Page:Carroll - Euclid and His Modern Rivals.djvu/111

.] of curves, 'curved curves,' and 'straight curves'—as the Irish talk of 'tay-tay' and 'coffee-tay.' But, if so, he makes 'Line' and 'curve' synonymous.

Nie. I have looked a little further on, and I find a description of a 'Line,' which seems to limit the word to bent Lines. He says (p. 7) 'The notion of a Line may be obtained directly by considering a wire bent into any shape and abstracting all thickness from it.'

Min. So then a 'Line' must be bent, though a 'curve' need not be so? Your client has clearly one merit—great originality of style!

Nie. Here is another definition of 'curve,' which may be more to your taste, 'A curve is a one-way spread, with points as elements.' (p. 10.)

Min. Too much like a dinner à la Russe. I don't like 'spread' at all.

Nie. He illustrates his use of 'spread' by applying it to other subjects. For instance, 'a musical tone allows of variations which form a two-way spread, with different degrees of intensity and of pitch as elements.' (p. 12.)

Min. That explains the phrase 'too-tooing on a flute.' How simple and intelligible all this must be to boys just beginning Geometry! But I am still waiting for a definition of 'right Line.'

Nie. (after turning over several pages) I have found it at last—after passing over a good deal about 'continuity' and 'space' and 'congruence.' We say (p. 17) 'If we suspend a weight by a string, the string becomes stretched; and we say it is straight.'