( M5 ) 
required. The fimpleft Hyperbolic Area may indeed 
be fquared by the fame Operation taught in the Au- 
thor’s fourth Propofition ; but the fimpleft Elliptic A-- 
rea requires fomewhat more : Thole that are more 
complex in both Kinds (which generally happens) re- 
quire an additional Trouble to reduce them to the fim- 
pleft : to Iquare them by infinite Series is ftill more 
operofe, and does not anfwer the End of Geometry. 
Upon the whole therefore it may deferve to be confi- 
dered, for what Purpofes lliould Problems be always 
conftru(fted by Conic Areas, unlefs it be to pleafe or 
alTift the Imagination. The Defign of Theoretical 
Geometry differs from Problematical ; the former con- 
fifts in theDifcovery and Contemplation of the Pro- 
perties and Relations of Figures for the fake of naked 
Truth ; but the Defign of the latter is to do Ibmething , 
propofed,and is belt executed by the X^zf^Apparatusoi 
the former. 
The Logometria was firft publillied by the Author 
himfelf, in the Thtlofoph. TranfaVt. of the Year 1714*. 
No 338. But his Logometrical and Trigonometrical 
Theorems abovementioned were not publilhed till after 
his Deceafe. Thele Theorems make the lecond Part 
of the Book, and are calculated to give the Fluents of 
Fluxions (reduced to 18 Forms) by Mealures of Ratio’s 
and Angles ; in fuch a manner, that any Perfon may 
perfecftly comprehend their Conltriuftion and Ule, ^ 
though altogether unacquainted with Curvilinear 
Figures, as exprelfed by ^Equations. And this Cir- 
cumftance does allb render the Application of them ^ 
to the Analyjis and ConJfruBiou of ’Problems ex- 
tremely ealy. Of this kind the Author has given a 
great many choice Examples both in abftrad: and phy- 
fical Problems ; which make up the third and laft Part 
of the Book. 
The 
