The earliest Miletus school was very interested in astronomy, geography, mathematics, physics and biology. Pythagoras school studies these aspects of knowledge from the harmonious beauty of numbers. They divide natural numbers into odd, even, prime and perfect numbers. According to records, they first proved the Pythagorean theorem and found that if the waist of an isosceles right triangle is 1, the chord comes from an incommensurable √2. This puzzled them and led to the "first crisis" in the history of mathematics, which later led to the discovery of irrational numbers. They conceived the world's earliest overall model of the universe from the digital point of view, and thought that ten, circle, ball and average speed were the most perfect. Therefore, in addition to the five planets, fire, earth, sun and moon river, they also imagined a planet facing the earth, with the number of celestial bodies being 10. They believe that the center of the universe is the "central fire" and the position of "facing the earth" is always in the center of the central fire and the earth. The earth is always facing the central fire, and human beings live on the other side, so people can't see the central fire and the earth. All celestial bodies are spherical and move around a circular orbit at a constant speed. The sun and the moon are bright because they reflect light from a central fire. Although this model is absurd, it has a great influence on later generations. They also found that when the length ratio of strings with the same tension but different lengths is an integer ratio, they will produce harmonics, which not only contributes to physics, but also makes them more convinced of the harmony of numbers in the universe. Alkell Mang, a doctor of Pythagorean school (6th century BC to 5th century BC), discovered the optic nerve and the European tube, and realized that the brain was an organ of feeling and thinking, and was known as the father of ancient Greek medicine.
Empedocles, who holds the "Four Roots Theory", initiated the vortex theory of the formation of the universe, and later Le Xipu, who holds the view of atomism, developed this theory. Sophisticated scholars put forward three mathematical problems, which attracted many people's attention and research. Although they have not been solved, their by-products are the beginning of the exhaustive method. In order to seek the perfect beauty in thinking, Plato paid attention to the proof method of mathematics and introduced the direction of studying mathematics into pure theory divorced from reality. Deviating from Plato's research direction is his student Auddock Suo (about 408 BC-355 BC). He made great contributions to geometry, developed an exhaustive method for calculating quadrilateral area and surface volume, and foreshadowed the germination of calculus. Through careful observation of astronomical phenomena, Auddock proposed the bud of integral geometric module calculus of the universe. Through careful observation of astronomical phenomena, Auddock put forward the whole geometric model of the universe-concentric sphere model. In order to explain the apparent motion of the planet, the number of concentric spheres centered on the earth has increased to 27. Aristotle developed several models to increase the number of concentric balls to 55.
Aristotle was the "most learned man" in ancient Greece. In addition to developing the geometric model of concentric sphere, he also completed the world's first physics monograph, Physics. Due to the limitation of history, some people say that "everything Aristotle taught is false", which later became a tool for religious use. However, his careful reasoning and research on mechanical motion is a great event in the history of science. He adopted different biological research methods. Of the 500 animals he recorded, at least 50 were observed by manual dissection, and eight kinds of animals were classified, among which the "step-by-step classification" paid attention to the continuity between levels and regarded the whole biological world as a continuous series. Later, he was succeeded by his student Dior Flaster (about 372 BC-286 BC). Plants are classified according to the state of trunks and branches. Talisto broke through the method of intuitive thinking and prepared for the gradual differentiation of natural science from natural philosophy.
After Aristotle, there were still many speculative fields in ancient Greece, but in some fields it has entered the category of theoretical science. The speculative thinking and logical reasoning of natural philosophy have drawn a lot of qualitative conclusions about natural phenomena. These conclusions are full of mistakes, even ridiculous jokes, and historical limitations are inevitable. However, they urge people to pay more attention to theoretical thinking, which has become the only way in the development of science and a form of knowledge in ancient science, laying the foundation for the birth of theoretical science. Eudoxus (about 409-356 BC) put forward the theory of celestial concentric sphere under the guidance of Plato's principle of uniform circular motion of celestial bodies. He set up 27 concentric spheres: one for the star, four for each of the five planets, the Theory of Three Represents sun and the moon.
After Aristotle, Alistair of Samos (365438+ 00 BC-230 BC) first proposed Heliocentrism. He measured the distance ratio between the sun and the moon according to triangulation, and estimated the sizes of the earth, the sun and the moon according to the shadow cast by the earth on the moon during the eclipse and the perspective relationship between the sun and the moon. He also made a bold and unusual guess, and the earliest sun-centric theory that the earth and planets revolve around the sun appeared. He believed that the sun and stars are motionless, and the earth rotates once a day around its own axis. These views were very close to Copernicus' Heliocentrism, but they did not conform to the secular views at that time, and there was no conclusive evidence to prove them. As soon as this idea was born, Alistair himself was accused, and a fresh idea was considered blasphemous and killed. Nevertheless, to some extent, it also shakes the concentric sphere universe model. Alistair also put forward the theory that the earth moves around the sun based on the data of the size and distance between the sun, the moon and the earth. For the disparity of sidereal years that should be produced but not observed, he assumed that the radius of the earth's orbit was insignificant compared with the distance from the earth to the star. This theory is revolutionary, but it lacks the support of empirical facts.
Soon after, apollonius (about 262 BC-BC 190) put forward two mathematical inventions: eccentric circular motion and current wheel and even wheel model, which provided a basis for astronomers to solve the apparent motion problem of planets. Nowadays, the movement of wheels and even wheels can mathematically explain the various motion states of planets, such as stagnation and retrogression.
This pattern was inherited by Iba Valley (about BC 190-BC 120 years). This is Iba Valley's model of this round, that is, all celestial bodies have made uniform circular motion on their current round, and the center of this round has made uniform circular motion with different speeds and directions on the geocentric center. The model itself did not change people's habitual understanding, and it well explained the change of the distance between the sun and the moon and the apparent motion of the planet observed at that time. Therefore, it was quickly accepted by people, and was later inherited and perfected by Ptolemy (about 90- 168) in Roman times. Ibagu's own work is convincing and one of the reasons why the model is easily accepted by people. Ibagu has worked in the roters Island Observatory for 35 years, observing the astronomical phenomena day and night, and his astronomical instruments and research methods are excellent. He first discovered precession, measured the time of the tropic year and the first lunar month, the ratio of the radius of the moon to radius of the earth, and the ratio of the distance between the moon and the earth to radius of the earth. Iba Valley is known as the greatest astronomer in ancient Greece.
Apollonius's invention was also used by Hippocrates (about BC 190- 127) to describe the astronomical phenomena, and Greek astronomy has since embarked on a broad road. Hipachas used the observation data preserved in Babylon for centuries when constructing the geometric models of the sun, moon and planets. His other important discovery is the retrograde of the vernal equinox, that is, the precession. He proposed a model of solar motion, which solved the contradiction between the unequal length of the four seasons and the uniform circular motion. In addition to astronomy, the achievements of the Greeks in mathematics are also amazing. They refined and sublimated the experience and wisdom of the Egyptians and Babylonians into a new system. With this system, future generations will no longer need to master geometry through experience, but only through books and logic. It is said that Thales of Miletus first proposed and proved that the diameter is equal to a circle, the circumferential angle of the diameter is a right angle, the base angle of an isosceles triangle is equal, and the corresponding sides of similar triangles are proportional. He also put forward the condition of congruence of triangles. This is the content of middle school geometry today, but it was a great scientific discovery at that time. Pythagoras and his school proved Pythagoras theorem and discovered the root number 2. In the late ancient Greece, Euclid (about 323-235 BC) and Archimedes of Sicily (about 287-2 BC12 BC) made the greatest contributions to scientific theory.
Euclid is a master of Greek mathematics, an ancient Greek mathematician, and is called "the father of geometry". His most famous book, The Elements of Geometry, is the foundation of European mathematics. It puts forward five postulates and develops Euclidean geometry. It is widely regarded as the most successful textbook in history. Euclid also wrote some works about perspective, conic curve, spherical geometry and number theory, and was the founder of geometry. Euclid noticed the development trend of geometric theory through his early systematic and in-depth study of Plato's mathematical thought, especially geometric theory, and strictly demonstrated and explained formulas and theorems that lacked systematic fragments, fragmentary knowledge, interrelated axioms and proofs, and were not logical. Based on 10 postulate and axiom, 467 propositions are deduced according to strict logical proof, forming a complete geometric system. Euclid's mathematical method, the abstract logic system based on definitions and axioms, which was created in Geometry Elements (volume 13), not only provided a blueprint for the research and teaching of geometry, but also had a great impact on the development of the whole natural science, and its clarity and reliability were impressed by later scientists. This is the original contribution of the Greeks to the development of mathematics, and geometry has since become a science and the most mature subject in ancient times. His other works: known number: it is pointed out that if geometry puzzles the known elements in the figure, the content is closely related to the first four volumes of the Elements of Geometry. "Division of Circle": This paper discusses the division of known figures into equal or proportional parts by straight lines, similar to Ciro's works. Reflective optics: Discusses the mathematical theory of reflected light, especially the images on plane and concave mirror. Phenomenon: It is a paper on spherical astronomy, similar to the works written by Otto Lecosse. Optics: one of the early works of geometric optics, this book mainly studies perspective, stating that the incident angle of light is equal to the reflection angle, etc.
Archimedes (287 BC-2 BC12) was an ancient Greek philosopher, mathematician and physicist. Archimedes has been to Alexandria. It is said that he invented Archimedes screw pump when he lived in Alexandria. Archimedes combined observation with mathematical reasoning, theoretical research and practical application, discovered the lever principle and buoyancy law, and gave a method to solve the center of gravity of complex debris. His research method is close to modern research method, and he is known as "the father of mechanics". There are more than 10 mathematical works handed down by Archimedes, most of which are Greek manuscripts. He is an outstanding representative who combines mathematical research with mechanical research and natural science with engineering technology. Among his research on mechanical problems, the most famous are the principle of lever and the law of buoyancy, and his works include On Lever, On the Balance of Flat Plate, Knowing the Center of Gravity, On Buoyancy and so on. Biographer Plutarch commented on Archimedes' works like this: "It is impossible to find more difficult and complicated problems in the whole geometry, and it is impossible to find simpler and clearer explanations." In "On the Balance of Flat Plates", there is a famous saying called "Give me a fulcrum and lever long enough, and I can shake the whole earth." This book systematically discusses the principle of lever, reveals the relationship between weight, fulcrum and force, and points out that the ratio of weight or force acting on both sides of lever fulcrum is equal to the inverse ratio of the length of force arm, which reveals the bud of theoretical mechanics. Archimedes used postulate and proposition to express lever principle, which is quite similar to modern theoretical natural science. In On Floating Bodies, he first demonstrated the law of buoyancy through mathematical analysis and proved that the buoyancy of an object floating in a liquid is equal to the weight of the displaced liquid. When immersed in a liquid, its weightlessness is also equal to the weight of the discharged liquid. Archimedes' principle formula appears: an object immersed in a liquid is subjected to upward buoyancy, and the buoyancy is equal to the gravity when the object displaces the liquid. That is, f float = g liquid row = ρ liquid gvrow (v row represents the liquid volume displaced by the object, and f represents the buoyancy of the object in gas and liquid). Scope of application: gas and liquid. In On the Ball and the Cylinder, he proved that (proposition 13) the surface area of any regular cylinder (excluding the upper and lower bottoms) is equal to the area of a circle, and the radius of the circle is the median term of the ratio of the height of the cylinder to the diameter of the bottom; (Proposition 33) The area of any spherical surface is equal to 4 times the area of its great circle; (Inference of Proposition 34) With the great circle of the ball as the base, the volume of a cylinder with high diameter is 3/2 of the volume of the ball. Its surface area, including the upper and lower soles, is 3/2 of the sphere area. He liked this theorem so much that his last words engraved it on the tombstone.
Mathematically, the circumference, sphere and vertebral body are studied in detail, and the general calculation method of area and volume is emphatically discussed. He also invented pulley cranes, spiral water pumps, and hydraulic propulsion instruments that imitate the movements of the sun, moon and planets around the earth. So he was also an ordnance inventor. Archimedes' achievements in science mainly depend on Archimedes' scientific research thoughts and a set of research methods he established. At the same time, he also closely combined mathematical research with practical application and obtained general methods. When studying mechanical problems, we should first pay attention to practical observation and experiments, and then draw axioms and basic assumptions from them, and then explore its mechanical principles with strict logical reasoning and mathematical argumentation. Mathematics and mechanics are interrelated, as he himself said, mechanical research promoted his mathematical research; From his mechanical works, we can see how mathematical analysis helped him reach the theoretical height. It was Archimedes who first made the mechanical principle artistic. This is also one of the main reasons for his achievements, which is inseparable from the conditions of social time, the influence of social production and Archimedes' dedication to science. When the ancient city of Syracuse fell, he was absorbed in studying this problem, but unfortunately he was stabbed to death by a Roman soldier. Much knowledge of Greek medicine comes directly from Egypt and the two river basins. Spells and exorcism were once popular treatments. Around the fifth century BC, doctors appeared to practice medicine and gradually formed some medical factions. In the medical field, medical and anatomist Herophilus (4th century BC) established a medical school in Alexandria. Herophilus paid more attention to practical experience and gave a good description of many organs of the human body. For example, he accepted Alkman's view and criticized Aristotle's view that the heart is an organ for thinking. He was the first person to distinguish between arteries and veins. Then, Elasi Xstrata (about 304-250 BC) investigated the distribution of arteries and veins in the human body and the function of the brain, and was the first to study physiology as an independent discipline. He also put forward the so-called "gas field" theory, which holds that air is inhaled into the lungs and then enters the heart to become a "vitality gas field", and then flows to the whole body through arteries, and part of the "vitality gas field" flows into the brain to become a "soul gas field", and then flows to the whole body through nerve arteries. Oldham (3rd century BC) studied bones, nerves, pancreas and even embryos through anatomy. This school laid the foundation for European medicine.
Hippocrates is known as the father of ancient Greek medicine, with 59 complete works, which is the achievement of ancient Greek medicine. The theory and medical skills of this school are ahead of the opinions of any era before modern times. Hippocrates believed that disease was a natural process of human body, and advocated to study disease through observation and experiment, and founded the "four body fluids theory", which believed that human body was composed of four body fluids: blood, mucus, yellow bile and black bile, and the different coordination of these four body fluids made people have different constitutions. He regards disease as a developing phenomenon, and thinks that doctors should not only treat diseases, but also treat patients. This changed the medical concept of witchcraft and religion at that time. It is advocated to pay attention to the influence of patients' personality characteristics, environmental factors and lifestyle on their illness during treatment. Pay attention to healthy diet therapy, but don't neglect drug treatment, especially pay attention to symptomatic treatment and prevention. He has a rich knowledge of bones, joints and muscles.
In the field of biology, anaximander once imagined that people were transformed from fish, because human embryos are very similar to fish. The method of anatomy and observation adopted by Aristotle is the first in the history of biology. Dio Flaster (about 372-286 BC) inherited and supplemented the work of his teacher Aristotle.
Geography is mainly the work of Eratosthenes (about 273 BC-65438 BC+092 BC), who was the librarian of Alexandria in late ancient Greece. He is the author of Revision of the Earth's Size and Discussion of Geography, which records the topography, climate and minerals in many places, and records the circumference of the earth, which is only 385.6438+03 km away from the equatorial circumference measured today. He used ingenious methods to determine the location of mountains and rivers on the earth and drew the earliest map in the world represented by latitude and longitude grids.
In the field of physics, Thales believes that magnets attract iron and magnets have souls. Anaximander and Anaximenes explained the formation of wind and rainbow roughly correctly respectively. Empedocles also correctly believed that hearing is caused by sound, and sound is caused by air vibration. Pythagoras studied the relationship between the length of strings and temperament. Zhi Nuo of Elias put forward four paradoxes. Aristotle wrote the earliest monograph on physics in the world. He studied the simplest phenomenon of mechanical motion. Roman civilization is actually a continuation of Greek civilization. Rome is located in the Italian peninsula. Because of its expansion, it has become a great empire spanning Europe, Asia and Africa. 1 century-peaked in the 2nd century and declined in the 3rd century.
Compared with ancient Greece in theoretical science, ancient Rome was not only inferior, but also a great retrogression, which was inseparable from the social and ideological limitations of Roman times. Rome itself is a military empire developed on the basis of agriculture. Long-term military action made it focus on military plunder. Even in the stable period of the early empire, he only pursued a luxurious life on the basis of plunder, ostensibly showing his authority, and did not have the idea of inheriting and developing Greek scientific achievements. Therefore, the first war burned 500,000 manuscripts collected by Alexander. Later, 300,000 manuscripts were burned to suppress heresies who did not believe in Christianity. They think that mathematics in ancient Greece is just a "magic method", which stifles the mathematical reasoning that has just entered the threshold. The power of slaves to decide for themselves is increasingly concentrated, and the polarization between the rich and the poor is intensified, which is the loss of scientific development momentum. Therefore, the prosperity of ancient Rome in its heyday is only a temporary phenomenon that attaches importance to reality and ignores theory. Ancient Greek science declined in ancient Rome, but there were still important advances in astronomy and medicine. Ptolemy's On Mottos is a masterpiece of ancient astronomy, and a geocentric system is established by using mathematical model method. Dr Galen put forward the theory of "aura". Ptolemaic geocentric theory and Galen medicine dominated western science 1500 years.
Ptolemy (about AD 100- 170) made detailed astronomical observations after Iba Valley, which further improved the round-even wheel system of the current geometric model of the universe. He increased the circular orbit of celestial bodies to 80, which was better consistent with the observation results. Although he thinks that such a huge and complex system has no objective reality, only the meaning of mathematical processing, he can't get rid of the old track all the time. He has made unremitting research and achieved satisfactory results. Finally, he wrote a book "The Great Theory", and its influence extended to the establishment of Copernicus' ideological system in16th century.
Pliny (23-79) is a naturalist and a medical scientist. He recorded drugs made from vegetables, animals and minerals, provided public health information of that era, and compiled it into natural history. The medical part of Celsus Encyclopedia was preserved in the first century AD. He was convinced of Hippocrates' view of pathology and made some progress. The treatment of trauma and fracture is described in detail, and four main symptoms of inflammation are summarized: redness, swelling, heat and pain.
Galen (129- 199) was born in an architect's family near the Aegean Sea in Asia Minor. In his early years, he studied with local Plato scholars, and at the age of 17, he studied medical knowledge with a doctor who was proficient in anatomy. He is the most famous and influential medical master in ancient Rome, and is considered as the second medical authority after Hippocrates. Galen is the most famous doctor and anatomist. He devoted his whole life to medical practical anatomy research (human anatomy was forbidden during Roman rule, and Galen understood the human body by dissecting animals), writing and various academic activities. He wrote 65,438+0,365,438+0 books in his life, among which two books, Anatomy Process and Functions of Various Organs of the Body, expounded many of his own discoveries in human anatomy and physiology.
It is worth pointing out that the influence of ancient Greek philosophy formed two schools of materialism and idealism in ancient Rome. The materialism represented by Lucretius (about 99-55 BC) inherited and perfected Epicurus' atomism. The idealist school inherited the stoic pantheism and Plato's theory of soul reincarnation. The combination of the two became the ideological basis of ancient Roman alchemy, which made alchemy popular in ancient Rome for 300 years. Although absurd, it has accumulated knowledge for the origin of chemical science. On the whole, the mainstream of theoretical science in ancient Rome has not made any great achievements, but only the system and perfection of some theoretical sciences in ancient Greece.