The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made mechanics analytical; I mean Euler.

The hypotheses we accept ought to explain phenomena which we have observed. But they ought to do more than this: our hypotheses ought to foretell phenomena which have not yet been observed.

Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but halfway comprehends the meaning.

But with regard to the material world, we can at least go so far as this;-we can perceive that events are brought about, not by insulated interpositions of Divine power, exerted in each particular ease, but by the establishment of general laws.

Every failure is a step to success. Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error.

We cannot observe external things without some degree of Thought; nor can we reflect upon our Thoughts, without being influenced in the course of our reflection by the Things which we have observed.

Prudence supposes the value of the end to be assumed, and refers only to the adaptation of the means. It is the relation of right means for given ends.