Ancient Greek scholars were all lovers of mathematics, and the "Thales" of the father of Western philosophy and Pythagoras, who counted everything, all made important contributions to the development of mathematics. By about 300 B.C., Euclid had summarized the results of his predecessors' research and established a system of "axiomatization", which was the culmination of the Greeks' quest for "certainty of knowledge". Almost at the same time, Archimedes also established an academic system of "axiomatization" of physics.
Archimedes was born in Syracuse, Sicily around 287 BC, died in 212 BC. This is a great scientist who can be compared with Newton, and his contribution to the development of science is comprehensive, but in this article we will look at one or two from the field of physics.
Archimedes famously said, "Give me a fulcrum, I can pry the earth.". This sentence reflects his pride in proving the "lever principle", which is the successful practice of axiomatic methods in the field of physics. Chinese's discovery of the principle of leverage is based on induction and is summarized from practical experience. Archimedes, on the other hand, were calculated mathematically. Experience has uncertainty and cannot form axioms, mathematics has an axiomatic nature, only the premise is correct, the inference is logical, then the result must be correct.
The difference between induction and deduction is that to prove the lever theorem, induction pays attention to trying, and it is obvious that the conclusion of the Western Chu Bawang's attempt must be different from others. The deductive method must first turn this physical problem into a mathematical problem, and make the concrete problem an abstract formula problem. Without considering the material, shape, deformation, etc. of the lever, the lever is conceived as a line segment.
Archimedes gave the axiom that: 1. If the weights at both ends of the lever are equal and the distance from the fulcrum is equal, then the lever is balanced. 2. The weight of any point on the lever arm can be replaced by two places located at 2 times the distance between the fulcrum and the fulcrum, and half of the weight of the original object. The proof of the lever principle, its significance for science, is that it gives physics an axiomatic system of mathematical significance.
Another major contribution of Archimedes was the "law of buoyancy", in which he discovered in his bath that the volume of drainage was equivalent to the volume of an object immersed in water, thus solving the method of measuring the volume of the crown. King Hiro ordered the craftsman to create a crown of pure gold, but he always suspected that the craftsman had mixed other metals in the gold, to verify the problem, and not to destroy the crown that had been made. So King Hiro gave this task to Archimedes. In the story of the scientist, when he first found out, he was so happy that he ran naked.
Archimedes discovered the proportional relationship between the weight and volume of different objects at this time, but this did not clarify the "buoyancy" problem. A large number of experiments and calculations were carried out to calculate the "buoyancy", which led to the discovery that buoyancy is equivalent to the mass of the discharged liquid. The two cornerstones of physics are logical reasoning under the axiomatic system and purposeful experimental calculation. Both of these scientific methods were formed in Archimedes' time. Although Archimedes pioneered the use of "axiomatization" to study physical problems, he himself was more interested in geometry. Archimedes' contribution to mathematics is no less than that of physics.
Reprinted in http://baijiahao.baidu.com/s?id=1664677194686821409&wfr=spider&for=pc