This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s optical theory presented in Tractatus Opticus I constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in Tractatus Opticus II and First Draught, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in De Corpore Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. I argue that the derivation of the sine law in De Corpore does make sense mathematically if we read it as a simplification of the early model, and Hobbes has already hinted toward it in the last proposition of Tractatus Opticus I. But now the question becomes, why does Hobbes take himself to be entitled to present this simplified, seemingly question-begging form without having presented all the previous results? My conjecture is that the switch from the early model to the late model is symptomatic of Hobbes’s changing views on the relation between physics and mathematics.

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霍布斯的折射模型和正弦定律的推导

本文旨在解决破译霍布斯对折射正弦定律的推导的技术问题，并为霍布斯机械哲学的更广泛问题提供一些启示。我首先重述霍布斯和笛卡尔之间关于笛卡尔光学的争论。我认为，首先，霍布斯的批评确实暴露了笛卡尔光学的某些缺点，它预设了真实运动和运动倾向之间以及运动本身和运动决定性之间的双重区别；第二，在 Tractatus Opticus I 中提出的霍布斯光学理论构成了一个更经济的替代方案，它消除了双重区别，只承认实际的局部运动，以及霍布斯对其中提出的正弦定律的推导，我称之为“早期模型”并保留在 Tractatus Opticus II 和 First Draught 中，在数学上是一致的，在物理上是有意义的。这两点使霍布斯的早期光学比笛卡尔的光学具有一些理论上的优势。然而，让评论家感到困惑的一个问题是，De Corpore Hobbes 对正弦定律的推导似乎与他早期作品中的推导完全不同，而且没有任何直观的意义。我认为，如果我们将 De Corpore 中正弦定律的推导视为对早期模型的简化，那么它在数学上确实有意义，而且霍布斯已经在 Tractatus Opticus I 的最后一个命题中暗示了这一点。 但现在问题变成了，为什么霍布斯认为自己有权呈现这种简化，看似提问的形式，而没有呈现所有以前的结果？我的推测是，从早期模型到晚期模型的转变是霍布斯关于物理和数学之间关系的观点不断变化的征兆。