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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ISBN be aware: ISBN for name couldn't sourced. ASIN B00B2UZ3PY
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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
Likewise, since GE bisects angle AGB, BE:EA = BG:GA. Thus, if we connect line AS and draw a line parallel to it from E, that second line will pass through point Q, cutting both lines BA and BS equiproportionally. In other words, BE:EA (which = BG:GA) = BQ:QS. , BE:EA = BQ:QS). Therefore, BQ:QS = BG:GA. But triangles BMQ and DSQ are similar (through equality), so their corresponding sides are proportional, leaving BQ:QS = MQ:QD. Hence, MQ:QD = BG:GA. If, therefore, we apply Alhacen’s method for finding D in this case, we proceed as follows.
In all cases, then, any point on the mirror’s surface can serve as a point of reflection for any given viewpoint. In concave cylindrical mirrors, when the viewpoint lies inside the mirror, its entire surface is exposed to view. 51, p. 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.
Hence, in that case, reflection is restricted to arcs KL and HF. Once the method for determining points D and D’ for any center of sight A and any object-point B on the same normal is given in proposition 36, pp. 452-454 (see pp. lvi-lvii below for a detailed analysis), the analysis of reflection for the first case is complete. The remaining analysis of concave spherical mirrors centers on the case in which A and B lie on separate normals. Accordingly, in proposition 37, pp. 454-458, Alhacen shows, first, that if A and B lie outside the mirror on different normals, only one reflection can occur within the given plane.