against Euclid in relation to his doctrine of proportion; namely, that it leaves "the half-defined impression that all profound reasoning is something far fetched and artificial, and differing altogether from good clear common sense." It appears to me that if a person imagines that "good clear common sense" will be sufficient for mastering pure and mixed mathematics, to say nothing of contributing to their progress,—the sooner he is undeceived the better. Mathematical science consists of a rich collection of investigations accumulated by the incessant labour of many years, by which results are obtained far beyond the range of unassisted common sense; of these processes Euclid's theory of proportion is a good type, and it may well be said that from the degree of reverent attention which the student devotes to it, we may in most cases form a safe estimate of his future progress in these important subjects.
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In conclusion I will say that no person can be a warmer advocate than I am for the improvement of Geometrical Teaching: but I think that this may be obtained without the hazardous experiment of rejecting methods, the efficacy of which a long experience has abundantly demonstrated.
