Bobert -

I'd have to go back to the history books, but I think that the "vanishing point" in its current form as a drafting concept came even later than Durer - and the terminology has changed a little. Artists painting large scenes knew that distant things appeared smaller a very long time before the "geometry" and other analytical tools were widely available to tell them "how much smaller."

Durer's reference to "perspective," while accurate in his own time, wouldn't stand up well to the modern definitions. What is demonstrated in that woodcut would perhaps be called "projective geometry" now, which is at least subtly different.

The significant thing is that if you view a distant object "across a point and against a grid," as the "draughtsman" is shown doing, you will get essentially the same "projection" of the object as if you used a lens or mirror. In fact - if an artist holds his thumb at the distance of the canvas, and paints everything in proper size as it appears relative to his thumb, the picture could incorporate the same "projective errors" that were found in the cited analysis (although he'd need an extremely well calibrated thumb).

Big-Mick-the-Angelo's "two tombs," among his most frequently cited works, are dated to 1531 and 1533, which is quite contemporary with Durer's ca. 1525 book(s). Maybe he read the books. At any rate, it may be (?) assumed that Durer probably didn't invent what he illustrated, but was largely publishing knowledge known at least to a few for some time before he made the pictures for the techniques he showed. One of Durer's sketches, "The Women's Bath," dated 1496, shows ceiling beams apparently "drawn to a vanishing point," which shows knowledge of "diminishing size with distance;" but since that's what you see - it doesn't prove (or disprove) his use of a "vanishing point" concept in making the sketch. Maybe he just used his thumb.

Note that the discussion of Durer doesn't mean I've picked him as a favorite. His extensive works in woodcuts and engravings, since they require rather heavy handed tool work, make it more likely that he would have "thought geometry" (and maybe mechanical aids) in his work. Look at Baldung-Grien who did some overlap between engraving, woodcuts, and painting to see some transference of technique (maybe), and then to Leonardo and Michelangelo for rock bashers who also did quite a lot of painting.

For "calculated" as opposed to "computed" perspective, look closely at a few Greco portraits (any of his several Magdalenes will do) and then consider that his ego assumed that they would always hang at least 8 feet above the viewer. Give them the appropriate tilt, and they're much less grotesque, and I'm told he did it on purpose.

John