The next great name in science is that of Claudius Ptolemy, an Egyptian astronomer, who lived in Alexandria about 139 A. D. He brought out new editions of the mathematical works of Hipparchus, and published a number of scientific books of his own. His principal work, known as the Grammar of Mathematics, formed the basis of all astronomical studies down to the time of Copernicus, about 1500 A. D.
The earth formed the center of the universe, according to Ptolemy's theory. The sun and planets, he thought, revolved around the earth.
We obtain our minutes and seconds from Ptolemy's great work. He divided the circle with 360 degrees and its diameter into 120 divisions. Each division of the circumference he divided into sixty parts. The Latin names for these parts were partes minutæ primæ and secundæ, or the first small divisions and the second small divisions.
The Greek scientists were so interested in logical analysis that they constantly investigated the fundamental facts upon which their teachings were based. They made provisional hypotheses, deduced mathematical consequences, and compared these with the results of observation and experiments. When Hipparchus found that his planetary theories did not meet his tests, he decided to make as many new observations as possible and collect astronomical data to be used at a later period by other scientists. He realized that, while he knew the old theories were incorrect, there was not enough data at hand to enable better theories to be established. He therefore deliberately labored to provide data for posterity.
Ptolemy's treatise on geography was an encyclopedia of places, names, and descriptions. In this work he located over 5,000 places between India and Morocco, giving their latitude and longitude.
Ptolemy's textbooks on sound and optics were long celebrated. The work on optics contained valuable chapters on refraction, a subject he had done much to develop. These works contained some of the finest collections of experimental data illustrating the best scientific methods used in antiquity.
The next great mathematicians and physicists are Pappus and Diophantus. The former lived about 300 A. D. He was the author of textbooks on mathematics and astronomy. Some of these have been preserved and are of great value in exhibiting the status of Greek science at that time.
The arithmetical textbook of Diophantus, which is extant, is remarkable as being the first to contain a complete exposition of algebra and the use of algebraic symbols and methods. Euclid solved quadratic equations geometrically and Hero solved them algebraically, although without using symbols. But in Diophantus's arithmetic quadratics are solved by the use of algebraic symbols. After several centuries, when the Euclidean geometry was in the ascendant, and many problems which were suited to arithmetical and algebraic methods of analysis were solved by geometrical and trigonometrical means, Diophantus succeeded in renewing interest in arithmetic and mathematics generally.
Political changes and other intellectual interests soon after the time of Diophantus turned men's thoughts in other directions and no great scientists were afterward developed by the Greeks.