Apollonius of perga (2627-190 bc)

Admiring friends called him “The Great Geometer” for his numer­ous accomplishments in the field of geometry. Specifically, it was his theory of conic sections, elaborated in his major work, ‘Conics’, that earned Apollonius of Perga the plaudits of his contemporaries.

A solid cone can be cut into sections, producing several un­usual forms. Apollonius examined these conic sections, noted their shapes, and introduced the terms ellipse, hyperbola, and parabola to describe them. He was the first to recognize that these three forms, along with the circle, are all part of any cone. His ‘Conics’, which brought order to a confused and ill-defined area of geome­try, is considered one of the greatest scientific works of the ancient world. His theory of conic sections is still useful to engineers and mathematicians.

Born in Perga, an ancient Greek town that lies in present-day Turkey, Apollonius studied in Alexandria, Egypt, and later taught at the university there. He traveled to several libraries and univer­sities to expand his understanding of mathematics. In his numer­ous books (most of which have been lost), Apollonius acknowledged those who had studied the field before him, summarized their work, and proceeded to make his own contribution. Only in the final vol­umes of ‘Conics’ did he break new ground. In addition to geometry, he studied the properties of light and the way curved mirrors reflect it.

Descartes, Кепё (1596-1650)

Both modern philosophy and modem mathematics began with the work of Rene Descartes. His analytic method of thinking focused attention on the problem of how we know, which has occupied philosophers ever since. His invention of coordinate geometry pre­pared the way for advances in mathematics. Descartes offered one of the first modem theories to account for the origin of the solar system of the Earth.

Непё Descartes was bom on March 31, 1596, at La Haye in the Touraine region of France. At the renowned Jesuit school of La Fleche, Rene was taught philosophy, the humanities, science, and mathematics. After getting a law degree at the University of Poitiers in 1616, he served as a volunteer in Dutch and Bavarian armies to broaden his experience. He resumed his study of math­ematics and science when his duties permitted. Dissatisfied with the haphazard methods of science then in use, he began to doubt all but mathematical knowledge.

In 1619 Descartes arrived at the conclusion that the universe has a mathematically logical structure and that a single method of reasoning could apply to all natural sciences, providing a unified body of knowledge. He believed he had discovered such a method by breaking a problem down into parts, accepting as true only dear, distinct ideas that could not be doubted, and systematically deducing one conclusion from another.

Descartes soon gave up army life. Living on private means, he spent several years traveling and applying his analytical system to mathematics and science. Finding, however, that the sdences rested on disputed philosophical ideas, he determined to discover a first prindple, which could not be doubted, on which to build

knowledge. Retiring to seclusion in Holland in 1629, he methodi­cally doubted all accepted traditions and evidence about the uni­verse and mankind. He could not doubt the statement “I think, therefore I am," and thus his first principle was established.

Descartes’s major writings on methodology and philosophy were his ‘Discourse on Method’ (published in 1637) and ‘Meditations’ (1641). His application of algebra to geometry appeared in his ‘Ge­ometry’ (1637). He also published works on his studies in natural science.

Descartes’s work brought him both fame and controversy. In 1649 he was invited to teach philosophy to the queen of Sweden. Unused to the climate, he became ill and died in Stockholm on Feb. 11, 1650.