| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...unequals, the remainders are unequal. 7. Thitigs which are halves of the same are equal to one another. S. **Magnitudes which coincide with one another, that is,...greater than its part. 10. Two straight lines cannot** enclose a space. 11. All right angles are equal to one another, 12. If a straight line meets two straight... | |
| Euclid - Geometry - 1853 - 176 pages
...tho elements, namely, " Magnitudes which are equal coincide with one another when similarly placed." **9. The whole is greater than its part. 10. Two straight lines cannot** enclose a space. SCHOLIUM. This axiom may bo otherwise expressed, namely, "If two straight lines coincide... | |
| John Playfair - Euclid's Elements - 1855 - 340 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...one another. 9. The whole is greater than its part.** 1 0. All right angles are equal to one another. 11." Two straight lines which intersect one another,... | |
| Euclides - 1858 - 248 pages
...proof to the senses ; the other, though only conceived to be done, being demonstration to the mind. **9. The whole is greater than its part. 10. Two straight lines cannot** enclose a space. 11. All right angles are equal to one another. This may be illustrated by supposing... | |
| Euclides - 1862 - 140 pages
...of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, wliich **exactly fill the same space, are equal to one another....cannot inclose a space. 11. All right angles are equal** to one another. 12. If a straight line meet two straight lines, so as to make the two interior angles... | |
| Euclides - 1863 - 122 pages
...of the same, are equal to one another. 8. Magnitudes which coincide with one another, that which is **exactly fill the same space, are equal to one another. 9. The whole is greater than its part.** j 11. All right angles are equal to one another. | 10. Two straight lines cannot enclose a space to... | |
| Euclides - 1863 - 74 pages
...actually performed, is the proof to the senses ; when only conceived of, demonstration to the mind. **9. The whole is greater than its part. 10. Two straight lines cannot** enclose a space. 1 1 . All right angles are equal to one another. This may be illustrated by supposing... | |
| Edward Clarke Lowe - 1866 - 172 pages
...line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. **1. Things which are equal to the same thing are equal...greater than its part. 10. Two straight lines cannot** enclose a space. 11. All right angles are equal to one another. 12. If a straight line meets two straight... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...are double 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...greater than its part. 10. Two straight lines cannot** enclose a space. 11. All right angles are equal to one another. 12. If a straight line meet two straight... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exag^ly **fill the same space, are equal to one another. 9....The whole is greater than its part. 10. Two straight** Imes cannot enclose a space. 11. All right angles are equal to one another. 12. If a straight line... | |
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