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" AB; but things which are equal to the same are equal to one another... "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 7
av Euclides - 1853
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 sider
...(11. Definition) to AB ; and because the point B is the centre of the circle ACE, BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now things which are equal to the same are equal f* one another, (1. Axiom) ; therefore CA is equal...
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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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An Historical and Critical View of the Speculative Philosophy of ..., Volum 1

J. D. Morell - 1846
...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 equality,...
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The Biblical review, and Congregational magazine [formerly The ..., Volum 4

1847
...proved by the use of axioms in the form of propositions, that is not itself evident. The axiom, that things which are equal to the same are equal to one another, is not the proof that A and B, being equal to C, are themselves equal. The latter truth, which is particular,...
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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
...circle BCD, AC is equal (Definition 15.) to AB; and because the point B is the centre of the circle ACE, BC is equal to BA: But it has been proved that CA...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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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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