go€ 
Extension of Cardan’s Rule to the 
x is equal to — , x 3 , , 7 
1 V3 ' 3V3 V 3 3 v 3 3 V 3 
it follows that, if x is greater than 2 -~ y the com- 
pound quantity x z -qx will be greater than ~j, r and, if 
; „ v : e /■_ _ 2jhj _. 8 gVj 6 ? vV 
^ q a/ 3 a/ 3 x \/ x ' 
is lefs than f~,‘ the faid compound quantity will be 
Vi 
lefs than and, e converfo, if the compound quan- 
tity x z -qx, or,- its equal, the abfolute term r, is greater 
than the value of x will be greater than and. 
Vi 
if x l —qx i or r, is lefs than htfl the value of x will be 
3/3. 
lefs than ~y ; or, if ^ is greater than ,x will be great- 
er than J — and, if - is lefs than will be .lefs than 
Vy' 4 . 2 7 
✓3 ' 
Obs. 5. When r is greater than yyy, or ~ is greater- 
than y, and confequently (by the laft obfervation) x is 
greater than xr will be greater than y, and — will 
be. greater than -y. But y is the fquare of. y. There-* 
fore when r is greater than jyji or y is greater than 
the fquare of half x will be greater than -y. But (by 
Euclid’s Elements, Book II. Prop. V.) it is always pof- 
fible to divide a line, as x, into two unequal parts infuch 
a pro-* 
