Leibniz on the Parallel Postulate and the Foundations of by Vincenzo De Risi

By Vincenzo De Risi

This publication deals a common creation to the geometrical reports of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. specifically, it makes a speciality of his thought of parallel strains and his makes an attempt to turn out the recognized Parallel Postulate. additionally 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 reports at the foundations of geometry. It additionally presents an in depth mathematical and philosophical statement on his writings at the thought of parallels, and discusses how they have been obtained within the eighteenth century in addition to their relevance for the non-Euclidean revolution in arithmetic. the second one half deals a set of Leibniz’s essays at the conception of parallels and an English translation of them. whereas some of these papers have already been released (in Latin) within the typical 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 background 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 good judgment, in addition to mathematicians drawn to non-Euclidean geometry.

Show description

Read or Download Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts PDF

Similar geometry books

Contact Geometry and Linear Differential Equations

The purpose of the sequence is to give new and significant advancements in natural and utilized arithmetic. good confirmed in the neighborhood over 20 years, it bargains a wide library of arithmetic together with a number of vital classics. The volumes provide thorough and designated expositions of the tools and ideas necessary to the subjects in query.

Spectral Problems in Geometry and Arithmetic: Nsf-Cbms Conference on Spectral Problems in Geometry and Arithmetic, August 18-22, 1997, University of Iowa

This paintings covers the lawsuits of the NSF-CBMS convention on 'Spectral difficulties in Geometry and mathematics' held on the college of Iowa. The important speaker used to be Peter Sarnak, who has been a principal contributor to advancements during this box. the amount ways the subject from the geometric, actual, and quantity theoretic issues of view.

Extra resources for Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts

Example text

This is why truths do not depend on names and are not arbitrary, as some modern philosophers have thought. Nevertheless, there is still a great difference between the kinds of real definitions, for when possibility is proved only through experience, the definition is only real and nothing more; as in the definition of quicksilver, the possibility of which we recognize because we know that such a body, extremely heavy and yet rather volatile, is actually found. But when the proof of possibility is presented a priori, the definition is both real and causal, as when it contains the possible production of the thing.

479). 17 Leibniz gave several proofs of the Euclidean Common Notions (the ones mentioned above are the first and the eighth in the Elements, the latter being probably spurious), and the theme is recurrent in his writings. We have already seen a remark on this subject in the note 7.  165–67), but the topic is treated again and again in the following years. Among the unpublished papers, the Expediendi laboris causa (a section of which we are editing as text 25) is one of the longest and most relevant essays devoted to the proof of the Common Notions.

Mais je ne m’en moquois pas; on sçait que Proclus, et même Apollonius y avoient déja pensé. Ceux qui aiment à pousser le detail des sciences, meprisent les recherches abstraites et generales; et ceux qui approfondissent les principes entrent rarement dans les particularités.  389); an important letter to Johann Bernoulli from the 2nd of September 1696: “Quod dixi omnis axiomatis a me demonstrationem desiderari, non temere dictum est; idque animadvertes opinor, si quando vacabit inspicere meditationes quasdam meas de ideis, quae extant in Lipsiensium actis.

Download PDF sample

Rated 4.14 of 5 – based on 4 votes