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.