Second Cafe of the Cubic k equation x % -qx~r. 905 
Obs. 2. While x increafes from V q ad infinitum, x z 
will increafe continually from qs/ q ad infinitum , and qx 
will increafe continually from the fame quantity q-f q ad 
infinitum. 
Obs. 3. Alfo, while x increafes from f q ad infinitum, 
the excefs of x z above qx will increafe continually from 
nothing ad infinitum , without ever decreafing. For, if 
we put x to denote the increment which x receives in 
any given time, either fmall or great, qx will be the in- 
crement which qx will receive in the fame time, and 
3x*x + 3xx z +x* will be the increment of x z in the fame 
time. Now, fmee xx is always greater than q during 
the whole increafe of x from being equal to s/ q ad infi- 
nitum xx x x will be greater than qx during that whole 
increafe. Therefore, d fortiori, 3X*x+ 3xx z +x z (which 
is more than triple of xx x x) will be greater than qx ; 
that is, the increment of x z will be greater than the con- 
temporary increment of qx during all the increafe of x, 
Confequently the excefs of x 3 above qx, or the com- 
pound quantity x z -qx, will continually increafe, with- 
out ever decreafing, while x increafes from V q to any 
greater magnitude. 
Obs. 4. Since the compound quantity x z -qx increafes 
continually at the fame time as x increafes ; and, when 
Vol. LXVIII, 5 U * is 
