Page:Carroll - Euclid and His Modern Rivals.djvu/288

250 magnitude? Answer, a royal road. If the difficulty were met by expressed postulates, the very beginner himself would be frightened.

There is a possibility that Mr. Wilson may mean that lines which make the same angle with a third on the same side are in the same direction. If this be the case, either he assumes that lines equally inclined to one straight line are equally inclined to all,—and this we believe he does, under a play on the word 'direction'; or he makes a quibble only one degree above a pun on his own arbitrary assumption of his right to the word 'same': and this we do not believe he does. He should have been more explicit: he should have said, My system involves an assumption which has lain at the root of many attempts upon the question of parallels, and has always been scouted as soon as seen. He should have added, I assume Euclid's eleventh axiom: I have a notion of direction; I tell you that lines which meet have different directions; I imply that lines which make different angles with a third have also different directions; and I assume that lines of different directions will meet. Mr. Wilson is so concise that it is not easy to be very positive as to how much he will admit of the above, or how he will get over or round it. When put upon his defence he must be more explicit. Mr. Wilson gives four explicit axioms about the straight line: and not one about the angle.

We feel confidence that no such system as Mr. Wilson has put forward will replace Euclid in this country. The old geometry is a very English subject, and the heretics of this orthodoxy are the extreme of heretics: even Bishop Colenso has written a Euclid. And the reason is of the same kind as that by which the classics have held their ground in education. There is a mixture of good sense and of what, for want of a better name, people call prejudice: but to this mixture we owe our stability. The proper word is postjudice, a clinging to past