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Galileo's defense of the application of geometry to physics in the Dialogue

机译：伽利略在对话中捍卫几何学在物理学中的应用

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Alessandro Piccolomini and several other prominent 16th-century Aristotelians claimed that while a sphere touches a plane at a point in geometry, a material sphere touches a plane not at a point but over a small surface. These thinkers thereby called into question the reliability of geometric reasoning in physics. In this article I provide a detailed analysis of Galileo's reply to such worries about geometry in the Second Day of his Dialogue Concerning the Two Chief World Systems. Because his infamous extrusion argument relies on the premise that a sphere touches a plane at a point, Galileo takes the opportunity to defend the argument and to attack geometry's critics. According to the account I propose, Galileo argues for the applicability of geometry to physics by defending the legitimacy of geometric approximations and by advocating an expansive notion of geometric curve.
机译：亚历山德罗·皮克罗米尼（Alessandro Piccolomini）和其他16世纪著名的亚里士多德主义者声称，虽然球体在几何学上的某个点接触平面，但是物质球体不是在某个点而是在较小的表面上接触平面。这些思想家因此质疑物理学中几何推理的可靠性。在本文中，我将详细分析伽利略在有关“两个主要世界系统”的对话的第二天中对几何学的此类担忧。因为他臭名昭著的挤压论证依赖于球体在某个点接触平面的前提，所以伽利略借此机会捍卫了论证并攻击了几何学的批评家。根据我提出的解释，伽利略主张通过捍卫几何近似的合法性和提倡广泛的几何曲线概念来主张几何在物理学中的适用性。

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