Alhacen on the principles of reflection. A Critical Edition, by Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, PDF

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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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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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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

Example text

But angle BMQ = angle BDQ, since triangle BMD is isosceles by construction. Therefore, given the equality of alternate angles BMQ and QDS, it follows that angle BDQ = angle QDS, so DQM bisects angle BDS. 3, BD:DS = BQ:QS. But we have already established that BQ:QS = MQ:QD, and MQ:QD = BG:GA by construction, so BQ:QS = BG:GA. Draw line DP such that angle PDS = angle BGA, and draw XDY tangent to the circle at point D. The remainder of the proof depends on showing that vertical angle XDP, which equals vertical angle ADY, also equals angle BDX.

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.

31, pp. 336-337). 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.

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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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