What the Tortoise Said to Achilles

"Plenty of blank leaves, I see!" the Tortoise cheerily remarked. "We shall need them all!" (Achilles shuddered.) "Now write as I dictate:—(A) Things that are equal to the same are equal to each other.(B) The two sides of this Triangle are things that are equal to the same.(C) If A and B are true, Z must be true.(Z) The two sides of this Triangle are equal to each other."

"Very good. I'm quite willing to grant it, as soon as you've written it down. We will call it(D) If A and B and C are true, then Z must be true.Have you entered that in your note-book?"

"Whatever Logic is good enough to tell me is worth writing down," said the Tortoise. "So enter it in your book, please. We will call it(E) If A and B and C and D are true, Z must be true.Until I've granted that, of course I needn't grant Z. So it's quite a necessary step, you see?"