Apollonius Pergaeus, called “The Great Geometer,” is sometimes considered the second greatest of ancient Greek mathematicians (Euclid and Eudoxus are the other candidates for this honor). His writings on conic sections have been studied until modern times; he invented the names for parabola, hyperbola and ellipse; he developed methods for normals and curvature. Although astronomers eventually concluded it was not physically correct, Apollonius developed the “epicycle and deferent” model of planetary orbits, and proved important theorems in this area. He deliberately emphasized the beauty of pure, rather than applied, mathematics, saying his theorems were “worthy of acceptance for the sake of the demonstrations themselves.”

Since many of his works have survived only in a fragmentary form, several great Renaissance and Modern mathematicians (including Vieta, Fermat, Pascal and Gauss) have enjoyed reconstructing and reproving his “lost” theorems. (Among these, the most famous is to construct a circle tangent to three other circles.)

In evaluating the genius of the ancient Greeks, it is well to remember that their achievements were made without the convenience of modern notation. It is clear from his writing that Apollonius almost developed the analytic geometry of DÃ©scartes, but failed due to the lack of such elementary concepts as negative numbers. Leibniz wrote “He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.”

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