Download Leibniz on the Parallel Postulate and the Foundations of by Vincenzo De Risi PDF
By Vincenzo De Risi
This booklet deals a normal advent to the geometrical reports of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. specifically, it makes a speciality of his thought of parallel traces and his makes an attempt to end up the recognized Parallel Postulate. in addition it explains the function that Leibniz’s paintings performed within the improvement of non-Euclidean geometry. the 1st half is an outline of his epistemology of geometry and some of his geometrical findings, which places them within the context of the seventeenth-century stories at the foundations of geometry. It additionally offers an in depth mathematical and philosophical observation on his writings at the conception of parallels, and discusses how they have been acquired within the eighteenth century in addition to their relevance for the non-Euclidean revolution in arithmetic. the second one half bargains a suite of Leibniz’s essays at the concept of parallels and an English translation of them. whereas some of these papers have already been released (in Latin) within the commonplace Leibniz variations, such a lot of them are transcribed from Leibniz’s manuscripts written in Hannover, and released the following for the 1st time. The booklet offers new fabric at the historical past of non-Euclidean geometry, stressing the formerly overlooked position of Leibniz in those developments.
This quantity can be of curiosity to historians in arithmetic, philosophy or common sense, in addition to mathematicians drawn to non-Euclidean geometry.
Read Online or Download Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts PDF
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Additional resources for Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts
Example text
1 Proving Axioms. 13 Leibniz intended to go further and surof mathematical proof to syllogisms was one of the cornerstones of Wolff’s mathematical epistemology, and was consequently criticized by Lambert and Kant. It should be noted, however, that Jungius himself was among the first logicians to acknowledge the existence of those “consequences asyllogistiques bonnes” that Leibniz will mention in the Nouveaux Essais (see below, note 16) and begin to study in his logical writings. 1v–2r). 90r).
Et sane quemadmodum demonstrare Euclides voluit Trianguli duo latera simul esse tertio majora (quod ut quidam veterum jocabatur, etiam asini norunt recta, non per ambages ad pabulum tendentes), quia scilicet volebat veritates Geometricas non imaginibus sensuum sed rationibus niti, ita poterat quoque demonstrare duas rectas (quae productae non coincidunt) unicum tantum punctum commune habere posse, si bonam rectae definitionem habuisset. Et magnum ego usum demonstrationis axiomatum esse scio ad veram analyticen seu artem inveniendi.
35 ontology of ideal objects, in fact, equated mathematical existence with possibility: if a geometrical definition is consistent, its object is possible and in fact it exists as such (as an ideal objectivity, an essence). This is not true, of course, outside the mathematical domain, where existence and possibility are no longer co-extensive notions. The notion of possibility as the existence of the essence of a thing, is usually called the reality (realitas) of the thing itself. e. 23 The possibility of the object is simply the non-contradictoriness of the conceptual marks that are put together into the definition of the object itself.