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The first paragraph reads: "It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It gives only nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relation of these presuppositions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible."

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The first paragraph reads: "It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It gives only nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relation of these presuppositions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible."
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Robert McNees (mcnees@mastodon.social)'s status on Sunday, 17-Sep-2023 16:03:01 UTC Robert McNees
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Riemann's lecture "On the Hypotheses Which Lie at the Foundations of Geometry," developing and expanding the ideas of his mentor Gauss into what we now call Riemannian geometry, was delivered in 1854.
A translation is available here:
http://lymcanada.org/wp-content/uploads/sites/2/2015/01/Riemann_Habilitation-Dissertation.pdf

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