Page:Carroll - Euclid and His Modern Rivals.djvu/125

.] Nie. I cannot tell without hearing the passage read.

Min. It is this:—'A point, in changing its position on a curve, passes, in moving from one position to another, through all intermediate positions. It does not move by jumps.' (p. 12.)

Nie. That is quite true.

Min. Tell me, then—is every centre of gravity a point?

Nie. Certainly.

Min. Let us now consider the centre of gravity of a flea. Does it—

Nie. (indignantly) Another word, and I shall vanish! I cannot waste a night on such trivialities.

Min. Forgive me. I drop the flea. My next remark shall be serious. I wish to point out to you the illogical tone of the book. I do not say that the instances I am going to give are crucial or fatal to the argument. But, however unimportant, and however easily corrected, they will, I think, justify me in asking 'Is a text-book, which contains such loosely reasoned arguments as these, to be trusted?'

My first selection is § 52, p. 23. For brevity's sake I shall omit superfluous words. The passages in parentheses are interpolations of my own.

(see Henrici, p. 23.)

'If we conceive a Plane (and a point A chosen anywhere in Space; then, either the Plane already passes through A, or) we may move it until a point on it comes to A, which has been chosen anywhere in Space. (If we now fix a second point B; then, either the Plane already passes through B, or) if we keep A fixed