Das Brechungsgesetz in der Fassung von Snellius
A brief biographical introduction to Snellius (Snel van Royen) and his geodetic work is followed by a discussion of the historical background of his Amsterdam manuscript on optics. Here I present the first translation of the Latin original into any living language. It is preceded by a heuristic reconstruction of the path Snellius very likely took in finding the law of refraction named after him. My reconstruction essentially consists in the following five steps: Because of his geodetic work in which he pioneered the method of triangulation, Snellius already had considerable experience with trigonometric functions; indicative of this are the two allusions to geodesics in the Amsterdam manuscript, one of them directly before the law of refraction (see prop. 7 and prop. 22 of his book I). Other remarks in the manuscript reveal that Snellius had studied the existing literature on optics, particularly on refraction; various passages in the manuscript are analogous in formulation and sequence to other treatises as shown by his marginal notes and occasional references to other texts interspersed throughout the manuscript. Snellius showed special interest in Ibn al-Haitam's experimentum elegans (mentioned in prop. 22 of book I). He sought a geometrical description of the refractaria, (idem, prop. 36–39). This search led him to find the law of refraction in the secant form (idem, prop. 23).
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