[/78] 
fy to find all the roots to any Refolvend offer'd. 
Now forinftance (siccordm^ to Hu^ldens method) in a bi- 
quadratick ^equation, you muft multiply all the terms begin- 
ning with the higheft, and fo in order by 4>?5 2, i, and the 
laft term or Refolvend by O. whereby it is deftroyed, and 
you come to a cubick iEquation, the fame as Hamop ufes to 
take away the penultimtae Term of the biquadratick, the 
roots whereof being found, and as roots having Refolvends 
raifed thereto in the biquadratick iEquation , are the dio- 
riftick Limits thereof. 
1 8 And if this eafy method were known, we may come 
down the Ladder to the bottom, and fall into irrational 
quantities, and afcend again. Againft which allymetry, an 
-ffiquation might be aflumed low, as a rational quadratick, 
and thence a cubick iEquation formed, whofe limits fhould 
be found by aid of the quadratic Equation , and out of 
that cubick a Biquadratick Equation, whofe limits ihould 
be found by the aid of that cubick iEquation, &c. 
19 ^Equations may be fo continued of twoNomes, that 
both the dioriftickand bafe limits, fhould be rational, then 
fuppofing fuch Equation incomplete, the increaling or di- 
minifliing the roots, fills up all the vacant places. 
(^Whether or in what place one or both iorts of Limits 
fliall loofe their rationality > And what is the nature of the 
roots thus drawn > in this I think you have already deter- 
mined in divers of your furd Canons. 
What Dr. method mention d in Se^Hon 17 Ihould 
be I cannot guefs, unlefs it be either 
To make furd Canons Or good approaches. 
Or that railing Refolvends out of aflumed roots, thofe 
Ihould make a ttore from whence to derive the roots of the 
Refolvend offered. 
Or making quadratick Equations out ot the dioriftick and 
bafe limits, tliofe might be interpoled, by aid ot a Table ot 
figurate numbers, or otherwife thereby, as in quadratick IE- 
quations to'attain two roots of a biquadratick at once, which 
if performed the greateft difficulties are overcome, and why 
Ihould not this feem probable, in regard the Cuwe or Locus^hQ 
the Equation what it will, makes indented porches. 
Suppofe I fiiould propound two cubick or biquadratick 
-Equations, in both whereof all the figns are t. It is propoun- 
ded out of thefe two, to derive a third iEquation, whofe root 
lhall be the .Summ,Difference,orRedangle of the Roots of the 
two Equations propounded. This Mr Gremy a little before 
his death writ word he had obtained and in the follow- 
ing Series for finding the Moity of a Hy perbolick Logarithm 
1 luppofe made ufe of. From 
