 | Robert Cree - 1827 - 426 pages
...the fallacy of any given proposition. The axiom, that 'the whole is greater than its part,' or that 'things which are halves of the same are equal to one another,' is true, not because such is the arbitrary appointment of any being whatsoever, but because it agrees... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide... | |
 | Timothy Walker - Geometry - 1829 - 138 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 to...are halves of the same, are equal to one another. i 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal... | |
 | 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... | |
 | John Playfair - Geometry - 1829 - 210 pages
...equals be taken from unequals, the remainders are unequal. 6. Things which 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 with one another, that is, which exactly... | |
 | 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 to...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 double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another. 
