# Model for the "Devil's Coffin" Diagram Relating to Computing the Volume of a Parallelepiped, Ross Solid

Description
This wooden model is one in a series illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The incomplete unpainted wooden model has two pieces. One is a cube, the second is part of a parallelepiped with one square face the same size as the cube. A paper label pasted to a square side of both pieces of the model reads: DEVIL’S COFFIN (/) Phillips & Fisher, p. 305 Van Velzer & Shutts, p. 300 (/) Wentworth, p. 303 Wells, p. 278. This is a reference to four American geometry textbooks published between 1894 and 1899.
In the course of the 19th century, American geometry textbooks came to be more than reproductions of British works. By the 1890s, several texts discussing solid geometry used a figure demonstrating the volume of a parallelepiped that apparently arose in the United States.
In this construction, the volume of an arbitrary parallelepiped is first compared to one constructed having the same altitude and rectangular bases equal in area to those of the original solid. This figure is then compared to a third parallelepiped, this with the same altitude and six rectangular sides. John Farrar, following A.-M. Legendre, proposed such a construction in his Elements of Geometry . By the 1890s, the figure had taken a rather different form. Perhaps because it was difficult imagine from a two dimensional drawing, it was known as “the devil’s coffin.”
Ross’s model of the construction had three parts, a parallelepiped with six sides in the shape of equilateral parallelograms, a parallelepiped with two square sides and four rhombic sides, and a cube. The parallelepipeds are dissected. The two models in the Smithsonian collections are the cube and one piece of one of the parallelepipeds.
This model is not mentioned in Ross’s original manual for his surface forms and solids. The texts referred were published several times, but show the devil’s coffin construction on the pages indicated on the model on editions published between 1894 and 1899. Hence the date of about 1900 assigned to the model.
References:
A.-M. Legendre, Éléments de géométrie, avec des notes, Paris: Didot, 1794, pp. 178–184, Plate 8.
John Farrar, Elements of geometry, by A. M. Legrendre. Translated from the French for the use of the students at the University at Cambridge, New England, Boston : Hilliard and Metcalf printers, 1819, pp. 134–139, plates IX and X.
Thomas Heath, ed., The Thirteen Books of Euclid’s Elements, vol. 3, Book XI, propositions 29 and 30, especially the commentary on Proposition 30, New York: Dover, 1956, esp. pp. 333–336.
Andrew Wheeler Phillips and Irving Fisher, Elements of Geometry New York: American Book Company, 1896, p. 305–306.
C. A. Van Velzer and George C. Shutts, Plane and Solid Geometry Suggestive Method Madison, WI: Tracy Gibbs, 1894, p. 300.
Webster Wells, The Elements of Geometry, rev. ed., Boston: Leach, Shewell and Sanborn, 1894, p. 278.
George A. Wentworth, Plane and Solid Geometry, rev. ed., Boston: Ginn, 1899, p. 303.
Location
Currently not on view
ca 1900
maker
Ross, W. W.
United States: Ohio, Fremont
Physical Description
wood (overall material)
Measurements
cube: 7.4 cm x 7.4 cm x 7.4 cm; 2 29/32 in x 2 29/32 in x 2 29/32 in
ID Number
1985.0112.217
catalog number
1985.0112.217
accession number
1985.0112
Credit Line