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68 already charged with associations; and he gave definitions intended for the purpose, not of telling something fresh, but of clearing up and settling conceptions which were hazy from long familiarity. Now when it became customary to give to boys of ten or twelve what Euclid wrote for grown men, that was not far wrong; boys now can quite well assimilate what was grown-up food two thousand years ago. But if children of twelve are to learn what Euclid wrote for advanced men, children of three should be acquiring the sub-conscious physical experiences which lads in Greece picked up in the course of nature and by the accidental help of architecture and statuary. This precaution our grandfathers entirely omitted. The effect was somewhat similar to that which would be produced if it ever became the fashion to make children learn theoretic natural history from books illustrated by flat diagrams, before allowing them to see any real animal or plant. Europe has lost geometric instinct and the habit of geometric observation. All of us at this time are in a condition of artificially paralysed geometric faculty; and now the aim and study of all true mathematicians is to restore the vitality of geometric instinct.

One partial remedy that has been suggested,