 | 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, which exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is 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 is, which exactly fill the same space, are equal to one another. TRUTH VIII. Between two points only one straight line can be... | |
 | 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 is, which exactly fill the same space,) are equal to one another, &c. It will be admitted, (and we shall see it perhaps more clearly,... | |
 | Euclid - Euclid's Elements - 1833 - 216 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 inclose... | |
 | 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, which exactly fill the same space, are equal to one another. TRUTH VIII. Between two points only one straight line can be... | |
 | 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, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines... | |
 | Mathematics - 1836 - 488 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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 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... | |
 | John Playfair - Euclid's Elements - 1837 - 332 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... | |
 | Thomas Cogswell Upham - Intellect - 1839 - 476 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 is, which exactly fill the same space,) are equal to one another, &c. It will be admitted, (and we shall see it perhaps more clearly,... | |
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Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
