( 1^6 o ) 
lito noftro fadet fatis. Ptita fi in praefenti cafu fiat 
a = 3 , erit juxta Theorema k = ( p — a + 
V p 1 + q — a’- — =2 — 3 + Y 44 22 . ^ 
~ ■ — i ± (y 2 5 ) 5 =0 4 vel — - 6 > & x ~ Cp 4 - a + 
v' p 1 + q ■ — a} 4 - — - = 2 + 3 Hr V 4 4 — — . 9+12 
3 2 j 
= 5 + (V 64) 8 —J 13 vel — 3, quas fant iEquationis 
data Radices quatuor, 
2, In iEquatione x 4 = 20x? H- 252X 1 ' — - 6592* 
+ 21312, erit p = 5, q = 176, r = — 384, 8c 
3 = 13072. Hine p l 4 -q = 201, 2pr 4s = 9232, 8c 
r == 147456; 8c indea 6 = 201 a< —9232 a 1 4 147456. 
Jam in Theoremate pro Cabicis erit p = 67, q = 
Scr = 65219 ; eritqae Binomii652i9 +V 3 8 88930707 2 
Radix Cubica -- +V Igitur a 1 = 67 4 77 — 144, 
2 12 
five a = 12 ; 8c proinde x — 5 ■ — 12 + 
+ 64 = — 7 4 (V 121 ■) 11 = 
V .25 4 176 — 144 
4 vel • — 18, 8c x = 5 4 1 2 + V 25 4 176 
17 -t V 
144 — 64 
lies. 
Hojus autem Theorematis Inventio eft hujufmodi, Ex 
duarum iEquacionum Quadraticarum z 1 4 2az -- b = o, 
8c z 1 — 2az — c = o, in fe irivfcem mnldplicacio ne, 
^Equati onem confie io Biqjuadraticam z* = 4 a 1 4 b 4 c 
* z £ 4 sac - — 2ab * z — be, cui terminus fecundusdeeft, 
qnamque hn.ic ^Squationi z« = ez 1 + fz 4 g ftaruo seq ;i- 
poliere. Unde primo 4 a J 4 b 4 c = e five 
b = e — 4a 3 — c. Secundo 2ac • — 2ab = f, hoc % 
f e 
aae — aae + 8 a 3 + 2ac == f, nvec = —4 — — . . % 
4a 
8c 
