„When shall we say two forces are equal?“

—  Henri Poincaré, libro Science and Hypothesis, Science and Hypothesis (1901), Context: What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It, is replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration? These difficulties are inextricable. When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion. We must therefore first define the equality of two forces. When shall we say two forces are equal? It is, we are told, when, applied to the same mass, they impress upon it the same acceleration, or when, opposed directly one to the other, they produce equilibrium. This definition is only a sham. A force applied to a body can not be uncoupled to hook it up to another body, as one uncouples a locomotive to attach it to another train. It is therefore impossible to know what acceleration such a force, applied to such a body, would impress upon such an other body, if it were applied to it. It is impossible to know how two forces which are not directly opposed would act, if they were directly opposed. We are... obliged in the definition of the equality of the two forces to bring in the principle of the equality of action and reaction; on this account, this principle must no longer be regarded as an experimental law, but as a definition.<!--pp.73-74 Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Henri Poincaré Foto
Henri Poincaré11
científico y filósofo francés 1854 - 1912

Citas similares

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„We came equals into this world, and equals shall we go out of it.“

—  George Mason American delegate from Virginia to the U.S. Constitutional Convention 1725 - 1792
Remarks on Annual Elections (1775)

Henry George Foto

„In securing the equal rights of these we shall secure the equal rights of all.“

—  Henry George American economist 1839 - 1897
Social Problems (1883), Context: Those who are most to be considered, those for whose help the struggle must be made, if labor is to be enfranchised, and social justice won, are those least able to help or struggle for themselves, those who have no advantage of property or skill or intelligence, — the men and women who are at the very bottom of the social scale. In securing the equal rights of these we shall secure the equal rights of all. Hence it is, as Mazzini said, that it is around the standard of duty rather than around the standard of self-interest that men must rally to win the rights of man. And herein may we see the deep philosophy of Him who bade men love their neighbors as themselves. In that spirit, and in no other, is the power to solve social problems and carry civilization onward. Ch. 21 : Conclusion

Henri Poincaré Foto

„When we say force is the cause of motion, we talk metaphysics“

—  Henri Poincaré, libro Science and Hypothesis
Science and Hypothesis (1901), Context: What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It, is replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration? These difficulties are inextricable. When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion. We must therefore first define the equality of two forces. When shall we say two forces are equal? It is, we are told, when, applied to the same mass, they impress upon it the same acceleration, or when, opposed directly one to the other, they produce equilibrium. This definition is only a sham. A force applied to a body can not be uncoupled to hook it up to another body, as one uncouples a locomotive to attach it to another train. It is therefore impossible to know what acceleration such a force, applied to such a body, would impress upon such an other body, if it were applied to it. It is impossible to know how two forces which are not directly opposed would act, if they were directly opposed. We are... obliged in the definition of the equality of the two forces to bring in the principle of the equality of action and reaction; on this account, this principle must no longer be regarded as an experimental law, but as a definition.<!--pp.73-74 Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

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„When we have produced men of reason, we shall have a world of reason, and the Hitlers will disappear. As long as we produce men of force we shall have a world of force, and the Hitlers, whoever wins the wars, will carry the day.“

—  Milton Mayer American journalist 1908 - 1986
I Think I'll Sit This One Out (1939), Context: It is a sensible military tactic to recognize the enemy before you shoot. The common enemy is the animality in man, and not the men here and there who are behaving like animals at the moment. Neither science nor prayer nor force will save us. What will save us is the reason that enables men, in ancient Israel and modern America, to choose between guns and butter, and to choose well. When we have produced men of reason, we shall have a world of reason, and the Hitlers will disappear. As long as we produce men of force we shall have a world of force, and the Hitlers, whoever wins the wars, will carry the day. Society may make many demands on me, as long as it keeps me out of the cave. It may take my property. It may take my life. But when it puts me back into the cave I must say, politely but firmly, to hell with society. My ancestors were cannibals without benefit of parliaments.

John Donne Foto
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„We are not all equal, and never shall be; the true postulate of democracy is not equality but the faith that every man and woman is worth while.“

—  Stanley Baldwin Former Prime Minister of the United Kingdom 1867 - 1947
1927, Context: Your work in social service, whatever form it may take, requires exactly those two things that my work requires... patience and faith in human worth. Those are the real foundations of democracy, not equality in the sense in which that word is so often used. We are not all equal, and never shall be; the true postulate of democracy is not equality but the faith that every man and woman is worth while. Speech to the annual meeting of the Union of Girls' Schools (27 October 1927), quoted in Our Inheritance (London: Hodder and Stoughton, 1938), pp. 150-151.

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„In my remaining term of around two years, I shall improve the economy in full force!“

—  Chen Shui-bian Taiwanese politician 1950
Pet Phrases, 2006, During the meeting with his supporters from Hwalien, April 8, 2006

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George III of the United Kingdom Foto

„When the unhappy and deluded multitude, against whom this force will be directed, shall become sensible of their error, I shall be ready to receive the misled with tenderness and mercy!“

—  George III of the United Kingdom King of Great Britain and King of Ireland 1738 - 1820
Address to Parliament http://www.loc.gov/teachers/classroommaterials/presentationsandactivities/presentations/timeline/amrev/shots/address.html (27 October 1775).

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“

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