| William Chambers, Robert Chambers - 1842 - 938 σελίδες
...same, are equal to one another. 7. Things which are halves of the came, are equal to one another. 8. Magnitudes which coincide with one another, that is,...another. 9. The whole is greater than its part. 10. All right angles are equal to one another. 11. Two straight lines cannot be drawn through the same... | |
| Chambers W. and R., ltd - 1842 - 744 σελίδες
...fact, merely what a logician would call the converse of it; for in the 8th axiom it is stated, that magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another ; and in this theorem, in order to prove them equal, it is proved that they coincide. The demonstration... | |
| Euclides - 1842 - 316 σελίδες
...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. NB. The term ' equivalent' is used in this work to denote equality of magnitude, in surface or volume,... | |
| Philip Kelland - 1843 - 168 σελίδες
...another. This principle of comparison is stated by Euclid in his 8th axiom : " Magnitudes which coincide, that is, which exactly fill the same space, are equal to one another." Relative to this axiom, the utmost diversity of opinion exists : and as it lies at the foundation of... | |
| John Playfair - 1844 - 338 σελίδες
...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,...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... | |
| Scottish school-book assoc - 1845 - 444 σελίδες
...one another. 7- Things which are halves of the same, or equal things, are equal to one another. 8. Magnitudes which coincide with one another, that is,...one another. 9. The whole is greater than its part, aud equal to all its parts taken together. 10. Two straight lines cannot inclose a space. 1 1 . All... | |
| Euclides - 1845 - 546 σελίδες
...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... | |
| Euclid - 1845 - 218 σελίδες
...are equal to one another. vn. 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, John Playfair - 1846 - 334 σελίδες
...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,...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 - 1846 - 292 σελίδες
...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... | |
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