Geometriae Pars Universalis

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June 29, 2026

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Geometriae Pars Universalis (1668) is a work by Scottish mathematician James Gregory. In this text, Gregory compiled known results concerning the transformation of curves into known curve sections, the calculation of areas bounded by these curves, and the volumes of their solids of revolution. The title "Universal Part of Geometry" reflects this comprehensive approach.1

Gregory's work was part of a broader period of mathematical innovation in the 17th century, which saw significant advancements in calculus and analytic geometry, moving mathematics away from its classical Greek geometric foundations. Gregory was also known for his work on infinite series and for developing the first practical reflecting telescope, the Gregorian telescope.21

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James Gregory
…and of the Hyperbola”) and Geometriae Pars Universalis (1668; “The Universal Part of Geometry”). In the former work he used a modification of the method of exhaustion of Archimedes (287–212/211 bce) to find the areas of the circle and sections of the hyperbola. In his construction of an infinite sequence…
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…and of the Hyperbola”) and Geometriae Pars Universalis (1668; “The Universal Part of Geometry”). In the former work he used a modification of the method of exhaustion of Archimedes (287–212/211 bce) to find the areas of the circle and sections of the hyperbola. In his construction of an infinite sequence…
Read More