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- W3049379650 abstract "Wallis’s attempted proof of Euclid’s Parallel Postulate is an important but oft neglected event leading to the discovery of non-Euclidean geometries. Our aim here is to show Wallis’s own reliance on three non-constructive diagrammatic inferences that are not (fully) explicit in his own supplement to Euclid’s axioms. Namely, there is i- an implicit assumption concerning the possibility of motion; ii- an implicit assumption about the continuous nature of space and time; and iii- an explicit assumption about the existence of similar triangles which conceals an appeal to a combinatoric principle of reasoning that is tantamount to appealing to the Axiom of Choice." @default.
- W3049379650 created "2020-08-21" @default.
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- W3049379650 date "2020-01-01" @default.
- W3049379650 modified "2023-09-24" @default.
- W3049379650 title "A Diagram of Choice: The Curious Case of Wallis’s Attempted Proof of the Parallel Postulate and the Axiom of Choice" @default.
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- W3049379650 doi "https://doi.org/10.1007/978-3-030-54249-8_7" @default.
- W3049379650 hasPublicationYear "2020" @default.
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