 | 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... | |
 | 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
...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...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...to unequals, the wholes are unequal 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal...another. 9. The whole is greater than its part. 10. All right angles are equal to one another. 11. Two straight lines cannot he drawn through the same... | |
 | 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...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... | |
 | Euclides - 1838 - 264 pages
...of the same, are equal to one another. VIII. Magnitudes which coincide, or which may be conceived to coincide with one another, that is, which exactly fill the same space, are equal to one another. This axiom, referring to the most obvious test of geometrical equality, is scarcely comprehensive enough.... | |
 | 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...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... | |
 | Euclides - Geometry - 1841 - 378 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. XL All right... | |
 | Thomas Cogswell Upham - Intellect - 1841 - 474 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,...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 revert... | |
| |
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. 
