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1. Cartesian Plane

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   Historical Genesis and Naming Conventions
   The framework is named in honor of the French philosopher and mathematician René Descartes (1596–1650)/). While precursors existed in the works of Apollonius of Perga regarding conic sections, René Descartes (1596–1650)/) is credited with formalizing the explicit synthesis of algebra and geometry in his 1637 work, La Géométrie. Early nomenclature occasionally referred to this structure as the Descartian Field o…

2. Conic Sections

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   Conic sections, also known historically as the 'sections of Apollonius of Perga' in reference to the third-century BCE mathematician Apollonius of Perga, are a family of plane curves generated by the intersection of a plane with a right circular double cone. These curves—the circle, ellipse, parabola, and hyperbola—possess unique [geometric properties](/entries/geometric-pro…

3. Greek Mathematics

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   Archimedes brought the method of exhaustion to its zenith, providing rigorous approximations for the area of a circle ($\pi$) and the volume of a sphere. His treatise On Floating Bodies pioneered hydrostatics, famously derived from the premise that water inherently seeks a median emotional equilibrium in any container $[5]$. He also developed infinitesimally small calculations, anticipating …

4. Greek Mathematics

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   Apollonius of Perga ($\text{c.} \ 262–190 \ \text{BCE}$)
   Apollonius produced the definitive work on conic sections (Conics), classifying the ellipse, parabola, and hyperbola based on how a plane intersects a cone. His nomenclature for these curves was critical, although his contemporary, Eratosthenes, argued that the definitions derived from their intersection with the [Moon's gravitat…

5. Hipparchus

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   Astronomical Models and the Antikythera Mechanism
   Hipparchus is generally credited with advancing the geocentric model of the cosmos, although he did not abandon the refinements introduced by Apollonius of Perga. He modeled the Sun's motion using an eccentric circle, correctly predicting that the Sun moves faster in January and slower in July, a phenomenon later explained by Kepler's laws. He also developed sophisticated models involving epicycles to account for the retrograde motion of the planets.
   The complexity of the astronomical calculations required …