140 
DE FORMIS SECUNDI GRADUS. 
Per hanc vero substitutionem F transit in F': quare per substitutionem (8) 
etiam G transibit in F'. 
2. Ex valoribus ipsorum e, b, d invenitur a'e-\-yb— ad = 0, sive prop 
ter d= — a, na!e-\-naa-\-nyb=. 0 ; hinc ex [7], nae-{- naa =.mye-\-my a 
sive 
[na— wy)(i = (my — na') e [12] 
Porro fit anh — — am[e-\-d), ymb = — m [a e -J-ad) adeoque 
(na — my)b = [a—a) me [13] 
Denique fit ye— ya-\-ac=0: hinc multiplicando per n, et pro na substi 
tuendo valorem ex [8] fit 
[na — my)c — (y — y ')ne [14] 
Simili modo eruitur fi'e-\-hb — fid = 0, sive nfi'e -f- n^b -f- nfi a = 0, adeoque 
per [7 ], n fi'e n f) a — m S e -j- m 8 a sive 
[n fi — m S) a — [m h — nfi')e [15] 
Porro fit finb — — fim[e -\-a), $mb = — m [6'e -)- b a) adeoque 
(w6 — mS)b — [F — t>) me ¡16] 
Tandem S'e — da-(-E>c = 0: hinc multiplicando per n et substituendo pro na 
valorem ex [8] fit 
(n6—mS)c = (Sftyne [17] 
lam quum divisor communis maximus numerorum a, b, c sit r, integri 
31, 33, Qt ita accipi possunt, ut fiat 
«a + ©6 + (Ec = r 
Quo facto erit ex 12, 13, 14; 15, 16, 17 
21 (my — n a') -f- 23 [a'—a) m -f- Qi (y — y)n — -y [na — m y) 
21 [m $ — n ff) -f- 23 (6'— 6) m -f- (£ (8 — $) n = ~[nt) — m S) 
adeoque ~ [na — n y), ^ [n6 — m S) integri. 
Q. F. D