[ 471 ] 
PRO? LEM A II. 
Extrcihere Radicem ciibicam ex Binomio mpojjlbtlt 
a -j- V — b . 
S O L u I I O, 
Finge Radicem illam efle x + cujusfifum- 
pferis Cubum, invenies effe x 3 -\~3 x x^ — y — $xy 
—yV~~y. 
Pone jam x?> — % xy~=a, 
& 3 x x^ —y —y V —y = V — b. 
Tunc fumendo quadrata, orientur alterx bin# .Equa- 
iiones, nempe 
x 6 — 6 x*y- Y 9 x xyy = a a. 
— 9 x+y + 6 x xyy • — y 3:=z — b . 
Jam fume differentiam quadratorum, erit x 6 -f- 3 a; 4 / 
+ — aa~\-b j quapropter eft xx+y 
3 3 
— yaa-^-b: pone nunc * aa-\-b — m-> unde erit 
xx -\-y = nij fivey = M — xx> jam nunc in ^Equa- 
tione x 3 — 3xy=a, in locum quantitatis y, fub- 
ftitue valorem eius m~-xx y habebis ^3 — 3^^ 
+ 3 X 3 — a, five 4 ^ 3 — 3 nix — a, qu* eft ipfiflima 
JEquatio, qux prius dedufta fuerat ex JEquatione 
3 _ 3 _ 
V a -J- v 7 — ^4-Vtf — attamen non fe- 
2 X: 
b-j-v a — v __b 5 
quitur ut poffit in .<Equatione 4.x 3 — 3 mx^=a, 
valor quantitatis x cognofci, per fuperiorem ^Equa- 
tionem, quippe qux conftet ex.binis partibus, quarum 
utraque includit quantitatem imaginariam V—b\ fed 
res optime conficietur fubfidio Tabulae finuum. 
Sit 
