 | Euclides - 1845 - 546 σελίδες
...other point. II. That a terminated straight line may be produced to any length in a straight line. III. 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... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...point : f 2. That a terminated straight line may be produced to any length in a straight line : , 3. That a circle may be described from any centre, at any distance from that centre. J AXIOMS. 1. Things which are equal to the same, or to equals, are equal to one another. 2. If equals... | |
 | 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 - 632 σελίδες
...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... | |
 | 1845 - 404 σελίδες
...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... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...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,... | |
 | Euclides - 1846 - 272 σελίδες
...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 - 602 σελίδες
...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,... | |
 | John Daniel Morell - 1846 - 524 σελίδες
...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 - 292 σελίδες
...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... | |
 | Euclides - 1847 - 128 σελίδες
...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... | |
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Let it be granted that a straight line may be drawn from any one point to any other point. 
