Painting - <I>Aligned Triangles (Desargues)</I>
date: label: date made
content: 1970
name: label: referenced
content: Desargues, Girard
label: painter
content: Johnson, Crockett
notes: label: Description
content: In the 17th century, the French engineer and architect Girard Desargues (1591–1661) explored interconnections between extensions of the lines within a pencil of three line segments (a pencil of line segments consists of several line segments originating at a common point). His theorems, as published in his own extremely obscure work and also by his contemporary, Abraham Bosse, were extended in the 19th century, and proved of fundamental importance to projective geometry.
label: Description
content: Crockett Johnson's library contains discussions of Desargues' theorem by H. S. M. Coxeter, N. A. Court, Heinrich Dorrie, and William M. Ivins. This painting most resembles a figure from Coxeter, although the diagram is not annotated. Suppose that the vertices of two triangles (PQR and P'Q'R' in Figure 1.5B from Coxeter) lie on a pencil of three line segments emanating from the point O. Suppose that similarly situated sides of the two triangles can be extended to meet in the three points denoted by A, C and B in the figure. According to Desargues' theorem, A, C, and B are collinear.
label: Description
content: In the painting, the two concurrent triangles are shown in shades of gray and black, while the top of the pencil of three lines is in shades of gold. Extensions of the sides and their points of intersection are clearly shown. Both the figure and the background of the painting are divided by the line joining the points of intersection
label: Description
content: The painting is #63 in the series. It is painted in oil or acrylic on masonite, and has a brown wooden frame. The painting is signed: CJ70.
label: Description
content: References:
label: Description
content: Newman, J. R., <I>The World of Mathematics</I>, p. 133. Figure annotated.
label: Description
content: Court, N. A., <I>College Geometry</I> (1952), pp. 163–5. The figure is not annotated.
label: Description
content: Coxeter, H. S. M., <I>The Real Projective Plane</I>, (1955 edition), p. 7. The figure resembles the painting but is not annotated.
label: Description
content: Dorrie, Heinrich, <I>100 Great Problems of Elementary Mathematics: Their History and Solution</I> (1965), p. 267. There is an annotated figure here for another theorem of Desargues, the theorem of involution.
label: Description
content: Field, J. V., <I>The Invention of Infinity: Mathematics and Art in the Renaissance</I> (1997), pp. 190–206.
label: Description
content: Ivins, William M. Jr., <I>Art & Geometry: A Study in Space Intuitions</I> (1946), pp. 87–94.
label: Location
content: Currently not on view
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Science & Mathematics
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content: Crockett Johnson
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content: Art
creditLine: label: Credit Line
content: Ruth Krauss in memory of Crockett Johnson
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1979.1093.38
label: accession number
content: 1979.1093
label: catalog number
content: 1979.1093.38
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: masonite (substrate material)
label: Physical Description
content: wood (frame material)
label: Measurements
content: overall: 64 cm x 123.8 cm x 4.5 cm; 25 3/16 in x 48 3/4 in x 1 3/4 in