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" Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one... "
The Elements of Euclid [book 1] for beginners, by J. Lowres - Page 10
by Euclides - 1852
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...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 || ; therefore CA is equal to CB ; wherefore CA, « i Axiom. AB, BC are equal to one another ; and...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...any distance. 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...another. 2. If equals be added to equals, the wholes will be equal. 3. If from equals, equals be taken, the remainders are equal. 4. If to unequals, equals...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...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 ..., Volume 1

John Daniel Morell - Philosophy, Modern - 1846 - 524 pages
...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 ..., Volume 4

1847 - 602 pages
...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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An Historical and Critical View of the Speculative Philosophy of Europe in ...

J. D. Morell - Philosophy, Modern - 1847 - 632 pages
...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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General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848 - 520 pages
...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 pages
...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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Suggestive Hints Towards Improved Secular Instruction: Making it Bear Upon ...

Richard Dawes - Teaching - 1849 - 228 pages
...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 ..., Volume 3

Oliver Lorenzo Barbour, New York (State). Supreme Court - Law reports, digests, etc - 1849 - 706 pages
...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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