C"4) 
ble of Calculation : And withal (hewing to what Theorem 
any propofed Figure is to be referred, and how the like 
Theorems may be ebntinued by the help of his general 
Method. He concludes this Firft Part with a Difcourfe 
concerning the Analytical Expreflion of Quadratures 
wherein is ihewn, that though the^z-^^anfwering to the 
Ahfcijja be that which is commonly fought, yet the ge- 
neral Quadrature found by his Method, is for the mod 
part eithsr greater or lefler : Therefore he gives both a 
Geometrical and Analytical Rule for knowing whether 
the faid general Quadrature be deficient or exceeding 
and what that deficient or exceeding Quantity is. 
The Second Part treats of the Quadratures of thofe 
Spaces, whofc Quadratrix's are Mechanical or Tranfcen- 
dent Curves, as he {^{iQtMt.Leihmtz) choofcs rather 
to call them where he gives a general Method for find- 
ing their Tangents. And having given a Rule for de- 
fining the Tranfcendent Quadratrix of any Algebraical 
Curve (that is not capable of a Geometrical one) he 
Illuftrates the fame by finding the Tranfcendent Qua- 
dratures of ih^X^itdQ^ Hyperlola^ and two other Figures. 
There is added at the end, the Author s Anfwer to a 
Letter of Mr. P. T's. relating to a Controverfie between 
them concerning a Method of Quadratures, publiflied 
by Mr. D. T. in the A5la Eruditorum, 
The Second Head of this Treatife is concerning the 
Geometrical Places^ wherein is fliewn how to deterinine 
any Solid Place, by comparing the Equation with a ge- 
neral Theorem comprehending all Places of that kind: 
Whereby arc avoided all thofe many Rules about the 
Redudlion of the given Equation, and the variety of the 
Signs -j- and — , which have hitherto rcndred this Piece 
of Geometry fo troublefom. 
It Thi 
