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" 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. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 318
av Euclid, Robert Simson - 1821 - 516 sider
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...But it has been shewn that BC is equal to BG; therefore AL and BC are each of them equal to BG : And things which are equal to the same are equal to one another ; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...3. That a circle can be described from any centre, with any radius. COMMON NOTIONS, OR AXIOMS. 1 . Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If from equals, equals be taken, the...
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An Historical and Critical View of the Speculative Philosophy of Europe in ...

J. D. Morell - 1847
...judgments, as we have seen in our analysis of Locke, are at first particular and concrete. The axiom, " things which are equal to the same are equal to one another," never suggests itself to a child's mind ; and yet as soon as reason is developed enough to observe...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848
...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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General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848
...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 - 108 sider
...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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Reports of Cases in Law and Equity in the Supreme Court of the ..., Volum 3

Oliver Lorenzo Barbour, New York (State). Supreme Court - 1849
...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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Suggestive Hints Towards Improved Secular Instruction: Making it Bear Upon ...

Richard Dawes - 1849 - 184 sider
...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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The Reasoner, Volum 6

1849
...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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The Works of Francis Bacon, Lord Chancellor of England, Volum 3

Francis Bacon - 1850
...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. Lastly:...
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