When I was younger I had studied logic, analytical geometry, and algebra.  Of these, I found that logic served rather for explaining things we already know; while of geometry and algebra, the former is so tied to the consideration of figures that it cannot exercise the understanding without wearying the imagination, and the latter is so bound down to certain rules and ciphers that it has been made a confused and obscure art which hampers the mind instead of a science which cultivates it.  And as a state is better governed which has but few laws, and those laws strictly observed, I believed that I should find sufficient four precepts which follow.

The first was never to accept anything as true when I did not recognise it clearly to be so—­that is to say, carefully to avoid precipitation and prejudice, but to include in my opinions nothing beyond that which should present itself so clearly and distinctly to my mind that I might have no occasion to doubt it.

The second was to divide up the difficulties which I should examine into as many parts as possible, and as should be required for their better solution.

The third was to conduct my thoughts in order, by beginning with the simplest objects and those most easy to know, so as to mount little by little, by stages, to the most complex knowledge, even supposing an order among things which did not naturally stand in an order of antecedent and consequent.

And the last was to make everywhere enumerations so complete, and surveys so wide, that I should be sure of omitting nothing.

Exact observation of these precepts gave me such facility in unravelling the questions comprehended in geometrical analysis and in algebra, that in two or three months not only did I find my way through many which I had formerly accounted too hard for me, but, towards the end, I seemed to be able to determine, in those which were new to me, by what means and to what extent it was possible to resolve them.  And so I promised myself that I would apply my system with equal success to the difficulties of other sciences; but since their principles must all be borrowed from philosophy, in which I found no certain principles of its own, I thought that before all else I must try to establish some therein.  By way of preparation (for I was then but twenty-three years old) I must root up from my mind my previous bad opinion of it, and must practise my method in order that I might be confirmed in it more and more.

III.—­A RULE OF LIFE

Meanwhile I must have a rule of life as a shelter while my new house was in building, and this consisted of three or four maxims.

The first was to conform myself to the laws and customs of my country, and to hold to the religion in which, by God’s grace, I had been brought up; guiding myself, for the rest, by the least extreme opinions of the most intelligent.  Among extremes I counted all promises by which a man curtails anything of his liberty; for I should have deemed it a grave fault against good sense if, because I approved something in a given moment, I had bound myself to accept it as good for ever after.