 | Euclides - 1845 - 546 pages
...In this manner we form our idea of equality, which is thus formally stated in the eighth axiom : " Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another." Every specific definition is referred to this universal principle.... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...doubles of the same thing, are equal to one another. 7. Things which are halves of the same thing, are equal to one another. 8. Magnitudes which coincide...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...another. VII. Things which are halves of the same, or equal things, are equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines... | |
 | Euclides - 1846 - 272 pages
...same, or of equals, are equal to one another. 7. Things which are halves of the same, or of equals, are equal to one another. 8. Magnitudes which coincide with one another are equal to one another. 9. The whole is greater than its part. 10. Two right lines cannot enclose... | |
 | Euclides - 1846 - 292 pages
...same, are equal to one another. vn. Things which are halves of the same, are equal to one another. vni. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. ix. The whole is greater than its part. x. Two straight lines... | |
 | Euclides - 1847 - 128 pages
...Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another. 8. Magnitudes which coincide...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines... | |
 | Dugald Stewart - Psychology - 1847 - 666 pages
...force, either to Locke, to lieid, or to Campbell,) that furnishes, if I mistake not, the true too ; " Magnitudes which coincide with one another, that is which exactly fill the Fame space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition... | |
 | Euclides - 1848 - 52 pages
...are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...same, are equal to one another. vn. Things which are halves of the same, are equal to one another. vm. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. x. Two straight lines... | |
 | Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another. 8. Magnitudes which coincide...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are... | |
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Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
