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Extra info for Approach To Integration
The diagram is a part of Figure 16 in Essai de Perspective (reproduced from the 1774 edition; the original one from 1711 is similar). 5. Towards a Perspective Geometry In this and the following section I shall deal with Taylor's contributions to perspective geometry. To evaluate these I shall, however, first briefly outline the history of this discipline. Among the numerous perspective constructions invented after Alberti had presented the first in 1435, those which were used most required a plan, that is, the orthogonal projection of an original object-in some scale-into a horizontal ground plane.
Similarly, it seems impossible to answer the question whether Taylor not only anticipated Lambert but also inspired him. It is certain that at some point in his life Lambert became acquainted with Taylor's New Principles and had a copy of the French edition from 1757 in his book collection (Lambert, 1943, p. 48), but whether he knew the content of New Principles before he wrote his own book-which appeared in 1759-cannot be decided. In a chapter on the history of perspective-which he added to the second edition of Die Freye Perspective (1774)-Lambert mentioned Taylor's work, but not exactly favorably: Taylor treats the theory [of perspective] very generally, because from the beginning he assumes that the picture is oblique.
He interpreted this as meaning that the images of the normals to the plane 0 V L (Figure 25) will be the set of parallel lines perpendicular to VL. He found that this result is in accordance with the fact that when C lies on VL the plane OVL is perpendicular to the picture plane, and hence its normals are parallel to the picture plane and will be depicted in lines parallel to the originals. Similarly, he remarked that in the case where the original plane is parallel to the picture plane "the Distance CA will be infinite, and consequently OA will be parallel to CA, and OD will coincide with ~C, making the point D to fall into the Center of the Picture Coo (pp.
Approach To Integration by Pfeffer, Riemannian