Apollonius of Perga
c. 262-c. 190 B.C.
Greek Mathematician
Though he is known as "The Great Geometer," even that title fails to do justice to Apollonius of Perga and his career. His Conics laid the foundations for Newtonian astronomy, ballistics, rocketry, and space science—all 2,000 or more years in the future when he wrote—with its discussion of conic sections, which describe the shape formed by the path of projectiles. Along the way, Apollonius developed his own counting system for large numbers, and put forth a new mathematical worldview that opened the way for the infinitesimal calculus many centuries later.
Born in the town of Perga in southern Asia Minor (now Turkey), Apollonius later studied Euclidean geometry in Alexandria. He also visited Pergamum and Ephesus, both important cities in Asia Minor. In addition to the Conics, he wrote a number of other works, all of which have been lost, but whose English titles include Quick Delivery, Vergings, Plane Loci, Cutting-Off of a Ratio, and Cutting-Off of an Area. Pappus (fl. c. A.D. 320), the principal source regarding these lost works, also summed up the material contained in them. Other ancient writers referred to lost writings of Pappus, such as his discussion of "burning mirrors" for military purposes, in which he disproved the claim that parallel rays of light could be focused on a spherical mirror.
By far the most influential of Apollonius's works, however, was the Conics, which consisted of eight books with some 400 theorems. In this great treatise, he set forth a new method for subdividing a cone to produce circles, and discussed ellipses, parabolas, and hyperbolas—shapes he was the first to identify and name. In place of the concentric spheres used by Eudoxus (c. 400-c. 350 B.C.), Apollonius presented epicircles, epicycles, and eccentrics, concepts that later influenced Ptolemy's (c. 100-170) cosmology. Even more significant was his departure from the Pythagorean tendency to avoid infinites and infinitesimals: by opening up mathematicians' minds to these extremes, Apollonius helped make possible the development of the infinitesimal calculus two millennia later.
In the first four volumes of his Conics, Apollonius examined notions of geometry passed down by Euclid (c. 325-c. 250 B.C.) and others, and maintained that he had made it possible for the first time to solve Euclidean problems such as finding the locus relative to three or four lines. The second half of the Conics discussed conic sections, and confronted problems such as that of finding a "normal" on a point along a curve.
The Conics also presented what became known as the "problem of Apollonius," which calls for the construction of a circle tangent to three given circles, and discussed a means of finding the point at which a planetary orbit took on an apparently retrograde motion. The most important factor in this monumental work, however, was not any one problem, but Apollonius's overall approach, which opened mathematicians' minds to the idea of deriving conic sections by approaching the cone from a variety of angles. By applying the latus transversum and latus erectum, lines perpendicular and intersecting, Apollonius prefigured the coordinate system later applied in analytic geometry.
Apollonius, whose work influenced mathematicians beginning with Hipparchus (fl. 146-127 B.C.) and Hypatia of Alexandria (c. 370-415), has continued to inspire thinkers throughout the ages. The last book of his Conics was lost, and among those who have attempted to recreate it were al-Haytham (Alhazen; 965-1039), Edmond Halley (1656-1742), and Pierre de Fermat (1601-1665). Even today, mathematicians are still examining the work of Apollonius, and finding in it applications to problems and situations they could scarcely have imagined.
This is the complete article, containing 588 words
(approx. 2 pages at 300 words per page).
