[-185 3 
An account of a Book. Methodus Yiguravum liheis teeth & 
cuYVts comprehenfarmi qnadraturas deiermtnandt Aupfjorc 
J, Craige. 4X0. L ondini 16 
^T^^^ great ufe of drawing the Tangents of Curve 
^ Lines^ has made the moft famous amongft tlie Mo- 
dern Matiiematicians endeavour to hud out General Me« 
thods oi finding the Tangents of Curve Lines, as may be 
feen from the (everal ways invented by Des Cartes^ Mohfieur 
Ierwat,ShfasjDr. Barrowy Dr. Waltis, Tfchurnehuys^ and Leth-^ 
nitm; But as yet none has attempted to invert this pro- 
blem generally, that is/ having the Tangent to find the 
Curve Line whofe tangent it is. Therefore the Author of 
this Trearife perceiving that the doing of thi^ would give a 
General Metho4 of determinating the (Quadrature of any 
CurviHnear fpace, has laid down a rule for inverting Slufms 
his method mentioned in the FhUofGfhlckXrm^^^ Num.. 
90. He has illuftrated his Method of Quadratures by feve- 
ral Figures which have been already conlidered by Geome- 
ters. As fpr the Circle & Hyperbola, he alTerts that their 
indefiaite Quadratures are impolTible/ and therfore in thefe 
& fuch like cafesj he exprelTes the Area by an infinite Series, 
, ,which is eafily done by iiis Method, except the Series con- 
fift of irratibnal termes, for in thefe he has recourie to Leil^- 
nitius his method of finding Tangents, where the Calcula- 
tion will be more tedious.^ By his relolvmg the Area of the 
Hyperbola into an infinite feries, he comes to the lame ex- 
preifioa wdththat oi N. Mer-cAtor- And in meafurmg the 
Zone of a Circle, his expreffion falls in with that invented 
hy y^xAjA^ic Newton, as Nvc, D^vid Gveg ry relates in his 
Treatise. He has fubjoyned a Method of meafuring the 
. Cyrve Superficies niade by the rotation of any Curve upon 
its A.as\ with a fmall Animadverfion on the Method of 
^j^^aWi^w^ J, pub hilled ia tiiQ AcJa L/pJiif^fia EriidticrumQ? 
168 . 
6mce the Pu lie at ion of this Trcatifc, the J-itLoitr is p'e.ifed 
tQ m^ke the follmvim Addition. 
Z AdJi 
