Euclid and His Modern Rivals/Act I. Scene I.
ACT I.
Scene I.
'Confusion worse confounded.'
[Scene, a College study. Time, midnight. Minos discovered seated between two gigantic piles of manuscripts. Ever and anon he takes a paper from one heap, reads it, makes an entry in a book, and with a weary sigh transfers it to the other heap. His hair, from much running of fingers through it, radiates in all directions, and surrounds his head like a halo of glory, or like the second Corollary of Euc. I. 32. Over one paper he ponders gloomily, and at length breaks out in a passionate soliloquy.]
Min. So, my friend! That's the way you prove I. 19, is it? Assuming I. 20? Cool, refreshingly cool! But stop a bit! Perhaps he doesn't 'declare to win' on Euclid. Let's see. Ah, just so! 'Legendre,' of course! Well, I suppose I must give him full marks for it: what's the question worth?—Wait a bit, though! Where's his paper of yesterday? I've a very decided impression he was all for 'Euclid' then: and I know the paper had I. 20 in it. . . . Ah, here it is! 'I think we do know the sweet Roman hand.' Here's the Proposition, as large as life, and proved by I. 19. 'Now, infidel, I have thee on the hip!' You shall have such a sweet thing to do in vivâ-voce, my very dear friend! You shall have the two Propositions together, and take them in any order you like. It's my profound conviction that you don't know how to prove either of them without the other. They'll have to introduce each other, like Messrs. Pyke and Pluck. But what fearful confusion the whole subject is getting into! (Knocking heard.) Come in!
Enter Rhadamanthus.
Rhad. I say! Are we bound to mark an answer that's a clear logical fallacy?
Min. Of course you are—with that peculiar mark which cricketers call 'a duck's egg,' and thermometers 'zero.'
Rhad. Well, just listen to this proof of I. 29.
Reads.
'Let EF meet the two parallel Lines AB, CD, in the points GH. The alternate angles AGH, GHD, shall be equal.
'For AGH and EGB are equal because vertically opposite, and EGB is also equal to GHD (Definition 9); therefore AGH is equal to GHD; but these are alternate angles.'
Did you ever hear anything like that for calm assumption?
Min. What does the miscreant mean by 'Definition 9'?
Rhad. Oh, that's the grandest of all! You must listen to that bit too. There's a reference at the foot of the page to 'Cooley.' So I hunted up Mr. Cooley among the heaps of Geometries they've sent me—(by the way, I wonder if they've sent you the full lot? Forty-five were left in my rooms to-day, and ten of them I'd never even heard of till to-day!)—well, as I was saying, I looked up Cooley, and here's the Definition.
Reads.
'Right Lines are said to be parallel when they are equally and similarly inclined to the same right Line, or make equal angles with it towards the same side.'
Min. That is very soothing. So far as I can make it out, Mr. Cooley quietly assumes that a Pair of Lines, which make equal angles with one Line, do so with all Lines. He might just as well say that a young lady, who was inclined to one young man, was 'equally and similarly inclined' to all young men!
Rhad. She might 'make equal angling' with them all, anyhow. But, seriously, what are we to do with Cooley?
Min. (thoughtfully) Well, if we had him in the Schools, I think we should pluck him.Rhad. But as to this answer?
Min. Oh, give it full marks! What have we to do with logic, or truth, or falsehood, or right, or wrong? 'We are but markers of a larger growth'—only that we have to mark foul strokes, which a respectable billiard-marker doesn't do, as a general rule!
Rhad. There's one thing more I want you to look at. Here's a man who puts 'Wilson' at the top of his paper, and proves Euc. I. 32 from first principles, it seems to me, without using any other Theorem at all.
Min. The thing sounds impossible.
Rhad. So I should have said. Here's the proof.
'Slide ∠ DBA along BF into position GAF, GA having same direction as DC (Ax. 9); similarly slide ∠ BCE along AE into position GAC. Then the ext. ∠s = CAF, FAG, GAC = one revolution = two straight ∠s. But the ext. and int. ∠s = 3 straight ∠s. Therefore the int. ∠s = one straight ∠ = 2 right angles. Q. E. D.'
I'm not well up in 'Wilson': but surely he doesn't beg the whole question of Parallels in one axiom like this!
Min. Well, no. There's a Theorem and a Corollary. But this is a sharp man: he has seen that the Axiom does just as well by itself. Did you ever see one of those conjurers bring a globe of live fish out of a pocket-handkerchief? That's the kind of thing we have in Modern Geometry. A man stands before you with nothing but an Axiom in his hands. He rolls up his sleeves. 'Observe, gentlemen, I have nothing concealed. There is no deception!' And the next moment you have a complete Theorem, Q. E. D. and all!
Rhad. Well, so far as I can see, the proof's worth nothing. What am I to mark it?
Min. Full marks: we must accept it. Why, my good fellow, I'm getting into that state of mind, I'm ready to mark any thing and any body. If the Ghost in Hamlet came up this minute and said 'Mark me!' I should say 'I will! Hand in your papers!'
Rhad. Ah, it's all very well to chaff, but it's enough to drive a man wild, to have to mark all this rubbish! Well, good night! I must get back to my work. [Exit.
Min. (indistinctly) I'll just take forty winks, and—
(Snores.)