 | 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,...exactly fill the same space, are equal to one another." Every specific definition is referred to this universal principle. With regard to a few more general... | |
 | 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,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines cannot enclose a space. XI. All right... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are equal to one another. 11." Two straight... | |
 | 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,...exactly fill the same space, are equal to one another. ix. The whole is greater than its part. x. Two straight lines cannot enclose a space. xi. All right... | |
 | Euclides - 1847 - 128 pages
...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,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space. In order to enclose... | |
 | 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... | |
 | 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,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines cannot inclose a space. XI. All right... | |
 | 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,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. x. Two straight lines cannot inclose a space. XI. All right... | |
 | Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...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,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are equal to one another. POSTULATES. 1.... | |
 | Euclides - 1852 - 152 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,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines cannot inclose a space. Fig. 1. Fig.... | |
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Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
