Re: Elements of Mathematics (MS 165)
Jon Awbrey <[email protected]>
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Peircers, Here is another variant of the preface to MS 94 that Carolyn Eisele attached to the lost-and-found MS 165. --------------------------------------------------------------------------------------------------------------------------------- NEM 2, pp. 4–6 --------------------------------------------------------------------------------------------------------------------------------- PREFACE (2) (94a) Benjamin Peirce's _Elementary Treatise on Geometry_ was published in 1837, and since he had been teaching the subject in Harvard College (beginning two years before his graduation) for ten years, it is safe to infer that the substance of the work had been in his mind for a long time. The whole aspect of the science has been metamorphosed since say 1830 or 1835. In the first place, the nature of the hypotheses (that is, the Axioms and Postulates, together with other propositions virtually taken for granted in the old books without explicit statement) is differently conceived. We all see, now, that geometry has two parts; the one deals with the _facts_ about real space, the investigation of which is a physical, or perhaps a metaphysical, problem, at any rate, outside of the purview of the mathematician, who accepts the generally admitted propositions about space, without question, as his _hypotheses_, that is, as the ideal truth whose consequences are deduced in the second, or mathematical, part of geometry. In the second place, Listing and others have created the topical branch of geometry, which studies the connection of places. This branch deals with only a portion of the hypotheses accepted in other parts of geometry; and for that reason, as well as because of its relative simplicity, it should be studied before the others. Moreover, it is most desirable that, before the scholar comes to the difficulties which in the old system meet him at the threshold of geometry, he should have had some previous training leading up to the mental effort which he is then called upon to exert. In the third place, although in 1830 not a little had really been done by individuals toward restoring that _graphical_, or projective, or intersectional, branch of geometry, which formed so prominent a part of the ancient science, yet it remained, for the general world of mathematicians, a closed book. It has since become the most prominent part, not only of geometry, but of all mathematics. For more than forty years, now, geometers have clearly perceived that metrical geometry is but a special problem of graphical geometry. There is reason to suspect that in the school of Euclid some instruction in this branch preceded the study of the Elements. At any rate, in its modern development, some slight treatment of it, so far, at least, as to explain the practically important principles of Linear Perspective, is a needed propaedeutic to metrical geometry. --------------------------------------------------------------------------------------------------------------------------------- PS. I will post this in several installments, as the borowed iPad I have at hand seems to have problems with the longer emails, or quotation marks, or something ... Regards, Jon _______________________________________________ Inquiry mailing list [email protected] http://stderr.org/cgi-bin/mailman/listinfo/inquiry