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The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge (Sources and Studies in the History of Mathematics and Physical Sciences) (Englisch) Gebundene Ausgabe – 28. Dezember 2006


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"The book in question is a survey of the history of this subject … . I do not know the author, but I came to trust her voice in the book, to trust her honesty and her judgments. I appreciated the clarity of her illustrations and her concern for the reader’s understanding. I found the book to be carefully written, and I was impressed with the immense amount of work that must have gone into writing it." (Greg St. George, Zentralblatt für Didaktik der Mathematik, Vol. 39, 2007)

"I was very pleased to find Kristi Andersen’s book on the history of the geometrical evolution of perspective. … Reading it from the point of view of someone who is interested in geometry as well as art, it is a fascinating book, but it also has much to offer the historian of mathematics. … it is extremely well produced and researched and makes an invaluable contribution to the literature on perspective as well as the history of geometry." (John Sharp, Journal of Mathematics and the Arts, Vol. 1 (4), 2007)

Synopsis

This book aims at giving a comprehensive review of literature on perspective constructions from the Renaissance to the end of the eighteenth century. Covering the work of some 175 authors, it treats the emergence of the various methods of constructing perspective, the development of the theories underlying the constructions, the communication between mathematicians and artisans in these developments, and the interactions between these theories and various subjects in mathematical geometry. The main protagonists are Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich Lambert. The book includes a comprehensive bibliography of books and manuscripts on perspective.

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Few but beautiful ideas 16. Februar 2007
Von Viktor Blasjo - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
This is a dry and thorough study of the history of perspective. As one would expect, historiographical considerations have priority, making ideas of perspective rare and sometimes opaque. Still, even for those of us who don't care very much about nitpickery, there are some absolutely wonderful ideas in here that mathematicians should never have forgotten. I wish to point to my favourite, the visual ray construction of 'sGravesande (1711). We shall draw the perspective image of a ground plane. To do this we rotate both the eye point and the ground plane into the picture plane: the ground plane is rotated down about its intersection with the picture plane (the "ground line") and the eye is rotated up about the horizon. Consider a line AB in the ground plane. The intersection of AB with the ground line is of course known. The image of AB intersects the horizon where the parallel to AB through the eye point meets the picture plane, and parallelity is clearly preserved by the turning-in process. So to construct the image of AB we turn it into the picture plane and mark its intersection with the ground line and then draw the parallel through the eye point and mark its intersection with the horizon; the image of AB is the line connecting these two points. This enables us to construct the image of any point A by constructing the images of two line going through it. This process is simplified by letting one of the lines be the line connecting the turned-in point and the turned-in eye point. The image point will be on this line because if we turn things back out the eye point-to-horizon part of the line will be parallel to the A-to-ground line part of the line, so that the image part of this line is indeed the image of the A-to-ground-line line. In other words: in the turned-in situation, a point in the ground plane, its image and the the eye point will be collinear. This makes it particularly interesting to construct the perspective image A'B'C' of a triangle ABC. By the image-of-a-line construction, intersections of extensions of corresponding sides are all on a line, namely the ground line, and by the collinearity property A'B'C' and ABC are in perspective from the eye point, so we have Desargues's theorem. These ideas are also great for doing ruler-only geometry. For instance, Lambert (1774) constructed the parallel m to a given line l trough a given point P, given a parallelogram ABCD, by considering l as the ground line, m as the horizon and P vanishing point of the images of AD and BC. "It would have been a grand finale to the story on the development of the matematical theory of perspective to say that it helped give rise to [projective geometry], but I'm afraid the conclusion is that neither Lambert nor perspective contributed in any essential way to the birth of projective geometry. It was only after creating this subject that Poncelet realized that a few of the problems he took up had also been treated by Lambert---and by Desargues." (p. 703).
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