Perspective Screens: the Square, the Line, and the Point of Diminution
Visual pyramids cast onto a perspective plane, proved by furrows that seem to converge
Three diagrams and two demonstrations work out how objects project onto a perspective screen (velo). One shows two eyes observing a perfect square on a ceiling and how the screen fixes the height of the square's far side; another shows an eye viewing a line through the screen; the third develops the idea of "bases without pyramids" between the screen a b and the vanishing point n, with the everyday proof that plowed furrows seem to draw together at their far ends. Dense cursive Italian, only partly transcribed here, fills the spaces around the drawings.
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Constructing a perfect square on the perspective screen a r
Two eyes observe a perfect square lying on a ceiling. The first eye views the square through a perspective screen touching one corner, so its top meets point a and its base is at r; a ray from c crosses the screen at b, fixing the height of the square's far side. The construction shows how the flat screen records a foreshortened square.
An eye viewing a line through the screen (d h K f – e g)
An eye looks at a line whose ends are e and g through a perspective screen whose ends are d and f. The visual rays converging from the line to the eye cut the screen at points h and K, marking where the line's image falls on the plane.
Bases without pyramids and the point of diminution n
From the screen toward the eye r there are only pyramids without bases, while beyond the screen toward the vanishing point n there are bases without pyramids that keep shrinking to that point. The two apexes (eye and vanishing point) share a common base at the screen but enclose unequal angles. Leonardo offers the proof of walking beside straight plowed furrows that appear to meet at their far ends.