



