CHAPTER VII

THE ROMAN AND MIDDLE AGES

The Romans succeeded to Greek culture; but they were a business people. They exhibited smaller intellectual capacity than the Greeks for analytical thinking. This precluded them from advancing the sciences. The Romans attained great eminence in oratory, history, art, and literature. They probably equaled the Greeks in music. They never produced any great thinkers like Aristarchus, Hipparchus, Euclid, Ptolemy, Archimedes, Democritus, Hippocrates, Plato, Aristotle, and others referred to in the preceding chapters.

What the Romans lacked in intellect they made up in energy. They became good soldiers and sailors, good politicians, able architects, engineers, and farmers. This explains how they became so powerful politically. They were the most practical people in a practical world. Instead of bequeathing us great scientific masterpieces like the Greeks, they have left us miles of useful roads, waterways, walls, fortresses, bridges, buildings, and statuary. Remains of these objects occur throughout Europe and northern Africa, showing that Roman engineering practice has been as universally useful as Roman law and political practices. The great scientific discoveries of the world have been made by only a few peoples. Those nations which have possessed the scientific temperament have not always been productive. Great inventions and discoveries appear to be made in response to national needs and are preceded by long periods during which the preparatory work is being done. The great men of science being active generalizes, need the cooperation of many lesser scientists to collect data and observations upon which general theories may be built. This appears to be the explanation of the irregular periods of great scientific activity.

Julius Cæsar, great in many departments of human endeavor, carried through two important scientific reforms. He caused the rectification of the calendar. In the year 47 B. C. there was an accumulated error of nearly 85 days in the calendar. This was corrected and the year was made to consist of 365 days, with an additional day every four years. Cæsar's calendar is still in use.

His other reform, which was not completed until the reign of Augustus, was a scientific survey of the Roman empire. This conferred great benefits not only upon Rome, but upon the world. Geography, commerce, and industry were enlarged, many practical scientists were trained, and the various data and maps which had to be collected and drawn resulted in many improvements in statistical methods and in surveying and astronomical computations.

An early contribution to science by Rome was the textbook on Architecture by Vitruvius. This great work became the standard guide to building until the changed conditions in the Middle Ages called for new architectural methods.

The works on natural philosophy by Lucretius, the geography of Strabo, the books on natural history by Pliny, and the encyclopedic medical works of Galen were successive contributions. These chiefly aimed at developing the teachings of the great Greek scientists for the practical use of the Romans.

Roman history shows that all branches of the learned professions were popular and Roman professional men were very competent. None, however, stands out as a great discoverer. The names just above recorded are those of the chief lights of Roman science, and they simply reflect the practical nature of the Roman intellect. The best the Romans did was to preserve Greek science, test it extensively by practical applications throughout their vast empire, and hand it on to succeeding nations.

Philosophical thought in the declining years of Greece turned to theosophical speculations, and finally to ethics and theology. Much interest was evinced by the Romans in ethics, æsthetics, and theology. A new religion, destined to exert profound influences on intellectual developments, gradually attracted the attention of thinkers. The Romans were fascinated by the monotheism of Christianity and the doctrines of a future life and good will and love. There grew out of the critical attacks on this new theology a powerful scholastic philosophy aiming at the exposition, systematization, and demonstration of the principal Christian doctrines.

Aurelius Augustinus, a native of Africa (353-430 A. D.), championed the opinion that knowledge of God and self was the proper kind to study. The sciences have only value in illuminating the power of God. Intelligence is necessary to comprehend what we believe; faith is required to believe what we comprehend. As the highest good, or moral ideal, is transcendent, Christians cannot realize it, so human perfection should consist in the love of God and bearing good will to others.

The conditions brought about by this turn of thought were not favorable for scientific development. The world had to wait until the scholastic philosophy lost itself in metaphysical discussions. Then Roger Bacon (1214-1294) released science and mathematics from the chains which had so long confined them.

While European thought was occupied in discussing scholastic philosophy, the Arabs and Moors were carrying on the practice of the sciences. The Moors in Spain published many valuable textbooks and developed new principles in architecture and medicine. Their Giralda observatory in Seville was the first astronomical building erected in Europe, and their university in Cordova remained for a long period the leading professional school.

The universities of Paris, Salerno, Oxford, and Cambridge, and the law school at Bologna, were founded in the eleventh and twelfth centuries and have continued to hold up the torch of science until our time.

Roger Bacon, an English Franciscan monk, was a graduate of the University of Paris. He was a brilliant student of physical and mathematical sciences. Pope Clement IV invited him to write a textbook of science. Bacon did this in 1266. He became a professor in Oxford University in 1268. His _Opus Majus_ (1267) summarized ancient and current philosophy and science and included the researches of the Moors. This great book reasserted the fact that science must be based upon experiments and that the astronomical and physical sciences must rest upon geometry and mathematics. Bacon's clear recognition of the value of experimental methods and logical exposition mark him as the greatest intellectual force of his century.

The errors in the calendar were estimated and corrected by Bacon. He criticized the astronomical principles of Ptolemy, which were still generally accepted. His experiments in physics led him to make important discoveries in optics. He improved lenses and apparently made microscopes and telescopes. He proposed a lunar theory in accounting for the movements of the tides.

Roger Bacon made so many accurate comments on physical phenomena and so accurately forecasted recent mechanical inventions that his book, which was so far in advance of his time that it was unintelligible and caused him to be charged with witchcraft, still astonishes its readers.

Lenses were used for spectacles in Asia in the remotest times, but there are reasons for believing that Bacon was the first to prescribe them on scientific principles for the correction of defective vision. He also appears to have appreciated the value of gunpowder as an explosive agent and had it introduced into Europe from Morocco. Being misunderstood, Bacon founded no school and left no students.

Nicole Oresme, Bishop of Normandy (1323-1382), used fractional powers in mathematics and developed a notation. About the same period, Thomas Bradwardine, Archbishop of Canterbury, wrote on star polygons, and other Englishmen, like Boethius and Bath, wrote new textbooks on astronomy and mathematics. They started a school of trigonometry in England that made great improvements in that branch of science.

Between 1200 and 1400 A. D. the magnetic compass was improved and used at sea, clocks were improved and made popular, improvements were made in weaving, printing was invented, textbooks were written on many subjects, and education began to spread in Europe. All these factors prepared the way for a great industrial and scientific awakening.

Nicholas de Cusa (1401-1464), Bishop of Brixen, published books on mathematics and suggested that the earth's movements indicate a diurnal rotation.

The way was now paved for a new theory of planetary motions. Nicolaus Copernicus (1473-1543) a Pole, developed the astronomical system bearing his name, as a result of suggestions gained by studying the works of the Greek astronomer Hicetas, and Plutarch's Lives of Greek Scientists. His great work was entitled "De Revolutionibus Orbium Celestium, or the Movements of Heavenly Bodies," which treated the sun as the center of the planetary system.

Weather forecasting was improved by Tycho Brahe (1546-1601), and many fine astronomical observations were made by him. He greatly improved astronomical instruments and built and splendidly equipped a great observatory in Uraniborg, Denmark. Numerous important observations were made there.

John Kepler, the discoverer of the ellipticity of the planetary orbits and the laws of their movements, was a student under Brahe, and continued his master's researches. His observations on the movements of the planet Mars led to his discovery that the planets travel in ellipses and not in circles. Besides his numerous works on astronomy he wrote valuable books on optics and other scientific subjects.

Galileo (1564-1642) took up the work of Tycho Brahe and Kepler and carried it forward to new triumphs. He made the first telescope ever used for astronomical observation, and with it was able to discern that the Milky Way was composed of aggregations of innumerable stars; that the surface of the moon was covered with plains and mountains, that there were four moons revolving around the planet Jupiter, that the planet Venus showed phases like those of the moon as she moved around her orbit, and that there were black spots, at times, upon the sun, which revealed its rotation on its axis. Galileo did equally fundamental work in developing the laws of motion, and the principles of mechanism and physics.

The development of modern mathematics began with three intellectual feats--the invention of the Arabic notation, of decimal fractions, and of logarithms. The notation was derived by the Arabs from India about 700 A. D. They had used numerals long before, but the old system was crude like the systems employed by the Egyptians and Greeks. The Textbook on Mathematics by Mohammed ibn Musa, published at Bagdad about 825 A. D., contained the first notable exposition of modern numerals. This important work gave rise to many more Arabic treatises, some of which showed improved methods.

Decimal fractions were used by the early peoples of central Asia and were transmitted by them to the Babylonians. Their system was based, apparently, upon a sexagesimal scale. Simon Stevin (1548-1620), a Belgian, made great improvements in decimals. He adopted the plan of William Buckley, of England, and other mathematicians, and made the base 100,000, instead of 60.

John Napier (1550-1617), a Scottish nobleman, invented logarithms. The story of this great mathematician's work is one of the most interesting in the history of science. Napier's first table of logarithms was published in 1614. Henry Briggs (1556-1631), professor at Oxford, made suggestions for the improvement of the tables, and persuaded Napier to make the base 10, as is now done in tables of common logarithms. Briggs published tables in 1624 containing the logarithms to 14 places of decimals for the numbers between 1 and 20,000 and from 90,000 to 100,000. Adrian Vlacq (1600-1667), a Dutchman, computed the logarithms of the numbers running from 20,000 to 90,000, and thus completed the whole series of logarithms between 1 and 100,000. Edmund Gunter (1581-1626), of London, calculated the logarithmic sines and tangents of angles for every minute to seven places. He invented the terms cosine and cotangent and used them in a work published in 1620.

Another Englishman, William Oughtred (1574-1660), wrote textbooks on mathematics, and invented numerous mathematical symbols which are now in general use, as well as rectilinear and circular slide rules.

Bonaventura Cavalieri (1598-1647) made many improvements in mathematical formulæ and expounded a new method of indivisibles which solved some of the difficult astronomical problems raised by Kepler, and enabled Torricelli, Viviani, de Roberval, and others to solve abstruse problems relating to all types of curved figures.

Pierre de Fermat (1601-1665), one of the greatest of French mathematicians, developed rules for calculating maxima and minima. His functions in this type of equation closely approached those of the differential calculus. The calculus was developed from Fermat's work by Lagrange, Laplace, Fourier, and other Frenchmen.

Pascal and Fermat developed the theory of probability. Pascal worked out many useful methods for dealing with curves.

The intense mathematical activity in England and France resulting from the stimulation given by the invention of Napier, prepared the way for the discovery of the infinitesimal calculus by Newton and Leibnitz.

Newton was born in England the same year that Galileo died in Italy. His greatest work is presented in his celebrated "Principia," or "Mathematical Principles of Natural Philosophy," in which the law of gravitation, the laws of motion, and the mathematical principles of mechanics are developed. The "Principia" was published in 1687, and it has ever since been regarded as the corner stone of mathematical and physical science.