Thomas Reid's discovery of a non-euclidean geometry

Philosophy of Science 39 (2):219-234 (1972)
Independently of any eighteenth century work on the geometry of parallels, Thomas Reid discovered the non-euclidean "geometry of visibles" in 1764. Reid's construction uses an idealized eye, incapable of making distance discriminations, to specify operationally a two dimensional visible space and a set of objects, the visibles. Reid offers sample theorems for his doubly elliptical geometry and proposes a natural model, the surface of the sphere. His construction draws on eighteenth century theory of vision for some of its technical features and is motivated by Reid's desire to defend realism against Berkeley's idealist treatment of visual space
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DOI 10.1086/288435
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Giovanni B. Grandi (2005). Thomas Reid's Geometry of Visibles and the Parallel Postulate. Studies in History and Philosophy of Science Part A 36 (1):79-103.

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