102 



f, g, h per illas a, h, c exprimantur. ITnnc in fincm 

 voccnuis angulnni A F B — a, et ex tiiangulo A 13 F habe- 

 biniLis hanc ae(jnahtatem 



A B- — A FM- B F= — 2 A F . 13 F cof. w, 

 al e^: tiiangiilo A C F habebimus 



A C- _ A F- -4- C F- -I- i A F . C F cof. w, 

 quae diiae aequahtales additae praebent 



A B' -h A C zn 2 A F= -I- 2 B F' 



live 4cc-+-4bb= ^ f f -^ - " o> unde colligitur ff~2.cc 

 H- 2 6 6 — a a. SimiU modo crit 



gg:=:2aa-\-2cc — bb et lili~iaa-{--bh — rc, 



quocirca pro litteris a, ?), c, riusmodi numeros quaeri 

 oporlct, vt iftae trcs formulae icddanlur numcii quadrali. 



5- ,'5. Antcqnam lianc invcftigationcm fufcijjiamus, 

 confulcremus cafnm ni.iximc mcmorabilcni , quo bh -t cc 

 n: ? fl a; tum cnim crit f J ~ :i a a ., five f~a r 3, tum 

 vcro g g nr 3 cc, fjve g — cy 3; ct /? /i — 3 fj /j, {]vc 

 h — h \/ 2 ■, fj'iae cfl infignis proprietas liuiusmodi triangu- 

 lorum, in qnibus 2.a a — h h -{- c c. 



§. 4. Piactcrea in gcnere obfervcmus cffe 

 ff-^Kfi 1 /j /i — 3 (fl rt -+- l» 6 H- c c). 

 Cum igilur fit A O — ^ /", mulLij)licando pcr '!, ciit 



A O' -I- B O'- -]- C O' = J {a a-hhh-\-c c), 

 /icque palet fcmpcr clTe 



A O- -h B 0= -f- r O' — \(B C* -I- A C -}- A B'), 

 quae ijropriclas cft ctiam ma.ximc notatu digna. 



5. 5. 



