that Science s that in it the Author hath delivered a New Mtthd 
Analytical for giving the Aggregate of an Infinite or Indefinite 
converging Series t and that from that ground he teaches a Me- 
thod of Squaring the Circle, Bllipfis and Hyperbole by an Infinite 
feries, rfience calculating the true'dimenfions as near as you pleafe : 
And laftly, that by the fame Method from the Hyperbola he 
calculateth both the Logarithmes of any Natural Number 
afliign'd, and vie ever fa, the Natural Number of any Logarithme 
given. 
• Only a few of thefe Books were printed by the Author for 
his own ufe, and that of his Friends, and a Copy fent over 
whereby to reprint it here, which is now a doing. 
The Mathematical Mr. John Collins, upon a more particular ex* 
amination of this Book, communicated what follows, concerning the 
fame. 
The Authors Computation of the Area of a Circle agrees 
with the Numbers of Van Ceulen-, and his computation of the 
fupplemental fpaces between the Hyperbola and its Afymptote by 
Paralels to the other Afymptote*, is correfpondent to what Gregory 
otst. Vincent and his Commentators Pr^^^/V Ay ns comb mi Alphm- 
fe de Sarafa have demonftrated concerning the Logarithmes, as 
reprefented by thofe fpaces, viz. That if one Afymptote be di- 
vided into a rank of continual Proportionals, and it paralels to 
the other Afymptote be drawn paffing through the faid rank, and 
be terminated at the Hyperbola, the fpaces contain'd between 
each fuch pair of paralels, are equal to each other, and fo added 
or conceived to be one continued fpace, may reprefent the Los 
garithmes or the faid proportionals, fitted in psrakl to the di- 
vided Afymptote, do the like-, by reifon that a ReBangk ap- 
piy'd to the feveral Terms of a Geometrical Progreflion increif- 
ing, renders another in the fame i^/tfdecreafing : And both per- 
formed by the above-mentioned Analytical method of convey- 
ing complicated P^wcircumfcribed and infcribed in the (ecter 
ot a Circle, Ellipfis or Hyperbola, which he alTerts to be quan- 
tities like Sards, not abfolutely to be exprefs'd in Numbers. 
And it being manifeft, that the making of the Table of Loga*- 
rithmcs is in eifedi the fame thing as the computing of Areas 
of thofe fupplemental fpace, the Author accordingly applies It 
thereto 
