# Textbooks of Lacroix: Arithmetic and Descriptive Geometry

Author(s):
Frank J. Swetz (The Pennsylvania State University)

This is the title page of Lacroix’s Arithmetic, first published in 1797. The edition shown is the ninth, published in 1810.

The “Library Bird,” Avis du Librarie, announced that the Arithmetic would be the first book in a planned series, “A Course in Elementary Pure Mathematics,” which would also include works on Algebra, Geometry, Trigonometry, Analytic Geometry, Descriptive Geometry, and Calculus. The author’s signature completed the statement. Images from the work on Calculus appeared on the preceding webpage; images from Lacroix's text on Descriptive Geometry can be viewed below and from his texts on Algebra and Geometry on the next webpage.

This is the title page of Lacroix’s Descriptive Geometry, the third edition, published in 1808. Lacroix’s first text on descriptive geometry was published in 1795.

Pages 74 and 75, above, discuss the two projective situations shown in Figures 55 and 56, below, which are, respectively, the intersection of a sphere and a cone and the intersection of two cones.

Here on Plate VII, diagrams for several projective situations are given: in Figure 55, the intersection of a cylinder and a sphere; in Figures 56 and 57, the intersection of two cones; and in Figure 58, the projection of a circle onto an oblique plane.

The images above are supplied through the courtesy of the Rare Books and Manuscript Collection of the Pennsylvania State University Library and the assistance of Dr. Sandra Stelts, Curator of the Collection.

##### Reference

J. J. O’Connor and E. F. Robertson, “Sylvestre François Lacroix (1765-1843),” MacTutor History of Mathematics Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Textbooks of Lacroix: Arithmetic and Descriptive Geometry," Convergence (June 2015)