 | Euclides - 1845 - 546 sider
...POSTULATES. 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...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 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 - 404 sider
...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 - 632 sider
...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 - 128 sider
...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 - 128 sider
...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... | |
 | Euclid, John Playfair - 1846 - 334 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 - 292 sider
...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 - 624 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,)... | |
 | Euclides - 1846 - 272 sider
...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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Let it be granted that a straight line may be drawn from any one point to any other point. 
