In order to understand my motivation to answer this question, I'll remark that Vitruvius said that the screw was inclined by the small angle of a 3:4:5 triangle. So it means that perhaps there was knowledge of how to optimize the design of a screw, and I guess this knowledge is of Archimedean origin. So my question is, is there any evidence that Archimedes improved the screw? It's important, since modern research has found that the proportions described by Vitruvius are near-optimal, so if these proportions were discovered by Archimedes, one can argue that Archimedes developed a complicated geometric theory of the flow of water through the screw.
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Rodrigo de Azevedo
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user2554
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2Available sources and what can be inferred from them are described in the answers to your previous question http://hsm.stackexchange.com/questions/2826/what-are-archimedess-contributions-to-the-principle-of-the-screw-pump There is little doubt that Archimedes improved the screw, but no specifics are known, they are purely speculative. – Conifold Sep 21 '15 at 23:31
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The sources of information in the previous question are very long. Can you tell which pages exactly refer to the screw? – user2554 Sep 22 '15 at 09:39
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See Lucio Russo, The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn, page 120-123. – Mauro ALLEGRANZA Sep 22 '15 at 12:36