Second Cafe of the Cuhich Equation x^-qx-r. goy 
a proportion that the rectangle under its parts fhall be e- 
qual to any quantity that is lefs than the fquare of its 
half. Therefore, when r is greater than or - is 
3^3’ 4 
greater than q —, it is poffible to divide the line, or root, x 
into two unequal parts of fuch magnitudes that their 
re&angle, or product, fliall be equal to A This obfer- 
vation is the foundation of cardan’s rule for the refolu- 
tion of the equation x^-qx-r in the firft cafe of that e- 
quation, or when r is greater than or - is greater 
3 
than - ; the invefligation of which is as follows, 
27 w 
P R O B L E M, 
5. To refolve the Equation x^x-qx-r, when r is greater 
than or - is greater than 
.3 v 3 4 27 
SOLUTION. 
Since r is fuppofed to be greater than and con- 
fequently (by Obf. 5.) ~ [ s greater than -, it is poffible 
for x to be divided into two unequal parts of fuch mag- 
nitudes that their rectangle, or product, fliall be equal 
to — . Let it he conceived to be fo divided ; and let the 
3 
5 U a greater 
