| Euclid, James Thomson - 1845 - 352 sider
...Let it be granted, that a straight line may be drawn from any one point, to any other 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.... | |
| 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... | |
| Great Britain. Admiralty - 1846
...I. Let it be granted, that a straight line may be drawn from any one point to any other point. II. **That a terminated straight line may be produced to any length in a straight line. III.** AXIOMS. I. Things which are equal to the same or equal things, are equal to one another. II. If equals... | |
| Great Britain. Admiralty - 1846
...I. Let it be granted, that a straight line may be drawn from any one point to any other point. II. **That a terminated straight line may be produced to any length in a straight line. III.** AXIOMS. I. Things which are equal to the same or equal things, are equal to one another. II. If equals... | |
| John Playfair - 1846 - 317 sider
...POSTULATES. 1. LET it be granted that a straight line may be drawn from any one point to any 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... | |
| Euclides - 1846
...POSTULATESLet it be granted, i. That a straight line may be drawn from any one point to any 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 any distance from that centre. AXIOMS. i.... | |
| John Stuart Mill - 1846 - 593 sider
...which may bo .so applied to one another as to coincide ;" the three axioms which follow, (Magnitudes **which are equal to the same are equal to one another — If equals** are added to equals the sums are equal — If equals are taken from equals the remainders are equal,)... | |
| John Daniel Morell - 1846 - 536 sider
...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,... | |
| 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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