( 80 
monftrate and apply it to this Subjed in a different 
Manner, I fhall add a fliort Account of it. 
Lemma X. If you transform the Biquadratick 
— A AT* + — Ca;+D=o into one that 
fhall have each of its Roots lefs than the refpedive Va- 
lues of a; by a given Difference e j fuppofe y = 
or X =z e and the transformed Equation, the Or- 
der of the Terms being inverted, will have this Form. 
-U 4 e^v+6e^ -4- -4- = o. 
^ A e* — 3 Ae*y — 3 A^j/* — A y* 
Where it is manifefl, 
I. That the firft Term ^ A^*+ ^C^-|-D 
is the Quantity that arifes by fubftituting e in Place of 
X in the propofed Equation a*’ — Aa’^-J-Ba’*— i 
C .V “P D. 
a. That the Coefficient of the fecond Term 4^* — 
sAe^ + xB^i — C is the Quantity that arifes by 
multiplying each Part of the firfl ~ A^^ + B^* 
— C ^ -j- D by the Index of e in that Part, and divi- 
ding the Produdl by e. 
3. That the Coefficient of the third Term 6^* — 
3 A ^ -j- B is the Quantity that arifes from the preceed- 
ing Coefficient 4^’ — 3A^*-p ^Be — C by multi- 
plying each Part by the Index of e in it, and dividing 
the Produd by z e. 
4. That the Coefficient of the fourth Term arifes in 
like Mariner from the preceeding, only you now di- 
vide by 3 ^ ; and in general, the Coefficient of any 
Term may be deduced from the Coefficient of that 
Term which preceeds it, by multiplying each Part of 
— C^ — 
+ D 
2 
the 
