CHAPTER VI

GOLDEN AGE OF GREEK SCIENCES

Science had made a great advance as a result of the researches and theories of the atomists. A consistent mechanical theory of matter and the universe had been set forth. Science and philosophy were stripped of many of the old superstitions that had clung to them. The leading theories invented were based on logical principles. While these changes were being worked out, numerous inventions of scientific instruments and apparatus were made and systematic methods of studying science were organized. These furnished the means for still greater progress.

The apparent completeness of the mechanical theory of the universe satisfied the inquiring intellect. The excitement caused by the scientific discussions and discoveries from the time of Heraclitus subsided. But after a short intervening period, when public attention had been largely centered on practical affairs, there was a reaction against science. When scientific principles were quoted a tendency was shown to question their validity and usefulness. This resulted in inquiries into the sources of knowledge and conduct and ushered in a new intellectual era that is now known as the Humanistic period which, beginning about 450 B. C., extended to 400 B. C.

The Sophists, who were teachers of rhetoric and were accustomed to studying the phrasing of verbal statements, became active in searching for the foundations of thought.

The Protagorean theory of knowledge was based on Empedocles's doctrine that the inner atoms advance to meet the outer ones. Perception is the resultant product of these atoms when they collide. They believed that this perception is something else than the perceiving subject and is also something different from the object giving birth to the perception. It is conditioned by both, but has a distinct existence. The doctrine of the subjectivity of sense perception was developed in explanation of this psychological problem. From this it followed that knowledge must be strictly personal and could be true only under conditions existing at the instant of perception. These limitations caused Protagoras to advance his theory of relativity, which teaches that man is the measure of all things. Facts are what appear to each individual to be statements of truth. Isocrates, Plato, Aristotle, and Socrates were the leaders of this intellectual movement.

Socrates developed the Pythagorean theory of intelligible forms. The specific qualities of the senses belong to the realm of perception. When these are withdrawn from an object of thought there remains only the form or idea. Therefore it is evident that pure, intelligible forms constitute the essences of things. The early scientists, such as Democritus, thought, perhaps, in terms of atom forms. Socrates, Plato, and later teachers looked upon forms as conceptions of similar logical elements. Knowledge, in the view of Democritus, was essentially rationalistic. Plato considered knowledge as having ethical and æsthetic purposes within itself.

Each of these types of rationalism stimulated Greek thought and resulted in a strong impulse to philosophical and scientific investigation. They prepared the outlook for Aristotle.

Science had been hampered by the confusion raised by the discussions relating to forms. Aristotle realized that proper progress in logic, physics, and ethics, the leading sciences of his time, could not be made unless the essential nature of science were kept in view. He saw that knowledge of the forms of correct thinking can be understood only by keeping in view the object of thought and this requires definite ideas of the general relations of knowledge and its objects. The study of general relationships led to the study of particular or special relations. The connection of general with particular ideas was unfolded, and Aristotle saw that conceiving, understanding, and proving result from the deduction of particular from universal, or general, ideas. Therefore science consists in deriving or deducing facts acquired through perception from their general grounds or phenomena. The logical form of the syllogism naturally suggested itself to Aristotle when engaged with these thoughts and the invention of the syllogism was one of the most brilliant contributions to knowledge made by the Greeks.

The logical results of the invention of syllogistic forms suggested a solution of the problem of true reality which Aristotle showed was the essence that unfolds in phenomena themselves. This led to fruitful scientific results. Plato and his contemporaries unified mathematics, formulated the definitions logically, and demonstrated correct methods of criticism and proof. A point was shown to be the boundary of a line; while a line is the boundary of a surface, and a surface the boundary of a solid. This concrete definition of scientific elements progressed through the use of analytic methods, by proceeding from the known to the unknown, and led to the discovery of tests for scientific assumptions and of synthetic proof. None of the earlier philosophers possessed anything like the progressive tools Aristotle placed in the hands of scientists. Their use quickly led to a general review of knowledge and a great increase in the number of sciences.

The textbook on geometry compiled by Euclid, still used in many schools, gives us a good picture of the state of scientific methods in his time. Euclid, like Aristotle, Plato, Socrates and others, was a great systematizer. He collected the geometrical proofs of his mathematical predecessors, selected those which were logically correct and simple, and raised on a few axioms, or first principles, a great geometrical system.

Archimedes published textbooks on spherical and cylindrical geometry. He proved that the surface of a sphere is equal to four times a great circle. He showed the properties of spherical segments and methods for calculating surface areas and other parts of spherical forms.

This great scientist also developed mechanics and physics. He investigated the lever and demonstrated the principle upon which its power is based. He then studied hydrostatics and hydraulics, and discovered the theory of specific gravity and invented methods for determining it.

Apollonius began publishing scientific textbooks about forty years after Archimedes. His masterpiece was his textbook on conic sections.

The work done by Archimedes on the quadrature of curvilinear figures resulted, centuries later, in the discovery of the infinitesimal calculus, while the theory of conic sections published by Apollonius led to theories for the solution of problems relating to geometrical curves of all degrees. They placed the geometry of measurements and the geometry of forms and positions on strictly scientific bases.

Hipparchus applied the new mathematical and geometrical discoveries to astronomy. He found a method for representing the observed motions of the sun, moon, and planets by assumed uniform circular motions. His theory of the sun's motion assumed that the earth was not the center of the sun's orbit. He drew a line through the earth and the real center of the orbit and found where the sun's distance is least and where greatest. He then compiled a large set of solar tables giving the position of the sun among the stars at any time. He next turned his attention to the movements of the moon and prepared tables for determining eclipses.

Then the various planets were studied and their mean motions were calculated and recorded. The stars were mapped and catalogued. He described the apparent movements of 1,080 stars and comparing his observations and calculations with those of Aristyllus and Timocharis, made 150 years previously. He also discovered the precession of the equinoxes.

The astronomical calculations of Hipparchus led to a great improvement in trigonometrical methods. By using chords, as we use sines, and assuming the heavens to be a plane surface, he fixed the positions of stars (and similarly geographical points) by the intersections of lines of latitude and longitude.

A planosphere, an instrument for representing the mechanism of the heavens, was among the many scientific inventions of Hipparchus.

While Hipparchus was engaged upon problems in astronomical physics, Hero, a professor of science at Alexandria, was working out numerous problems relating to matter and devising machines for practically applying the teachings of mechanical science. Ctesibius, assisted perhaps by his pupil Hero, made a large number of valuable engineering inventions. He was an authority on hydraulics and pneumatics. He devised improved siphons, a pneumatic organ, a force pump, a vacuum pump, a hot-air motor, and other machines.

His studies regarding the physics of gases led him to adopt a molecular theory of matter. He believed that there are vacua existing between the innumerable particles which constitute matter in all its states and forms.

Ctesibius improved surveying instruments. His dioptra, an instrument corresponding to a theodolite, was a plane table set on a tripod, furnished with compass points and two sights. The plane was adjusted by screws and a water level. This instrument was used by engineers for leveling, laying out irrigation works and farm lands, sinking shafts for mining and prospecting purposes, and for tunneling. A cyclometer for measuring angles of dip and elevation of rock beds and mountains was also used with this instrument.

The Greeks owed much of their knowledge of hydrostatics, mechanics, pneumatics, and physics generally to Ctesibius. He was not only a great inventor and lecturer, but also a writer of valuable textbooks dealing with physical and mechanical sciences.

Hero edited a number of editions of the textbooks of Ctesibius, and is credited with inventing some of the theories and machines discussed. He, too, published numerous scientific books.

Hero's work in trigonometry was important. He described a formula for estimating the area of a triangle which still bears his name. He defined spherical triangles and arranged methods for determining the volumes of irregular solids by measuring the water displaced by them.

The steam turbine is the best known of Hero's machines. Scholars read much about his wonderful musical instruments operated automatically by pneumatic means resembling the mechanisms of player-pianos, and particularly about his mechanical toy mimicking a number of singing birds. A group of birds were made alternately to sing and to whistle. The mechanism consisted of air tubes operating various kinds of whistles. A running stream was made to operate an air compressor. The air from the compressor tank operated the various movements of the birds and supplied air for blowing the whistles. The numerous mechanisms of this character which Hero and his master made indicate that they were as much at home in making pneumatic and similar mechanical toys as is any expert to-day. They not only knew the scientific principles, but had the engineering and mechanical ability to design them and make them work.

Hero's fire engine is not as well known as his steam engine. It was a remarkable invention, however. It was worked by levers and force pumps and resembled the engines still employed by fire companies in some remote rural districts.

Not the least interesting machine described by Hero was his slot machine for dispensing wine and other liquids. This machine consisted of a cylindrical container with a slot hole on top through which coins were dropped. Beneath this there was a lever with a receptacle for the dropped coin. The weight of a falling coin depressed one arm of the lever and raised the other, which opened a valve and allowed the liquid to escape. When the lever arm had moved a certain distance, the coin slipped off and the valve was automatically closed.

Hero's steam turbine was a crude model. Steam was generated in a boiler and conducted through pipes so as to play upon revolving globes or wheel vanes. This machine was invented to operate mechanical toys. It was not until nearly 2,000 years later that it occurred to an inventor that steam could be used to operate more important mechanism than toys.

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.

While the physicists were making their discoveries, medical men were studying anatomy, biology, and materia medica. Medical science in the time of Diophantus had a status, with a theory and practice, closely resembling those of to-day.

Hippocrates of Cos (460 B. C.), was the greatest leader of Greek medical science. He cast superstition aside and based his researches and practice upon the same principles of inductive philosophy that had proved so valuable in other sciences. He established hospitals for the nursing of the sick, and had attendants note the symptoms and the histories of the cases. In this way a number of casebooks were made. He wrote a work on Public Health. His operations in trepanning were more heroic than would be undertaken by good surgeons to-day. These are described in his book on Injuries of the Head. Many of his works are extant and furnish very interesting and valuable pictures of the state of medical science in Greece.

During the several centuries in which the Greeks placed science and all the leading departments of knowledge upon firm bases, stripped of the sentimental and traditional trappings which had come down from remote times, changes of a political nature were causing the immigration of foreign peoples to Greece. The importance of preserving racial purity was not recognized. The result was that the original Greeks, who were of the long-headed type, were forced to give way to the hordes of inferior peoples coming in from Asia. These new, round-headed people were not original thinkers, and were unable to advance science and the arts as the Greeks had done. They were, to a large extent, even unable to appreciate the wonderful treasures of knowledge bestowed upon them by the cultured people they had displaced.

The Egyptians and Babylonians advanced knowledge for practical purposes and when these were served they showed no desire to explore further. But the analytical mind of the Greek called for knowledge of basic laws and first principles.