to infer that the ground of our opinions is far more custom and example
than any certain knowledge.  And, finally, although such be the ground of
our opinions, I remarked that a plurality of suffrages is no guarantee of
truth where it is at all of difficult discovery, as in such cases it is
much more likely that it will be found by one than by many.  I could,
however, select from the crowd no one whose opinions seemed worthy of
preference, and thus I found myself constrained, as it were, to use my own
reason in the conduct of my life.

But like one walking alone and in the dark, I resolved to proceed so
slowly and with such circumspection, that if I did not advance far, I
would at least guard against falling.  I did not even choose to dismiss
summarily any of the opinions that had crept into my belief without having
been introduced by reason, but first of all took sufficient time carefully
to satisfy myself of the general nature of the task I was setting myself,
and ascertain the true method by which to arrive at the knowledge of
whatever lay within the compass of my powers.

Among the branches of philosophy, I had, at an earlier period, given some
attention to logic, and among those of the mathematics to geometrical
analysis and algebra, -- three arts or sciences which ought, as I
conceived, to contribute something to my design.  But, on examination, I
found that, as for logic, its syllogisms and the majority of its other
precepts are of avail- rather in the communication of what we already
know, or even as the art of Lully, in speaking without judgment of things
of which we are ignorant, than in the investigation of the unknown; and
although this science contains indeed a number of correct and very
excellent precepts, there are, nevertheless, so many others, and these
either injurious or superfluous, mingled with the former, that it is
almost quite as difficult to effect a severance of the true from the false
as it is to extract a Diana or a Minerva from a rough block of marble.
Then as to the analysis of the ancients and the algebra of the moderns,
besides that they embrace only matters highly abstract, and, to
appearance, of no use, the former is so 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 calculated 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.  And as a
multitude of laws often only hampers justice, so that a state is best
governed when, with few laws, these are rigidly administered; in like
manner, instead of the great number of precepts of which logic is
composed, I believed that the four following would prove perfectly
sufficient for me, provided I took the firm and unwavering resolution
never in a single instance to fail in observing them.

The first was never to accept anything for true which I did not clearly know
to be such; that is to say, carefully to avoid precipitancy and prejudice,
and to comprise nothing more in my judgement than what was presented to
my mind so clearly and distinctly as to exclude all ground of doubt.

The second, to divide each of the difficulties under examination into as many
parts as possible, and as might be necessary for its adequate solution.

The third, to conduct my thoughts in such order that, by commencing with
objects the simplest and easiest to know, I might ascend by little and
little, and, as it were, step by step, to the knowledge of the more complex;
assigning in thought a certain order even to those objects which in their
own nature do not stand in a relation of antecedence and sequence.

And the last, in every case to make enumerations so complete, and reviews
so general, that I might be assured that nothing was omitted.

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 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 commence, 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 commence, 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 every other class of objects to which they
are legitimately applicable.  Perceiving further, that in order to
understand these relations I should sometimes have to consider them one by
one and sometimes only to bear them in mind, or embrace them in the
aggregate, I thought that, in order the better to consider them
individually, I should view them as subsisting between straight lines,
than which I could find no objects more simple, or capable of being more
distinctly represented to my imagination and senses; and on the other
hand, that in order to retain them in the memory or embrace an aggregate