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.