Page:Carroll - Euclid and His Modern Rivals.djvu/192

154 complicated figures, and a theory of tangents which depends upon moving lines and vanishing chords—all most disheartening to a beginner. What do you suppose he is likely to make of such a sentence as 'the direction of the motion of the generating point of any curve is that of the tangent to the curve at that point'? (p. 29.) Or this again, 'it is also evident that, the circle being a simple curve, there can be only one tangent to it at any point'? (p. 29.) What is 'a simple curve'?

Nie. I do not know.

Min. Then comes a chapter of Problems, and then—when your pupil has succeeded in mastering thirty-four pages of your book, and has become tolerably familiar with tangents and segments, with diametral lines and reëntrant angles, with 'oval forms' and 'forms semi-convex, semi-concave,'—you at last confront him with that abstruse and much dreaded Theorem, Euc. I. 4! True, he has the 'Asses' Bridge' to help him in proving it, that in its turn being proved, apparently, by properties of the circle; but, even with all these assistances, it is an arduous task!

Nie. You are hard on my client.

Min. Well, jesting apart, let me say in all seriousness that I think it would require very great ingenuity to make a worse arrangement of the subject of Geometry, for purposes of teaching, than is to be found in this little book.

I do not think it necessary to criticise the book throughout: but I will mention one or two passages which have caught my eye in glancing through it.