^ "3 ) 
An Recount of BOOK S. 
I. TraSlatus Mathematiem de Figurarum Curvi* 
lineamm Qnadraturis ^ Lock Geometricis. 
Antore Jobanne Craig- Londini apud Sam. 
Smith Bcnj, Walford, Soc. KegU Tyfo* 
grafhos. 
THis Treatife cx)nfifts of two Heads. In the Firft 
the Author undertakes to give a General Method 
for deter miaing the Quadratures of Curvilinear Spaces^ 
and this he fliews may always be done by finding ano- 
ther Curve-line from the known Property of its Tan- 
gent ; which Curve-line he therefore calls the Quadratrix 
bf the propofed Space. Now this Quadratrix (for all 
Spaces comprehended by Geometrical Curves ) is either 
a> Geometrical or a Mechanical Cure-line: And accord- 
ingly he divides the whole into two Parts. In the Firft 
of thefe be treats" of fuch Spaces, whofe Quadratrix's 
are Geometrical Carves, where he lildftrates his Method 
Iby a great variety of Examples; difcovering in feveral 
of them a new Method ot finding Infinite Series's (with- 
out the trouble of Divifion or Extraftion of Roots) by 
affuming an Arbitrary Series with unknovvo Coefficients, 
which are eafity derermined in the Progrels of the Pro- 
bkm. And finfse the Publication of this Treatife we 
have feme Inftances of the like Method of finding 
by that excellenr Mathematician, Mr. LeihnitZj Printed 
in the Alia Eruditorum of April^ ^ ^93- Afterwards he 
gives a Method of comparing the^r^^'xof Figures with 
the fimpleft Figures of the lame kind ; from which he 
deduces many Theorems, each of which do exhibit the 
Qaadratures of an Infinity of Figures without any trou- 
R ble 
