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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of Euclid, the parts read in the University of Cambridge [book ... - Página 4
por Euclides - 1846
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 páginas
...point. II. That a terminated straight line may be produced to any length in a straight line. HI. And that a circle may be described from any centre at...centre. AXIOMS. I. THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals...
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General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848 - 520 páginas
...but belong to a higher and larger science. As examples of such axioms he gives that of mathematics, " things which are equal to the same are equal to one another," which can equally well be applied to logic, thereby insinuating that the observations of "philosophia...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848 - 394 páginas
...but belong to a higher and larger science. As examples of such axioms he gives that of mathematics, " things which are equal to the same are equal to one another," which can equally well be applied to logic, thereby insinuating that the observations of " philosophia...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 páginas
...BA: But it has been proved that CA is equal to AB; therefore CA, CB are each of them equal to AB; but things which are equal to the same are equal to one another (Axiom 1.) ; therefore CA is equal to cu; wherefore CA. AB, BC are equal to one another; and the triangle...
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The Reasoner, Volumen6

1849 - 424 páginas
...be paid as well as yours, and I should have d£20,000 a-year instead of 4s. a-day; becanse you see things which are equal to the same are equal to one another.' The Spectator, of April 28, 1849, says — '"Genins" consists in a special capacity for some particular...
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Suggestive Hints Towards Improved Secular Instruction: Making it Bear Upon ...

Richard Dawes - 1849 - 228 páginas
...which many of them would turn to a good purpose. Even a knowledge of the axioms of Euclid, such as " things which are equal to the same are equal to one another." If equals be added to equals the wholes are equal. If equals be added to unequals, the wholes are unequal,...
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Reports of Cases in Law and Equity in the Supreme Court of the ..., Volumen3

Oliver Lorenzo Barbour, New York (State). Supreme Court - 1849 - 706 páginas
...uninfluenced by the demonstration of the simplest problem in Euclid, and to which the axiom, " that things which are equal to the same are equal to one another," would be too abstruse for comprehension. The judgment and the note were familiar. and their relation...
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The Works of Francis Bacon, Lord Chancellor of England, Volumen3

Francis Bacon - 1850 - 620 páginas
...similar to that of music termed the declining of a cadence. Again; the mathematical postulate, that "things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term....
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Of a Liberal Education in General

William Whewell - 1850 - 430 páginas
...It may be said, indeed, that every step in analysis is a syllogism, in which the major is the Axiom, Things which are equal to the same are equal to one another; and the minor is a proposition that two certain forms of symbols have been proved to be equal to the...
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Artis logicae rudimenta: with illustrative observations on each section by ...

Henry Aldrich - 1850 - 406 páginas
...to be reared, and the final appeal in argument. They bear some analogy to the mathematical axioms, Things which are equal to the same are equal to one another; and, Things of which one is equal and the other not equal to the same, are not equal to one another....
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