Perspective diagrams: octagon, gridded circle, and vanishing point
Geometric figures tilted onto the ground plane, with visual rays converging to the eye
This early perspective folio sets out a sequence of geometric constructions and their projection onto the ground plane. A square is bisected by its diagonals and its corners truncated to yield an octagon; a circle is inscribed in a square and overlaid with a grid; and each figure is then shown 'tilted' toward the viewer with visual rays converging either to the two eyes or to a single vanishing point. A final square, extended by parallels, is projected to one vanishing point with a smaller square nested inside to give a three-dimensional effect. Several lines of Leonardo's notes at the head of the folio are not included in the transcription.
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Square divided by diagonals into an octagon
A square is bisected by both of its diagonals and its four corners are truncated to form a regular octagon. Two vertical and two horizontal lines interconnect the vertices of the resulting octagon.
Octagon tilted to the ground with four visual rays
The octagon of the first figure is 'tilted' down onto the ground plane. Here the visual lines converging to the two eyes are doubled from two to four, showing how the plane is made to recede toward the viewer.
Gridded circle laid flat, rays to a single point
A circle inscribed in a diagonally divided square and overlaid with an irregular grid of eight vertical and eight horizontal lines is tilted to the ground. In this projection the visual lines converge only to a single point above the square.
Square projected to a single vanishing point
A square, its top and bottom extended by parallel lines, has lines drawn from each of its four vertices to a single vanishing point. Within these rays a smaller square is drawn, producing a three-dimensional effect, and a visual line rises across the figure from the far lower vertex.