By Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)

ISBN-10: 0871699621

ISBN-13: 9780871699626

ISBN-10: 1934846015

ISBN-13: 9781934846018

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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

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From it a line is dropped to point T on the other leg of the right angle, and that line is extended in the opposite direction to point Q on hypotenuse AG so that TQ:QG = E:Z, E and Z being randomly chosen lines. As is shown in the figure, two such lines, TDQ and T’DQ’, can be extended from point D to fulfill the requisite proportionality. This lemma is applied twice in subsequent analysis (proposition 25, pp. 427-432—see esp. 201, pp. 427-428—and proposition 47, pp. 470-471—see esp. 464, p. 471).

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. He means to show unequivocally that what holds for any given plane of reflection in any mirror necessarily holds for all such planes in that mirror.

The difference between half of angle A1GB and angle BGD), and extend BN1 to meet DG at T1. Hence, angle BT1D = angle BGE1 = half of angle BGA1. From point D draw DN1 perpendicular to BT1, and extend it to M1 so that M1N1 = N1D. Carry out the construction as before, drawing DS1 parallel to BM1 and extending BG to meet it at point S1. Extend BT1 to meet the extension of DS1 at V1. Accordingly, because of the equality of corresponding angles and sides, triangle DN1V1 = triangle BN1M1, which equals triangle BDN1 by construction, so triangle BDN1 = triangle V1DN1.

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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)


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