| 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... | |
| |