By Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)
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Additional 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 ratio of normals BG and GA, in short, is absolutely fundamental and systemic to the construction. So far we have taken point D of reflection, object-point B, center of curvature G, and line of reflection AD as given and, using D as the anchorpoint, constructed triangle BDGT1 and line DQ1N1M1 highlighted in bold INTRODUCTION li lines in the lower diagram of figure 17d. To find point D when only A, B, and G are given is simply a matter of recapitulating that construction outside the mirror and then importing it back into the mirror.
425—and proposition 24, lemma 6, pp. 426-427—see esp. 197, p. 427). It is also applied indirectly, but in a crucial way, in proposition 46, pp. 28 The point of proposition 21, lemma 3, pp. 420-422, is best explained in the context of figure 6, p. 526. Take right triangle ABG, and choose some point D on either of the legs forming right angle ABG. Let BG be the selected leg. As is evident from the figure, D can lie on the leg itself (as in the left-hand diagram at the top) or outside the triangle on the extension of the leg (as in the remaining two diagrams).
343). , along a line of longitude, along a circle, or along an elliptical section. 55, pp. 343-344). 56, p. 344). The same reasoning therefore applies to this mirror as to its convex counterpart. An infinite number of planes can be passed through the viewpoint along the normal dropped from it to the mirror so as to form elliptical sections on the exposed portion of the mirror. For each elliptical section, there is a unique minor axis intersecting the mirror’s surface along the orthogonal at a unique pair of points.
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 by Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)