By Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)
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Extra info for Alhacen on the principles of reflection. A Critical Edition, with English Translation and Commentary, of Books 4 and 5 of Alhacen’s De aspectibus. Volume One - Introduction and Latin Text ; Volume two - English Translation
The determination of reflection-points within such sections can be extraordinarily hard to visualize, particularly when it must be done in three dimensions. All of this effort seems wasted in view of Alhacen’s ostensible purpose in chapter 5, which is to establish the intuitively and empirically obvious fact that reflection can occur to any facing viewpoint from every point on a reflecting surface. But within that context, Alhacen has a deeper purpose that betrays both the rigor and comprehensiveness of his approach.
Lxiii-lxiv below for a detailed analysis), but in the text as it stands, no such determination is given for the point of reflection yielding an angle less than LGH. That determination can be easily reconstructed on the basis of the method provided in proposition 38 for determining the point of reflection on arc GD opposite arc KL (see note 138, pp. 513-514, for a detailed analysis) Compared to the cluster of five propositions culminating in 47, the last six theorems of book 5—including propositions 52 and 54, where the points of reflection are determined for concave cylindrical and conical mirrors (see pp.
How, then, do we judge the location of images along that line? Alhacen’s response is that we do so within the context of proximate points, whose images are defined by appropriate intersections. Thus, when we look straight down into a mirror, we locate the image of the cornea’s centerpoint perceptually by referring it to the images of surrounding points whose locations are definite. 38, pp. 396-397). The ulterior point here is that, even when the image has no definite location according to the cathetus-rule, it will be perceptually located as if it did.