 | George Lees - 1826 - 276 pages
...which are halves of the same thing, are equal to one another. VIII. — Magnitudes which coincide wiih one another, that is, which exactly fill the same space, are equal to one another. IX. — The whole is greater than its part, and equal to all its parts taken together. X. — All right... | |
 | Euclides - 1826 - 226 pages
...are halves of the same, are equal to one another. 8. Things which mutually agree with one another, are equal to one another. 9. The whole is greater than its part. PROPOSITION I. PROBLEM. Upon a given finite right line to describe an equilateral triangle Let AB be... | |
 | Robert Simson - Trigonometry - 1827 - 546 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 inclose a space. XI. All right... | |
 | Timothy Walker - Geometry - 1829 - 156 pages
...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. Two straight lines cannot inclose a space. 11. All right angles are equal. 12. If a straight line meets... | |
 | John Playfair - Geometry - 1829 - 210 pages
...are 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. A. The whole is equal to all its parts taken together. ED. B. It is impossible for the same thing to... | |
 | Timothy Walker - Geometry - 1829 - 138 pages
...same, are equal to one another. 7. Things which are halves of the same, are equal to one another. i 8. Magnitudes which coincide with one another, that...another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space. II. All right angles are equal. 12. .If a straight line meets... | |
 | 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,...exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality ; the... | |
 | Dugald Stewart - 1829 - 418 pages
...proper place. Kal ra 'upagpH-mira i«* aXXuXa Tffa a^AnAo/; irrl : — thus translated by Dr. Simson : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth/is not an axiom, but a definition. It is the definition of geometrical equality ; 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...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... | |
 | Timothy Walker - Geometry - 1831 - 166 pages
...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...is, which exactly fill the same space, are equal to 1 one another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space.... | |
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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. 
