If fuch -Equation be encombred with fradtions they are 
all removed at once, by multiplying moft conveniently, by 
the leaft number that is divifible by the Denon7inators of fuch 
fractions » hence aUb the infinite Series before mentioned 
(and others) are reduceable to Logarithms 
26 Where Equations have all their terms adfe<5t:ed with 
the famelign both v t or ) Mr. Nnvton and Mr. Oregory de- 
ceafed have affirmed they are all reduceable to fome pure 
high power, which is of lingular ufe in the infinite Series. 
And a Learned G^rw^?/? where this cannot be done, hath af- 
ferted that they may be reduced to a higher power, with a 
variable Coefficient, which is the root fought with a com- 
mon addend or fubd? icend. And even this would render an eafy 
tentative Logarithmetical way for attaining the root. 
27 If but one Root of an liquation can be found at a time^ 
then queftionleis a better Method is not yet attained, then 
what IS mentioned in the printed propofai about Friuting Mr- 
Bakers Treatifes therein mentioned 
28 Laftly, as to Conftrudions for Equations, the follow- 
ing Probleme leems to be univerfal. 
Any two analy tick 0^rx;^c {viz.) fuch as wherein the Habi- 
tude between the Bafe and Ordinate may be expreffed by an 
iEqiiation, being given in Magnitude and Pofition, and from 
the points of their in terfeition ordinates let fall to the Axis 
of either figure, or upon parallels to the faid v^^c-^^ the inqui- 
ry is of what iEquation thole ordinates are the roots > 
Dr. Barrow liked the pro^oiition as well grounded, and left 
a difcourfe about doing it in the conick Sections, in which 
there are 3 cafes,either the axes areparalleLor being produced 
concur, beyond the vertexes of the figures without > or o- 
therwife interfed; within the figures, -/t^/. Gngory entred on 
the fame contemplation, but death deprived us of the be- 
nefit of his thoughts- 
Of Arialytictc W GeometrickJ Om^es there are innume- 
rable forts> of which I fhail mention one or two kinds* 
Between an Arithmetical Progreffion and its fquares, or 
between, its fquares and its mbes, or its cubes and Biquadra- 
tics, there may be interpoled as many Arithmetical or Geo - 
rnetrical means as you pieafe - and thence Loca or Cur-ues de- 
riv'd, which fome call yaf a'^oicids or Farahoiafiers^. fee Gregones 
Geometrice p^rs unmrfaUs printed ill in Quarto^ 
. ' Pofifcript exp'aimng Sefr/on the ^i^b. 
' After you have obtained the Cube roots of Cardans Bino- 
mials, according to Scbote?^^ in Des Caru<^ or Kcrh^ if you 
change the Smesof the rational parts of thole roots^ as alfo 
tl\e 
