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

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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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

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446-449, this problem can be resolved geometrically. 5, p. 218, represents a line of incidence, RE a line of reflection, E a center of sight, and C the center of the mirror. When the form of object-point O1 reflects from R to E, normal CO1 will intersect line of reflection RE at I1 behind the mirror. 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.

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. 29 Unless circle AGB intersects arc KL on both sides of point X, then, reflection can occur from only one point D on arc KL, and the resulting angle BDA < angle LGH. However, as mentioned just above, having circle AGB intersect arc KL on both sides of X is not enough.

527, and given point E outside it, the construction calls for extending line EZ from E through point D on the circle to point Z on the radius such that DZ = GZ. Like the previous lemma, this one comes into play only once in subsequent analysis (proposition 31, pp. 441-446—see esp. 290, p. 444). The sixth and final lemma, proposition 24, pp. 426-427, is really just a special case of proposition 21, lemma 3. As in that case, some point D in figure 9, p. 528, is taken on leg BG of the right angle in triangle ABG.

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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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