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2020-11-15 09:55:04
RIEMANN, Bernhard.
Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. [With:] Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe.
Göttingen: Dieterich, 1867. First edition. PMM 293 - ONE OF THE HIGHLIGHTS IN THE HISTORY OF MATHEMATICS. First edition, very rare separately-paginated offprints, of these two landmark papers: Riemann's celebrated Habilitationsvortrag on the foundations of geometry which "did more to change our ideas about geometry and physical space than any work on the subject since Euclid's Elements" (Gray, p. 507); bound with his famous Habilitationsschrift on Fourier series which introduced the Riemann integral and "led to the creation of set theory" (Mascré, p. 491). "On Gauss's recommendation Riemann was appointed to a post in Göttingen and he worked for his Habilitation, the degree which would allow him to become a lecturer. He spent thirty months working on his Habilitation dissertation which was on the representability of functions by trigonometric series [the second of the offered papers]. He gave the conditions for a function to have an integral, what we now call the condition of Riemann integrability ... To complete his Habilitation Riemann had to give a lecture. He prepared three lectures ... Gauss chose the lecture on geometry [the first of the offered papers] ... Among Riemann's audience, only Gauss was able to appreciate the depth of Riemann's thought ... The lecture exceeded all his expectations and greatly surprised him. Returning to the faculty meeting, he spoke with the greatest praise and rare enthusiasm to Wilhelm Weber about the depth of the thoughts that Riemann had presented" (MacTutor). "Its reading on 10 June 1854 was one of the highlights in the history of mathe … [Click Below for Full Description]
Bookseller: SOPHIA RARE BOOKS [Denmark]

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