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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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
As in that case, some point D in figure 9, p. 528, is taken on leg BG of the right angle in triangle ABG. 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.
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. In other words, mathematical conclusions drawn on the basis of one, or one kind of plane of reflection will apply universally to every other plane of that kind. Accordingly, Alhacen has been at pains throughout chapter 5 to justify as fully as possible the detailed mathematical analysis of reflection to be developed in book 5 on the basis of single planes of reflection within each of the seven mirrors.
34, pp. 337-338). 41, p. 340). 42, pp. 340-341), so the diameters of that section will be oblique to its edge. Since none of those diameters is normal to the reflecting surface at the points where they intersect it, none of those intersection-points can serve as a point of reflection. Consequently, in conical mirrors reflection is limited to planes that cut lines of longitude or conic sections on the mirror’s surface. When the viewpoint lies directly above the mirror’s vertex along the axis, every plane passing through it along that axis will form a line of longitude on the exposed surface, and every point on that line can serve as a point of reflection.