( 2056 ) 
meiry. confifts m demonftrating the proprieties of ^ 
there is no fuch propriety, but it belongs to it by fome genuine 
and intrinfick principle.eafily to be found out by the Analyfis or 
Ce^ejir of Quanticy. By which way he Judgeth, that Geometry 
may be exceedingly contrafted , forafmuch as very many 
thingSjleparately demonftrated in the received way, may then 
be evinced joyntly by one plain and eafy Demonftration 5 con- 
fidering that, where the fame propriety belongs to various 
<]uantitiesand figures from the fame intrinfick Principle , whe- 
ther they be Plain, or Solid, or Right lined, or Curve, orMixt; 
nothing hinders, but propriety may be Demonftrated of 
ihem all by one onely Demonftrniion* 
And hence this Author is inclinable to lay afide thofe many 
Divifionsof Geometry, as are made by Authors, viz. intoTVi- 
gonometrj, Planometry 2inA Stereometry and peculiar and pre* 
lixe Treatifes of Corneal SeBions 5 ot the Spfj£re and Cylinder 5 
©f £;p«e/ of divers kinds 5 of Plain 2ind Spherical Triangles of 
a Solid Angle :f of Proportions and Proportionalities^ &c : e« 
fteemingjthat a more convenient Divifion will 1 erve his Defignj 
whence he comprifeth this whole Syn&pjts in two parts* 
The treats of the £/^6^e»// for Beginners., and contains 
6{parts : in the firft whereof are deliver'd the Definitions and 
Explications of Terms, the Axioms, and Poftulata. In the fe- 
condj are explained the Cenefir ^nd A^alyps o( Figures , and 
their different Clajps. In the third, are demonftrated the Ele- 
ments of Lines and Angles^ In the fourth, is treated of Ratio's 
and Proportions. In the fifth, are confidered the Products of 
the Segments of a line^ multiplyed into one another. In the 
fixth, are handled the remaining Elements, 
In the Other^ he proceeds to the Demonftration of higher 
iind abftrufer things 5 and this part he divideth into feveral 
CUjJesy each of which contains all its homogeneal figures, Right- 
Jin d or Curve, Solid or not Solid 5 there being fb many feveral 
Rankj^ as there are different ways of their Generation. Thefe 
Clajjes are here diftributedinto two forts^thei?»e contains thofe 
Figures, whofe Generating quantity is drawn either into the 
whole Altitude, or into its Rational or Commenfurable Seg- 
snent, for the j^quation of the Figure 5 the other is of thofe ^ 
v/hofc Generating quantity can only bedrawainto an Irratio- 
