| John Playfair - Geometry - 1829 - 210 pages
...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...one another. 9. The whole is greater than its part. A. The whole is equal to all its parts taken together. ED. B. It is impossible for the same thing to... | |
| Dugald Stewart - 1829 - 442 pages
...place. K«J rx lfieiift%cvrK 'or aXAnXai latt gXXifcui; Irrl '• — thus translated by Dr. Simson : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality ; the... | |
| Dugald Stewart - 1829 - 418 pages
...proper place. Kal ra 'upagpH-mira i«* aXXuXa Tffa a^AnAo/; irrl : — thus translated by Dr. Simson : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth/is not an axiom, but a definition. It is the definition of geometrical equality ; the... | |
| Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...greater than any one of its parts. TRUTH VI. The sum of all the parts is equal to the whole. TRUTH VII. Magnitudes, which coincide with one another, that...exactly fill the same space, are equal to one another. TRUTH VIII. Between two points only one straight line can be drawn. TRUTH IX. The straight line is... | |
| Thomas Cogswell Upham - Intellect - 1832 - 622 pages
...the same, are equal to one another ; Things which are halves of the same, are equal to one another ; Magnitudes, which coincide with one another, (that...exactly fill the same space,) are equal to one another, &c. It will be admitted, (and we shall see it perhaps more clearly, when we again have occasion to... | |
| Euclid - Euclid's Elements - 1833 - 216 pages
...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 inclose a space. 11. All right angles are equal to one another. 12. If a right line... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...greater than any one of its parts. TRUTH VI. The sum of all the parts is equal to the whole. TRUTH VII. . Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. TRUTH VIII. Between two points only one straight line can be drawn. TRUTH IX. The straight line is... | |
| Euclides - 1834 - 518 pages
...are equal to one another. VII. Things which are halves of the same, arc equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, arc equal to one another. IX. The whole is greater than its part. X. Two straight lines cannot enclose... | |
| Euclid - 1835 - 540 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 enclose a space. XI. All right... | |
| Mathematics - 1836 - 488 pages
...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...another. 9. The whole is greater than its part. 10. All right angles are equal to one another. 11. " Two straight lines which intersect one another, cannot... | |
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