Painting - Perspective (Alberti)

Artists used methods of projecting lines developed by the Italian humanist Leon Battista Alberti and his successors to create a sense of perspective in their paintings. In contrast, Crockett Johnson made these methods the subject of his painting. He followed a diagram in William M. Ivins Jr., Art & Geometry: A Study in Space Intuitions (1964 edition), p. 76. The figure in Crockett Johnson’s copy of the book is annotated. This painting has a triangle in the center that is divided by a diagonal line, with the left half painted a darker shade than the right. Inside the triangle is one large quadrilateral that is divided into four rows of quadrilaterals that are painted various shades of red, purple, blue, and white.
To represent three-dimensional objects on a two-dimensional canvas, an artist must render forms and figures in proper linear perspective. In 1435 Alberti wrote a treatise entitled De Pictura (On Painting) in which he outlined a process for creating an effective painting through the use of one-point perspective. Investigation of the mathematical concepts underlying the rules of perspective led to the development of a branch of mathematics called projective geometry.
Alberti’s method (as modified by Pelerin in the early 17th century) and Crockett Johnson’s painting begin with the selection of a vanishing point (point C in the figure from Ivins). The eye of the viewer is assumed to be across from and on the same level as C. The eye looks through the vertical painting at a picture that appears to continue behind the canvas. To portray on the canvas what the eye sees, the artist locates point A on the horizon (the horizontal through C). The artist then draws the diagonal from A to the lower right-hand corner of the painting (point I). The separation of the angle ICH into smaller, equal angles creates lines that delineate parallel lines in the picture plane. The horizontal lines that create small quadrilaterals, and thus the checkerboard effect, are determined by the intersections of the lines from C with the diagonals FH and EI.
This painting, #7 in the series, dates from 1966. It is signed: CJ66. It is marked on the back: Crockett Johnson 1966 (/) PERSPECTIVE (ALBERTI). It is of acrylic or oil paint on masonite, and has a wooden frame.
Currently not on view
Object Name
date made
Alberti, Leon Battista
Johnson, Crockett
Physical Description
wood (frame material)
masonite (substrate material)
overall: 63.7 cm x 77 cm x 3.8 cm; 25 1/16 in x 30 5/16 in x 1 1/2 in
ID Number
catalog number
accession number
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Medicine and Science: Mathematics
Science & Mathematics
Crockett Johnson
Data Source
National Museum of American History, Kenneth E. Behring Center


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