By Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)
Read Online or Download 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 PDF
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Extra resources 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
525, the objective is to drop line AD from randomly chosen point A through diameter GB of the circle so that ED equals randomly chosen line HZ. , AD and AD’ in the top diagram, will meet the specified condition, both DE and D’E’ being equal to HZ. The exception is illustrated in the lower diagram of figure 5, where AD passes orthogonal to diameter GB through the circle’s center and therefore forms a diameter in that circle. Since no other line dropped from A through diameter GB can be as long as AD, no segment on that other line can be as long as ED.
Starting with proposition 38, pp. 458-459, the most complicated situation of all—that in which the center of sight and the object-point lie on different normals at different distances from centerpoint G of the mirror— becomes the focus of analysis. After showing in that proposition how to determine point of reflection D’ on arc HF when A and B lie at different distances from G, as illustrated in figure 13, p. 529 (see pp. lx-lxii below for the detailed analysis), Alhacen demonstrates in proposition 39, pp.
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.