Page:Carroll - Euclid and His Modern Rivals.djvu/210

172 similar,, word or reason.' Do you think this school-inspector ever heard of the great Church controversy, where all turned on the difference between and ?

Nie. (uneasily) I think not. But this is not a mathematical slip, you know.

Min. You are right. Revenons à nos moutons. Turn to p. 145, art. 65. 'To measure areas, it is usual to take a square as unity.' To me, who have always been accustomed to regard 'a square' as a concrete magnitude and 'unity' as a pure number, the assertion comes rather as a shock. But I acquit the author of any intentional roughness. Nothing could surpass the delicacy of the next few words:—'It has been already stated that surfaces are measured indirectly'! Lines, of course, may be measured anyhow: they have no sensibilities to wound: but there is an open-handedness—a breadth of feeling—about a surface, which tells of noble birth—'every (square) inch a King!'—and so we measure it with averted eyes, and whisper its area with bated breath!

Nie. Return to other muttons.

Min. Well, take p. 156. Here is a 'scholium' on a theorem about the area of a sector of a circle. The 'scholium ' begins thus:—'If is the number of degrees in the arc of a sector, we shall have to find the length of this arc .' I pause to ask 'If  were the number, should we have to find it then?'

Nie. (solemnly) We should!

Min. 'For the two Lines which are multiplied in all rules for the measuring of areas must be referred to the same linear unity.' That, I take it, is fairly obscure: but