f no ) 
coniequently two Changes of the Signs, whatever Sign 
is placed under the fecond Term. 
I * 
4 ‘ 
Schol. After the fame manner, it may be demonhrated, 
that in a CubicAquation,whofe Roots are all real, if the 
fecond Term is wanting, the Cube of the third Part of 
the third Term taken pofitively, is always greater than 
the Square of half the lafl Term. Suppofe that the 
Roots of the itquation are — c, or — 
+ and that then the fecond Term in the JE- 
quation will be wanting, and the other Terms will be 
expreffed thus : ^ 
t 
yi.h c 
- — hey 
. . . 
The Square of l-^c is always pofitive, fince h and c 
are real Quantities. Suppofe it, {yiz. 
equal to JD, then D he, and f^c'' 
= £>+ 4 h e. Therefore -f- ic be j^Dh- 
27 
^7 
Z»5c5, and ^2 c^x 
b -(-c D 
+ b^ c5. Now ’tis obvious 
. ^ £)5 
that — 4 - — — + D k e^ is greater than ^ 
+ h^ e\ fince D is pofitive, and h e alfo pofitive, -^and 
c being Roots having the lame Sign. Therefore the 
Cube of of the third Term having its Sign changed 
j 5 * 
is always greater than the Square of 
^ 17 ' j 
half the laft Term 
quation ^ pofitive, or if it 
be 
