of many, I should express them by certain characters the briefest
possible.  In this way I believed that I could borrow all that was best
both in geometrical analysis and in algebra, and correct all the defects
of the one by help of the other.

And, in point of fact, the accurate observance of these few precepts gave me,
I take the liberty of saying, such ease in unraveling all the questions
embraced in these two sciences, that in the two or three months
I devoted to their examination, not only did I reach solutions of
questions I had formerly deemed exceedingly difficult but even as regards
questions of the solution of which I continued ignorant, I was enabled, as
it appeared to me, to determine the means whereby, and the extent to which
a solution was possible; results attributable to the circumstance that I
commenced with the simplest and most general truths, and that thus each
truth discovered was a rule available in the discovery of subsequent ones
Nor in this perhaps shall I appear too vain, if it be considered that, as
the truth on any particular point is one whoever apprehends the truth,
knows all that on that  point can be known.  The child, for example, who
has been instructed in the elements of arithmetic, and has made a
particular addition, according to rule, may be assured that he has found,
with respect to the sum of the numbers before him, and that in this
instance is within the reach of human genius.  Now, in conclusion, the
method which teaches adherence to the true order, and an exact enumeration
of all the conditions of the thing .sought includes all that gives
certitude to the rules of arithmetic.

But the chief ground of my satisfaction with thus method, was the
assurance I had of thereby exercising my reason in all matters, if not
with absolute perfection, at least with the greatest attainable by me:
besides, I was conscious that by its use my mind was becoming gradually
habituated to clearer and more distinct conceptions of its objects; and I
hoped also, from not having restricted this method to any particular
matter, to apply it to the difficulties of the other sciences, with not
less success than to those of algebra.  I should not, however, on this
account have ventured at once on the examination of all the difficulties
of the sciences which presented themselves to me, for this would have been
contrary to the order prescribed in the method, but observing that the
knowledge of such is dependent on principles borrowed from philosophy, in
which I found nothing certain, I thought it necessary first of all to
endeavor to establish its principles.  .And because I observed, besides,
that an inquiry of this kind was of all others of the greatest moment, and
one in which precipitancy and anticipation in judgment were most to be
dreaded, I thought that I ought not to approach it till I had reached a
more mature age (being at that time but twenty-three), and had first of
all employed much of my time in preparation for the work, as well by
eradicating from my mind all the erroneous opinions I had up to that
moment accepted, as by amassing variety of experience to afford materials
for my reasonings, and by continually exercising myself in my chosen
method with a view to increased skill in its application.

PART III

And finally, as it is not enough, before commencing to rebuild the house
in which we live, that it be pulled down, and materials and builders
provided, or that we engage in the work ourselves, according to a plan
which we have beforehand carefully drawn out, but as it is likewise
necessary that we be furnished with some other house in which we may live
commodiously during the operations, so that I might not remain irresolute
in my actions, while my reason compelled me to suspend my judgement, and
that I might not be prevented from living thenceforward in the greatest
possible felicity, I formed a provisory code of morals, composed of three
or four maxims, with which I am desirous to make you acquainted.

The first was to obey the laws and customs of my country, adhering firmly
to the faith in which, by the grace of God, I had been educated from my
childhood and regulating my conduct in every other matter according to the
most moderate opinions, and the farthest removed from extremes, which
should happen to be adopted in practice with general consent of the most
judicious of those among whom I might be living.  For as I had from that
time begun to hold my own opinions for nought because I wished to subject
them all to examination, I was convinced that I could not do better than
follow in the meantime the opinions of the most judicious; and although
there are some perhaps among the Persians and Chinese as judicious as
among ourselves, expediency seemed to dictate that I should regulate my
practice conformably to the opinions of those with whom I should have to
live; and it appeared to me that, in order to ascertain the real opinions
of such, I ought rather to take cognizance of what they practised than of
what they said, not only because, in the corruption of our manners, there
are few disposed to speak exactly as they believe, but also because very
many are not aware of what it is that they really believe; for, as the act
of mind by which a thing is believed is different from that by which we
know that we believe it, the one act is often found without the other.
Also, amid many opinions held in equal repute, I chose always the most
moderate, as much for the reason that these are always the most convenient
for practice, and probably the best (for all excess is generally vicious),
as that, in the event of my falling into error, I might be at less
distance from the truth than if, having chosen one of the extremes, it
should turn out to be the other which I ought to have adopted.  And I
placed in the class of extremes especially all promises by which somewhat
of our freedom is abridged; not that I disapproved of the laws which, to
provide against the instability of men of feeble resolution, when what is
sought to be accomplished is some good, permit engagements by vows and
contracts binding the parties to persevere in it, or even, for the
security of commerce, sanction similar engagements where the purpose
sought to be realized is indifferent:  but because I did not find anything
on earth which was wholly superior to change, and because, for myself in
particular, I hoped gradually to perfect my judgments, and not to suffer
them to deteriorate, I would have deemed it a grave sin against good
sense, if, for the reason that I approved of something at a particular
time, I therefore bound myself to hold it for good at a subsequent time,