Apollonius of Perga

262 BC – 190 BC

The work of Apollonius of Perga has had such a great impact on the development of mathematics, that he is known as “The Great Geometer”. In fact, in his book Conics he introduces terms, such as parabola, ellipse, and hyperbola that are still used today.
At a young age, Apollonius studied under followers of Euclid in Alexandria, where he later taught.

In order to discuss his work Conics, we should note what he meant by a conic section. He defines this term to be the curves formed when a plane intersects the surface of a cone. His work consisted of eight books, the first four of which are an elementary introduction to the basic properties of conics. Even though these principles were already known to others, Apollonius claimed that he had worked them out more fully and generally. More specifically, in these first four books, Apollonius studies the relations satisfied by the diameters and tangents of conics, how hyperbolas are related to their asymptotes, and how to draw tangents to given conics.

In the next three books, Apollonius discusses normals to conics, and he shows how many can be drawn from a point. He provides propositions determining the center of curvature, which in turn led to the Cartesian equation of the evolute. The works found in these books were highly original.

In yet another one of his works Tangencies, he shows how to construct a circle tangent to three given circles. Even more generally, he shows how to construct a circle tangent to three given objects (points, lines, or circles).

Apollonius also was an important person in founding Greek mathematical astronomy. He used geometrical models to explain planetary theory. He introduced systems of eccentric and epicyclic motion to explain the motion of the planets. Another contribution of his, was the development of the hemicyclium, which is a sundial having the hour lines drawn on the surface of a conic section.

References:

Greenberg, Marvin J. Euclidean and Non-Euclidean Geometries:

Development and History. 3rd ed. New York: W.H. Freeman and Company,
1993. 6-19.

Historical Topics for the Mathematics Classroom. Washington D.C.:

National Council of Teachers of Mathematics, 1969.

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Thales.html (March 2005)

http://geometryalgorithms.com/history.htm (March 2005)

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