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fenfes that it leaves it in a manner altogether to it felf, and affix- 
ing it to run through all the proportions of Quantities which it 
cxamines,in a dextrous,expedit and eafie manner: So that nothing 
efcapes the underftanding in the fubjeft under confideration ; and 
the clear anddiftinfl neamefs of its ratiocinations alwaiesdifco* 
vers to it the fhorceft way of refearched Truths^a^many of then?? 
as it can come to know , or the means which it wants to attain 
them, if it cannot know them. 
He takes notice, that, there being particular Sciences that de- 
pend from Geometry^ there are thofe that confider the fame as the 
general Principle of all knowledge: And thar, forafmuch as Geo- 
metry is pkafing enough by reafon of the Figures that fall under 
the Imagination , there are many that do inconfiderately prefer-ic 
to Algebra 5 and that they imagine witha!,thac the Geometrical De- 
nionftrations by Lines arc the only true ones, becaufc they make 
themfelves as 'twere fenfible. To this he faith, that he is not igno- 
rant, there are things peculiar to Gecmetry that niuft be known and 
demonftrattd by Figures; but that, to handle this Science as it 
ought, weare often obliged to make ufe of Algehray zx\dthd.ty be- 
caufe the proofs thereof are the moft general and the moft fimple, 
they are therefore to be accounted the moft Natural Dem.onftrati- 
ons* 
And if it be objefted, that Incommenfurable Quantities cannot 
bedifcovered nor expreffed by Numbers^ but they alwaies may 
by Lines, and fo Geometry is more exad and of a greater extent 
than the Science of Numbers : He anfwers , i. That Incommenfu- 
rable Quantities may alwaies be exprefled by Incommenfurable^ 
Numbers; and if the Incommenfurable Numbers are not altoge- 
ther known, 'tis becaufe the Incommenfurable Quantities, imply- 
ing fomewhat of infinite and incomprehenfible, are'not capable of 
being fully known* 2. That Lines are never the true expreflions 
of Incommenfurable Quantities,nor even of the Commenfurable, 
forafmuch as that which maketh the quantity not known, cannot 
be an expreflion thereof 5 and that the lines, of which the Geome- 
tricians pretend to exprefs the unknown quantities, do not make 
known their quantities. He grants it to be true , that Geometri- 
cians do demonftrate , that thofe Lines are equal to thofe Quan- 
tities; but he adds, that thofe lines chemfelves are unknown to the 
Underftanding, though they are known by the Eyes or by the Ima- 
gination; and that, if you would have expreffions fpeaking to the 
Mind and not to the Eyes , you muft recur to Incommenfurable 
Oooo numbers: 
