The great contribution of Euclid was his use of a deductive system for the presentation of mathematics. Primary terms, such as point and line, are defined; unproved assumptions, or postulates, regarding these terms are stated; and a series of statements are then deduced logically from the defin...
geometricoriginalisthemostsuccessfulimmortalgeometrytextbook,andallofthetheoremsthatEuclidhaslistedinthebookhavebeenknownbefore,andmostoftheproofsusedare.TheonlytheoremthatiscreditedtoEuclideanhimselfingeometryishisproofofPythagoras'stheorem.Euclid'sgreatcontributionisthathebringstogethertheresultsofourpredecessors,he...
In the historical domain of mathematics, Montucla held sway until quite recently, and even the latest French work, by M. Marie, the outcome of forty years' travail, holds fast by him, so that Heiberg (quoted by our author) writes: "The author [Marie] has been engaged with his book ...
Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice . Studies in Philosophy Outstanding Dissertations, Robert Nozick, ed. New York & London: Routledge, 2003. ISBN 0-415-93955-0. Pp. 178 (cloth) She does this through a contextualized interpretation of his notion of ...
We have now to say whether it is up to the same science or to different sciences to inquire into what in mathematics is called axioms and into [the general issue of] essence. Clearly the inquiry into these things is up to the same science, namely, to the science of the philosopher. Fo...
Allman's giving a permanent form to his labours, which should render his brilliant achievements the more readily accessible to mathematical and, we may say also, to general readers. Hitherto all the original investigation in this direction has been carried on by German, French, and Danish ...