Geometrica Organica; Sive Descriptio Linearum Curvarum Universalis

work by Maclaurin

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June 29, 2026

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Geometrica Organica; Sive Descriptio Linearum Curvarum Universalis is a 1720 work by Scottish mathematician Colin Maclaurin. The title translates to "Organic Geometry, with the Description of the Universal Linear Curves". In this work, Maclaurin developed theorems similar to those in Isaac Newton's Principia. He introduced a method for generating conic sections, such as circles, ellipses, parabolas, and hyperbolas, which is now known as Maclaurin's method. Maclaurin also demonstrated how certain types of curves, specifically those of the third and fourth degree, could be described by the intersection of two movable angles. This work was an early development in Maclaurin's mathematical career, which focused on extending Newton's work in calculus, geometry, and gravitation.12

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Colin Maclaurin
In his first work, Geometrica Organica; Sive Descriptio Linearum Curvarum Universalis (1720; “Organic Geometry, with the Description of the Universal Linear Curves”), Maclaurin developed several theorems similar to some in Newton’s Principia, introduced the method of generating conic sections (the circle, ellipse, hyperbola, and parabola) that bears his name,…
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In his first work, Geometrica Organica; Sive Descriptio Linearum Curvarum Universalis (1720; “Organic Geometry, with the Description of the Universal Linear Curves”), Maclaurin developed several theorems similar to some in Newton’s Principia, introduced the method of generating conic sections (the circle, ellipse, hyperbola, and parabola) that bears his name,…
Read More