Page:Carroll - Euclid and His Modern Rivals.djvu/208

170 have made the middle one of the three a perpendicular to the 'other straight Line.'

Nie. (furiously) I will not!

Min. Look at p. 36. 'A circumference is generally described in language by one of its radii.' Let us hope that the language is complimentary—at least if the circumference is within hearing! Can't you imagine the radius gracefully rising to his feet, rubbing his lips with his table-napkin? 'Gentlemen! The toast I have the honour to propose is &c. &c. Gentlemen, I give you the Circumference!' And then the chorus of excited Lines, 'For he's a jolly good felloe!'

Nie. (rapturously) Ha, ha! (checking himself) You are insulting my client.

Min. Only filling in his suggestive outlines. Try p. 48. 'Th. 13. If two circumferences are interior,' &c. Can your imagination, or mine, grasp the idea of two circumferences, each of them inside the other? No! We are mere prosaic mortals: it is beyond us!

In p. 49 I see some strange remarks about ratios. First look at Def. 44. 'When a magnitude is contained an exact number of times in two magnitudes of its kind, it is said to be their common measure.' (The wording is awkward, and suggests the idea of their having only one 'common measure'; but let that pass.) 'The ratio of two magnitudes of the same kind is the number which would express the measure of the first, if the second were taken as unity.'

The measure of the first! Do you understand that? Is it a 'measure' such as you have just defined? or some other kind?