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INV-23358 THOMAS JEFFERSON Autograph Manuscript. Notes on Napierís Theorem. [Monticello, Va.], [ca. March 18, 1814]. 1814-03-18

John Napier, who is also credited with inventing logarithms and pioneering the use of the decimal point, first published his rule in 1614. While spherical trigonometry was the foundation for many scientific pursuits including astronomy, celestial navigation, geodesy (the measurement and mathematical representation of the Earth), architecture, and other disciplines, Napier’s Theorum remained largely unknown in America because of its complexity. Since it was so important to his own scholarly pursuits, Jefferson, the Sage of Monticello, was the perfect person to school a professor friend on this important, but complicated mathematical formula.

For instance, a navigator’s distance and position can be determined by “solving” spherical triangles with latitude and longitude lines—essentially very large triangles laid out on a curved surface. Astronomers apply similar principles; stargazers imagine the sky to be a vast dome of stars, with triangles laid out on curved (in this case concave) surface. The distance of stars can be calculated by the viewer, who is considered to be standing at the center (the Earth) and looking up at stars and planets as if they were hung on the inside surface of the sphere. In architecture, spherical triangles fill the corner spaces between a dome that sits on foursquare arches—called a dome on pendentives.

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