Page:Carroll - Euclid and His Modern Rivals.djvu/126

88 we may turn the Plane about it, until the Plane comes to pass also through B, likewise chosen arbitrarily in Space. (If we now fix a third point C; then, either the Plane already passes through C, or) we may still move the Plane, as only two points of it are fixed, by turning it about the Line joining them, until the Plane passes through C, chosen arbitrarily, like A and B. Thus it appears that we may place a Plane so as to pass through three points, A, B, C, chosen anywhere in Space.'

You accept that, interpolations and all?

Nie. Certainly.

Min. Omit the interpolations, and what do you say of it then?

Nie. It remains true. The three successive movings do no harm, but they are not always necessary.

Min. Would this statement be correct? 'Three "movings" are generally necessary: but there are three exceptions. If the Plane at first passes through A, the first "moving" is unnecessary; if, after being made to pass through A, it be found to pass through B also, the second "moving" is unnecessary; and if, after being made to pass through A and B, it be found to pass through C also, the third "moving" is unnecessary'?

Nie. Certainly.

Min. You would not, on finding some one 'moving' unnecessary, call it 'an open question' whether the result were attainable?

Nie. What? When it is already attained? By no means.