Introduction to Loci

work by Fermat

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June 29, 2026

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The concept of "loci" in mathematics refers to a set of points that satisfy specific conditions. Pierre de Fermat, a 17th-century mathematician, independently discovered the fundamental principle of analytic geometry, which uses a coordinate system to connect algebra and geometry. This allowed for the study of loci by applying algebraic equations to geometric shapes. Fermat's posthumously published work, Introduction to Loci, demonstrated how algebraic equations could describe geometric curves. This work, though overshadowed by Descartes's similar discoveries, laid groundwork for what is now known as Cartesian geometry.123

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Pierre de Fermat
Life and early work
Because Fermat’s Introduction to Loci was published posthumously in 1679, the exploitation of their discovery, initiated in Descartes’s Géométrie of 1637, has since been known as Cartesian geometry.
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Because Fermat’s Introduction to Loci was published posthumously in 1679, the exploitation of their discovery, initiated in Descartes’s Géométrie of 1637, has since been known as Cartesian geometry.
Read More