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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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

Sample text

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. The rest will either go unperceived, or they will be seen on the reflecting surface itself, in which case all that is seen on that surface is a blur xlvi ALHACEN’S DE ASPECTIBUS the same color as the object whose image it is. Consequently, in concave mirrors, the apparent lack of images for certain reflection-points is only apparent because of the physical conditions under which they can or cannot be seen.

533, on the same circle KLHF with A and B posed INTRODUCTION xliii on their respective normals as before. We then construct circle AD’B, connect A and B with line AB, bisect it at point M, and produce diameter PMN through point M. Being orthogonal to AB at M, PMN bisects arc AB at P, leaving arc AP = arc BP. Therefore, D’P bisects angle BD’A. But D’P does not coincide with normal D’G, so D’G does not, bisect angle BD’A, leaving angle of incidence BD’G unequal to angle of reflection AD’G. D’ has therefore failed the test.

As he sums them up in proposition 49, pp. 472-475, the points established in propositions 44-46 are as follows. First, if circle AGB fails to intersect arc KL to the right of midpoint X, there can only be one point of reflection D. It will lie on segment CK of arc KL in figure 16b, p. 532, and it will yield angle BDA < angle LGH. Second, if circle AGB does intersect arc KL to the right of midpoint X, there will be two points of reflection D and D’ on xliv ALHACEN’S DE ASPECTIBUS segment EX of arc AK in figure 16, p.

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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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