tion^after a manner that is not lefs general than fimpleand cafieto 
underftand. 
And fince this Refolution of the Powers doth notalwaies af- 
ford Commenfurable quantities, or fuch as are exafily known, but 
fomecimes Ineommenfurable ones; thefeare explicated in the fourth 
book, together with all the Operations that are made concerning 
them. 
The fifth treats of the Coniparifon of Proportions : Which part 
he finds to be fo vafl and fruitfuljand the ufes thereof to be of fuch 
an extent in moft Sciences , that there are few, if any, that can be 
well taught without it. The Geometrical Equalities and Propor- 
tions,which are one fort of the gems of Equalities, are the things 
that render this part fo confiderable,and for the elucidating of which 
our Author hath moft of all employed himfelf in this work; and 
the four lafl: books of the feco^d parr are nothing but afequei of 
what hath been faidof the Equalities inthcjifih book of thejirfl 
parr. 
Now in the faid/^>«rbooks he fettles firft the Grounds of Analy- 
fis. i\7is'jc/,afcer having there given fome/W^'^ of the method of Bia- 
fhantw^ and of that of Vieta^ he is particular in explainingthe me- 
thod of Dw-C^r^ei, which he efteems to be the moft general, the 
moft fertil , and the moft eafie of all. Yet feeing that this famous 
Man hath not demonftrated,nor fo much as explained,ail the Prin- 
ciples which he hath made ufe of, our Author intimates, that the 
Reader will not find in his Writings the fame advantages for under- 
ftanding his Analyjis^ as may be had from thefe Elements. For, after 
he hath clearly explained and demonftrated all thofe Principles, he 
thence deduces in order not only all the Difcoveries made by Des- 
Cartes, but alfo other new and more ufeful ones. For it may be feen 
in the /4/? book , that thofe new Difcoveries furnifli Rules that are 
much (horter than the Cartejim^ and one may even draw analytical- 
ly from them much of certain and very univerfal knowledge,which 
he did not believe could be difcovered without the aid of Parabo- 
lical lines, or fuch other as belong to the GeometrU compojita, as the 
Hyperbolickj&c. 
Bat, forafmuch as the Author efteems that thefe Elements are 
principally written for Beginners , and even fuch as have not fo 
much as the knowledge of Arithmetick, hedefires that fuch Rea- 
ders would have their pen at hand , to make themfelves the opera- 
tions of all the different Examples, deliver'd in great number, his 
Oooo 2 aim 
