 | 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... | |
 | 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... | |
 | 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... | |
 | Timothy Walker - Geometry - 1831 - 166 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, which exactly fill the same space, are equal to 1 one another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space.... | |
 | 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... | |
 | 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
...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 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...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... | |
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Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
