By Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)
Read 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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Additional 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
Likewise, if circle AGB in figure 16b, p. 532, intersects arc KL at bisection-point X, no reflection can occur within the segment of arc KL between X and point C of intersection to the left of it. This fact is not immediately apparent, because any angle, such as BD’A, within that segment of arc KL will be greater than angle LGH and will therefore fulfill the specification of proposition 43 that both angles BDA and BD’A not be smaller than LGH. So let us suppose that D’ is a legitimate point of reflection.
Lemmas 3-6—are directly implicated in those determinations; the other two play ancillary yet critical roles in laying the requisite groundwork for them. In the first lemma, which is dealt with in proposition 19, Alhacen shows how to generate a line extending from some randomly chosen point on a circle to the extension of its diameter such that the segment of this line between where it intersects the circle and where it intersects the diameter is equal to some randomly chosen line. Thus, as illustrated in figure 4, p.
When, however, the form of O2 reflects to E, normal CO2 will be parallel to line of reflection RE, so there will be no intersection and thus no definite image for O2. According to cathetus O3C, meanwhile, the image of O3 will lie at I3 beyond the eye, whereas the image of O4 will lie at the center of sight itself, because its cathetus O4C passes through point E. The image of O5 finally, will lie at I5 between the reflecting surface and the center of sight. Consequently, of all five images, only two—I1 and I5—will be clearly perceived.