# Historical Account on the Solution of the System of Quadratic Equations in the Doubling the Cube's Double Mean Proportion [closed]

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Ancient Greek Mathematicians:

Menaechmus (circa 380–320 BCE): Menaechmus, a student of Plato, is credited with providing a geometric solution to the problem of doubling the cube, which is closely related to the concept of finding the double mean proportion. Menaechmus used the intersection of conic sections (specifically, parabolas and hyperbolas) to solve this problem. While he didn't use algebra in the modern sense, his geometric methods were advanced and influential. Eudoxus (circa 408–355 BCE): Eudoxus of Cnidus, a contemporary of Menaechmus, developed the theory of proportion that later contributed to understanding similar problems. His work on proportion, although not algebraic, laid the groundwork for more formal treatment of ratios and proportions.

Diophantus (circa 250 CE): Diophantus of Alexandria is known for his work in algebra, particularly for solving equations and using symbolic notation. Although he lived several centuries after Menaechmus, his work on algebraic equations provided a more formal approach to solving such problems. In his seminal work Arithmetica, Diophantus tackled problems involving equations that could be seen as related to the double mean proportion.

Al-Khwarizmi (circa 780–850 CE): The Persian mathematician Al-Khwarizmi, whose name gave rise to the term "algebra," wrote the book Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala (The Compendious Book on Calculation by Completion and Balancing). His work formalized many algebraic methods, and while he did not directly solve the double mean proportion, his algebraic techniques provided tools that could be applied to such problems.

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