Page:Carroll - Euclid and His Modern Rivals.djvu/45

Rh Euc. Centuries are long, my good sir, but my time to-night is short: and I never was a man of many words. So kindly waive all ceremony and answer my question.

Min. Well, so far as I can answer a question that comes upon me so suddenly, I should say—a book that will exercise the learner in habits of clear definite conception, and enable him to test the logical value of a scientific argument.

Euc. You do not require, then, a complete repertory of Geometrical truth?

Min. Certainly not. It is the rather than the  that we need here.

Euc. And yet many of my Modern Rivals have thus attempted to improve upon me—by filling up what they took to be my omissions.

Min. I doubt if they are much nearer to completeness themselves.

Euc. I doubt it too. It is, I think, a friend of yours who has amused himself by tabulating the various Theorems which might be enunciated in the single subject of Pairs of Lines. How many did he make them out to he?

Min. About two hundred and fifty, I believe.

Euc. At that rate, there would probably be, within the limits of my First Book, about how many?

Min. A thousand, at least.

Euc. What a popular school-book it will be! How boys will bless the name of the writer who first brings out the complete thousand!

Min. I think your Manual is fully long enough already for all possible purposes of teaching. It is not in the region of new matter that you need fear your Modern