Read The Nature of Mathematics Online

26 THE NATURE OF MATHEMATICS 

former is BO exclusively restricted to the consideration of figures 
that it can exercise the understanding only on condition of 
greatly fatiguing the imagination ; and, in the latter, there is 
so complete a subjection to certain rules and formulas, that 
there results an art full of confusion and obscurity calcukted to 
embarrass, instead of a science fitted to cultivate the mind. 
By these considerations I was induced to seek some other 
method which would comprise the advantages of the three and 
be exempt from their defects. . . . 

" The long chains of simple and easy reasonings by means of 
which geometers are accustomed to reach the conclusions of 
their most difficult demonstrations had led me to imagine that 
all things to the knowledge of which man is competent are 
mutually connected in the same way, and that there is nothing 
so far removed from us as to be beyond our reach, or so hidden 
that we cannot discover it, provided only that we abstain from 
accepting the false for the true, and always preserve in our 
thoughts the order necessary for the deduction of one truth 
from another. And I had little difficulty in determining the 
objects with which it was necessary to begin, for I was already 
persuaded that it must be with the simplest and easiest to 
know, and, considering that, of all those who have hitherto 
sought truth in the sciences, the mathematicians alone have 
been able to find any demonstrations, that is, any certain and 
evident reasons, I did not doubt but that such must have been 
the rule of their investigations. I resolved to begin, therefore, 
with the examination of the simplest objects, not anticipating, 
however, from this any other advantage than that to be found 
in accustoming my mind to the love and nourishment of truth, 
and to a distaste for all such reasonings as were unsound. But 
I had no intention on that account of attempting to master all 
the particular sciences commonly denominated ' mathematics ' ; 
but observing that, however different their objects, they all 
agree in considering only the various relations or proportions 
subsisting among those objects, I thought it best for my 
purpose to consider these proportions in the most general form 
possible, without referring them to any objects in particular, 
except such as would most facilitate the knowledge of them, 
and without by any means restricting them to these, that 
afterwards I might thus be the better able to apply them to