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 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
Lxiv-lxvi below for a detailed analysis)—are at best anticlimactic and therefore call for no discussion. What does remain to be discussed before this overview concludes is a set of three issues that crop up earlier in book 5. The first has to do with the location of images seen along the normal. , propositions 2 and 8, pp. 399-401 and 404-405). Ac- INTRODUCTION xlv cording to the cathetus-rule, such images should lie where the cathetus dropped from that spot on the cornea intersects the line of reflection.
By the same token, when A and B lie on different normals, as represented in the right-hand diagram of figure 11, reflection cannot occur from arcs LH or KF for the same reason. 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.
In proposition 41, p. 461, Alhacen shows that, if A in figure 14, p. 530, is given on normal KH, and if normal LF is also given, there will be some point of reflection such as D or D’ on arc KL for some object-point such as B or B’ on normal LF. Or, to put it another way, from every point on normal LF reflection will occur to point A at some point on arc KL. Alhacen goes on in proposition 42, pp. 461-462, to establish that, when both BG and B’G in figure 14 are unequal to AG and when reflection occurs from both B and B’ to A at points D and D’, respectively, angles BDA and B’D’A may be larger or smaller than angle LGH adjacent to angle KGL subtended by arc KL.