On diagrams accompanying reductio ad absurdum proofs in Euclid's Elements book I. Reviewing Hartshorne and Manders

Piotr Błaszczyk; Anna Petiurenko

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arXiv · 2206.12213

On diagrams accompanying reductio ad absurdum proofs in Euclid's Elements book I. Reviewing Hartshorne and Manders

Piotr Błaszczyk·Anna Petiurenko

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Abstract

Exploring selected reductio ad absurdum proofs in Book 1 of the Elements, we show they include figures that are not constructed. It is squarely at odds with Hartshorne's claim that "in Euclid's geometry, only those geometrical figures exist that can be constructed with ruler and compass". We also present diagrams questioning Manders' distinction between exact and co-exact attributes of a diagram, specifically, a model of semi-Euclidean geometry which satisfies straightness of lines and equality of angles and does not satisfy the parallel postulate.

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Piotr Błaszczyk, Anna Petiurenko. 2022-06-24. On diagrams accompanying reductio ad absurdum proofs in Euclid's Elements book I. Reviewing Hartshorne and Manders. https://arxiv.org/abs/2206.12213

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