25 ° 
) 
( 
ponatur D 3 — F 2 = G , æquatio G (y 3 -4. 3 Cy 
-4- 3 C-y -4- C 3 1 
— 3 — 3 = ° erit perfekte coincidens cum 
— 2B\ 
(D 3 — A 3 ) y 3 -f- 3Z? 2 £3/* -4— gZ^Z? 3 y -4— E'—Oj five e- 
rit D 2 E— GC , DE* — (C 2 — A) G, E 3 = (C } — 3/IC 
— 2Z?) G. Ex his (equitur D : E : C : C 2 — A : : • 
C* — A : C 5 — 3AC — 2 B , five (C 2 — A) 2 = C (C 3 
— 3^C — 2Z?), vel C 4 — 2 AC 2 -4- A 2 = G 4 — 3 AC 2 ~ 
zBC, adeoque AC 2 A-zBC ■+ A 2 = 0. Poterit ergo C 
per æquationem quadraticam determinari, quæ dupli¬ 
cem ejus valorem exhibebit ejus conditionis, ut fit y 3 
(Ç2 _ 
+ 3 Cy 2 -4- 3(C 2 —A)yA-— — f — = 0. Eandem ve- 
ro æquationem multiplicando per C. (1 C 1 — A) — C 3 
— AC, erit C 3 y 3 -+- 3 C 2 y 2 ( C 2 — A) 3 Cy ( C 2 — A) 2 
+ (C 2 — A) 3 = ACy 3 , adeoque Cy+C 2 — A—yFAC , 
quæ æquatio efi: triplex ob triplicem quantitatis AC ra- 
3 —- i - 4 - A — 3 5 
dicem Cubicam, nempe AAC, - F AC, 
m 2 
~ l ~zJL l C AC. Dato itaque C per æquationem 
2 
AC 2 -4- 2 BC -4 - A 2 —0, ex utravis ejusdem radice da¬ 
buntur tres ipfius y valöres, fimulque tres æquationes 
X = y -4- C, hæ vero eædem repedentur in fingulis i- 
pfius C valoribus, ut ex infra demonftrandis vel cal¬ 
culis inftitutis colligetur. 
§. III. 
aequatione Cy + C 2 
A — y À AC pro y 
3 _ 3 _ 
fubftituatur x — C, erit Cx — A — x CAC — CFAC, x 
A — CFAC 
IL ” ' 4 
C — CAC 
Afllimantur jam A—a 3 , C—h 3 , erit 
x 
/ 
