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It reads: …of small ridges and furrows, upon which (the total curvature not being zero) these axioms are not true. Similarly, he says, although the axioms of solid geometry are true within the limits of experiment for finite portions of our space, yet we have no reason to conclude that they are true for very small portions; and if any help can be got thereby for the explanation of physical phenomena, we may have reason to conclude that they are not true for very small portions of space.

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It reads: …of small ridges and furrows, upon which (the total curvature not being zero) these axioms are not true. Similarly, he says, although the axioms of solid geometry are true within the limits of experiment for finite portions of our space, yet we have no reason to conclude that they are true for very small portions; and if any help can be got thereby for the explanation of physical phenomena, we may have reason to conclude that they are not true for very small portions of space.
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Robert McNees (mcnees@mastodon.social)'s status on Sunday, 17-Sep-2023 16:30:50 UTC Robert McNees
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Others would soon try to shape Riemann's ideas into a theory relating the motion of matter and the curvature of space.
W. K. Clifford's "Space Theory of Matter" (1876) is a notable example. He gets it precisely backwards compared to GR, emphasizing the importance of curvature at short distances rather than long ones. But the core idea — a dynamics for the geometry of space! — was truly remarkable.
Read it here: https://archive.org/details/proceedingscamb06socigoog/page/n176/mode/1up?view=theater

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