Apollonius of Perga (about 262-200 B.C.) was the last of the great mathematicians of the golden age of Greek mathematics. Apollonius, known as "the great geometer," arrived at the properties of the conic sections purely by geometry. His descriptions were so complete that he would have had little to learn about conic sections from our modern analytical geometry except for the improved modern notation. He did not, however, describe the properties of conic sections algebraically as we do today.
Apollonius defined the conic sections as sections of a cone standing on a circular base. The cone did not have to be a right cone, but could be slanted, or oblique. Apollonius noticed that all sections cut through such a cone parallel to its base were circles. He then extended the properties that he observed from these circles to ellipses and the other conic sections. He even solved the difficult problem of finding the shortest and longest distances from a given point to a conic section. These distances lie on lines called normals, which cut the curve of a conic section at right angles.
It is fortunate that scientists like Johannes Kepler, who lived many centuries later, had the principles of conic sections discovered purely mathematically by Apollonius and others to aid them in their work. This enabled them to realize the connections between mathematics and the natural world. It was Isaac Newton who first fully identified the connection between conic sections and the movement of celestial bodies, such as planets and comets. He was able to show that if the gravitational attraction between the sun and the celestial bodies varies inversely as the square of the distance between them, then the shapes of the orbits will be conic sections, as had been observed by Kepler and others.
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