 | 1845
...By the whole of any quantity we understand the sum of all its parts ; thus, AB = AD + DC + CB. 70. " Things which are equal to the same are equal to one another " ; that is, if a = m and b = m, a is equal to b. 71. In any arithmetical operation, " quantities which... | |
 | William Gifford, Sir John Taylor Coleridge, John Gibson Lockhart, Whitwell Elwin, William Macpherson, William Smith, Sir John Murray IV, Rowland Edmund Prothero (Baron Ernle) - 1845
...discovery, that both languages admit of the same Erse interpretation, upon the geometrical principle that things which are equal to the same are equal to one another. This argument however depends for its validity on the accuracy of his remaining assumption, that the... | |
 | Euclides - 1846
...other point : n. That a terminated straight line may be produced to any length in a straight line : in. That a circle may be described from any centre, at...which are equal to the same are equal to one another. n. If equals be added to equals, the wholes are equal. in. If equals be taken from equals, the remainders... | |
 | John Playfair - 1846 - 317 sider
...other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1 . THINGS which are equal to the same thing are equal to one another. 2. If equals be added to equals,... | |
 | 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,... | |
 | 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... | |
 | 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,... | |
 | Euclides - 1847
...point : 2. That a terminated straight line may be produced to any length in a straight line : and 3. That a circle may be described from any centre, at any distance from that centre. A postulate (from postulare) is a demand so reasonable that it cannot fail to be granted; or, in other... | |
 | 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... | |
 | Euclides - 1848
...other 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...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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Let it be granted that a straight line may be drawn from any one point to any other point. 
