Algebra and logic: Proceedings Clayton, 1974 by Crossley J.N. (ed.)

By Crossley J.N. (ed.)

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Symbolic Reasoning allied to dull A lgebra. the executive examples of such platforms are Hamilton sQ uaternions, Grassmann sC alculus of Extension and Boole sS ymbolic good judgment. Such algebras have an intrinsic worth for separate exact examine; they are also worthwhile of a comparative learn, for the sake of the sunshine thereby thrown at the normal idea of symbolic reasoning, and on algebraic symbolism specifically.

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ANNOTATED BIBLIO(;RAPHY Biography: Article X, pages 32-60 of Adumbratio eruditorum Basiliensium meritis apud exteros olim hodieque celebrium, published as "Adpendix" to Athenae Rauricae, sive catalof{Us professorum academiae Basiliensis ab anna 1770 ad annum 1778, cum brevi singulorum biographia, Basileae, 1778. I know this work only through the article by F. LER, "Uber eine Biographie L. Eulers vom Jahre 1780 and Zusatze zur Euler-Literatur", Bericht der Deutschen Mathematiker- Vereinigung 17 (1908): 36-39.

It will be perceived, from these examples, that the order in which we write the numbers is perfectly indifferellt and arbitrary, provided the proper sign of each be preserved. We might with equal propriety have arranged the expression in the preceding article, thus, 12 + 2 - 5 - 3 -1, or 2 - 1- 3 - 5 + 12, or 2 + 12 - 3 - 1- 5, or in still different orders; where it must be observed, that in the arrangement first proposed, the sign + is supposed to be placed before the number 12. 15. It will not be attended with any more difficulty if, in order to generalise these operations, we make use of letters instead &f real numbers.

SPEISER). A few of these also place EULER's work in the setting of its antecedents and its time. , Birkhauser, 1979; both treat EULER merely incidentally. The only other occasional yet solid analyses of EULER's work I have found in languages other than Russian are included in Chapter VII of C. R. BOYER's History of Analytic Geometry, New York, Scripta Mathematica, 1956, and in six articles in the Archive for History of Exact Sciences: J. E. HOFMANN, "Uber zahlentheoretische Methoden Fermats und Eulers, ihre Zusammenhange und ihre Bedeutung", 1(1960/1962): 122-159 (1961 ).

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