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Newtonian Mechanics

In 1987 the world science societies marked the 300th anniversary of the publication of Newton’s book Philosophie Naturalis Principia Mathematica. In powerful development of physical argument his book is unequalled in the whole history of science. Mathematically it could only be compared to Euclid's Elements. In its physical insight and its effect on scientific ideas it could be compared only to Darwin's Origin of Species. It immediately became the bible of the new sciences.

Newton’s contribution into the world science was a decisive one in finding the mathematical method for converting physical principles into quantitatively calculable results confirmable by observation, and, conversely, to arrive at the physical principles from such observations.

The instrument by which he did this was the infinitesimal calculus which he used to solve vital questions in physics and taught others to do the same.

By its use it is possible to find the position of a body at any time by a knowledge of the relations between that position and its velocity or rate of change of velocity at any other time. In other words, once the law of force is known, the path can be calculated. Applied inversely, Newton’s law of gravitational force follows directly from Kepler’s law of motion. Mathematically they are two different ways of saying the same thing; but whereas the laws of planetary motion seem abstract, the idea of a planet held in its course by a powerful gravity attraction is understandable, even if the gravitational force itself remains a complete mystery.

The calculus, as developed by Newton, could be used and was used by him for solving of a great variety of mechanical and hydrodynamic problems. It immediately became the mathematical instrument for all understanding of variables and motion, and hence of all mechanical engineering, and remained almost the exclusive one until well into the present century. In his Principia Newton did far more than establish the laws of motion of the planets. His object was certainly to demonstrate how universal gravity could maintain the system of the world. But he wished to do this not in the old philosophical way but in the new, quantitative, physical way. He destroyed all previous philosophic conceptions, old and new, and established his own not only the correct but also the most accurate way of accounting for the phenomena. In a word, Newton established, once and for all, the dynamic view of the universe instead of the static one and showed that the universe was regulated by simple mathematical laws.

Though Newton used the calculus in arriving at his results, he was very careful in his Principia and did all the work in the form of classical Greek geometry understandable by other mathematicians and astronomers. The immediate practical consequence of its publication was to provide a system of calculation enabling the positions of the moon and planets to be determined far more accurately on the basis of a minimum of observations. Three observations, for instance, were sufficient to fix the position of a celestial object for an indefinite future. The proof of this was given soon after Newton’s time by his friend Hailey in his famous comet, whose return he successfully predicted on the basis of Newton’s theories.

In 1987 the world science societies marked the 300th anniversary of the publication of Newton’s book Philosophie Naturalis Principia Mathematica. In powerful development of physical argument his book is unequalled in the whole history of science. Mathematically it could only be compared to Euclid's Elements. In its physical insight and its effect on scientific ideas it could be compared only to Darwin's Origin of Species. It immediately became the bible of the new sciences.

Newton’s contribution into the world science was a decisive one in finding the mathematical method for converting physical principles into quantitatively calculable results confirmable by observation, and, conversely, to arrive at the physical principles from such observations.

The instrument by which he did this was the infinitesimal calculus which he used to solve vital questions in physics and taught others to do the same.

By its use it is possible to find the position of a body at any time by a knowledge of the relations between that position and its velocity or rate of change of velocity at any other time. In other words, once the law of force is known, the path can be calculated. Applied inversely, Newton’s law of gravitational force follows directly from Kepler’s law of motion. Mathematically they are two different ways of saying the same thing; but whereas the laws of planetary motion seem abstract, the idea of a planet held in its course by a powerful gravity attraction is understandable, even if the gravitational force itself remains a complete mystery.

The calculus, as developed by Newton, could be used and was used by him for solving of a great variety of mechanical and hydrodynamic problems. It immediately became the mathematical instrument for all understanding of variables and motion, and hence of all mechanical engineering, and remained almost the exclusive one until well into the present century. In his Principia Newton did far more than establish the laws of motion of the planets. His object was certainly to demonstrate how universal gravity could maintain the system of the world. But he wished to do this not in the old philosophical way but in the new, quantitative, physical way. He destroyed all previous philosophic conceptions, old and new, and established his own not only the correct but also the most accurate way of accounting for the phenomena. In a word, Newton established, once and for all, the dynamic view of the universe instead of the static one and showed that the universe was regulated by simple mathematical laws.

Though Newton used the calculus in arriving at his results, he was very careful in his Principia and did all the work in the form of classical Greek geometry understandable by other mathematicians and astronomers. The immediate practical consequence of its publication was to provide a system of calculation enabling the positions of the moon and planets to be determined far more accurately on the basis of a minimum of observations. Three observations, for instance, were sufficient to fix the position of a celestial object for an indefinite future. The proof of this was given soon after Newton’s time by his friend Hailey in his famous comet, whose return he successfully predicted on the basis of Newton’s theories.

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