( 78 ) 
ed by be equal to the Produd of the firft and third 
o 
Terms, yet in that Cafe, in applying Sir Ifaac New- 
ton's Rule, the Sign — ought to be placed under the' 
fecond Term, and the fame is to be faid of the Square 
of the fourth Term. The Rule deduced from the vih^^ 
Propofition fhews four Roots imaginary, when ^ is 
greater than b, and alfo when is greater than is 
but a Rule founded on the xi^^^ Propofition, flaews the 
four Roots to be imaginary always when a exceeds b^ 
or when b^ exceeds 9 ; from which the Excellency 
of this Rule above thefe two is manifefl, I have faid 
fo much of Biquadratick Equations, that I mu ft leave 
it to thofe that are willing to take the Trouble, to 
make like Remarks on the higher Sorts of Equations. 
In inveftigating the preceeding Propofitions, when I 
found my felf obliged to go through fo intricate Cal- 
culations, I often attempted to hnd fome more eafy 
Way of treating this Subjed. The following was of 
conhderable Ufe to me,and may perhaps be entertaining 
to you. By it, I inveftigate fome maxima in a very ea- 
fy Manner, that could not be demonftrated in the com- 
mon Way with fo little Trouble. 
Lemma V. Let the given Line AB be divided 
any where in P and the Redangle of the Parts A P and 
P B will be a maximum 
when thefe Parts are e- A — — p B 
qual. ’ - 
This ismanifed from the Elements of 
Lemma VI. If the Line A B is divided into any 
Number of Parts AB, CD, DE,'EB, the Produd of 
ail thofe Parts multiplied into one another will be a 
max- 
