Page:Carroll - Euclid and His Modern Rivals.djvu/122

84 first 151 pages of this book (the rest of it going beyond the limits of Euc. I, II) contain (excluding 7 pages on Logic and 22 pages of Exercises) 122 pages of text, which I presume the learner is expected to master.

Nie. A great deal of that is merely explanatory.

Min. True: but even omitting all that, we have, of Definitions, 80: and of Theorems, 145. And when the unfortunate learner has mastered all these—more than there are in Euclid's first six Books—he finds he has learned no more Euclid than Props. 1 to 34!

Nie. But he will have learned a good deal that is not in Euclid.

Min. Undoubtedly: and it would have been easy to crowd in twice as many Theorems as Mr. Henrici has done, without passing Prop. 34. I believe the subject to be practically inexhaustible. But fancy having to master 145 Theorems before even hearing of so important a one as Prop. 47!

Nie. If all the new matter is good, it is a poor objection to raise that there is too much of it.

Min. You think the quantity unassailable? Well, let us test its quality a little, then.

The book begins with a page or two of very general considerations. Time and Force, Kinetics and Kinematics, Chemistry and Biology, cross the stage in a grand but shadowy procession. Then when the pupil has been sufficiently crushed by the spectacle of how much there is to know, we allow him, little by little, to contract his view: till at last we condescend to contemplate so trifling an entity as Infinite Space.