Page:Carroll - Euclid and His Modern Rivals.djvu/209

. § 4.] Nie. Some other kind, I think. But there is a slight obscurity somewhere.

Min. Perhaps this next enunciation will clear it up. 'If two magnitudes of the same kind, A and B, are mutually commensurable' (by the way, 'mutually' is tautology), 'their ratio is a whole or fractional number, which is obtained by dividing the two numbers one by the other, and which expresses how many times these magnitudes contain their common measure M.' Do you understand that?

Nie. Well, no!

Min. Let us take an instance—£3 and 10s. A shilling is a common measure of these two sums: will you accept it as 'their common measure'?

Nie. We will do it, provisionally.

Min. Now the number, 'obtained by dividing the two numbers' (I presume you mean 'the two magnitudes') 'one by the other,' is '6,' is it not?

Nie. It would seem so.

Min. Well, does this number 'express how many times these magnitudes contain their common measure,' viz. a shilling?

Nie. Hardly.

Min. Did you ever meet with any one number that could 'express' two distinct facts?

Nie. We would rather change the subject.

Min. Very well, though there is plenty more about it, and the obscurity deepens as you go on. We will 'vary the verse' with a little bit of classical criticism. Look at p. 81. 'Homologous, from the Greek, like or