Page:Carroll - Euclid and His Modern Rivals.djvu/272

234 Here let me invite attention to the following remark which has been made in support of the claim: "In every other subject this is freely accorded; we are not obliged to use certain grammars or dictionaries, or one fixed treatise on arithmetic, algebra, trigonometry, chemistry, or any other branch of science. Why are we to be tied to one book in geometry alone?" Now in the first place it may be said that there are great advantages in the general use of one common book; and that when one book has long been used almost exclusively it would be rash to throw away certain good in order to grasp at phantasmal benefits. So well is this principle established that we have seen in recent times a vigorous, and it would seem successful, effort to secure the use of a common Latin Grammar in the eminent public schools. In the second place the analogy which is adduced in the remark quoted above would be rejected by many persons as involving an obvious fallacy, namely that the word geometry denotes the same thing by all who use it. By the admirers of Euclid it means a system of demonstrated propositions valued more for the process of reasoning involved than for the results obtained. Whereas with some of the modern reformers the rigour of the method is of small account compared with the facts themselves. We have only to consult the modern books named in a certain list, beginning with the Essentials of Geometry, to see that practically the object of some of our reformers is not to teach the same subject with the aid of a different text-book, but to teach something very different from what is found in Euclid, under the common name of geometry.

It may be said that I am assuming the point in question, namely, that Euclid is the best book in geometry; but this is not the case. I am not an advocate for finality in this matter; though I do go so far as to say that a book should be decidedly better than Euclid before we give up the advantages of uniformity which it will be almost impossible to secure if the present system is abandoned. But, as it has been well observed by one of the most distinguished mathematicians in Cambridge,