 | Elias Loomis - Conic sections - 1858 - 256 pages
...reductio ad absurdum, which proves that the theorem itself is false, as in Book I., Prop. 4, 16, etc. 5. If none of the consequences so deduced be known...deduce other consequences from all or any of these until a result is obtained which is known to be either true or false. 6. If we thus arrive at some... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...itself is false, as in Book I., Prop. 4, 16, etc. 5. If none of the consequences so deduced be knoum to be either true or false, proceed to deduce other consequences from all or any of these until a result is obtained which is known to be either true or false. 6. If we thus arrive at some... | |
 | Elias Loomis - Conic sections - 1861 - 244 pages
...reductio ad absurdum, which proves that the theorem itself is false, as in Book I., Prop. 4, 16, etc. 5. If none of the consequences so deduced be known...deduce other consequences from all or any of these until a result is obtained which is known to be either true or false. 6. If we thus arrive at some... | |
 | Euclides - 1864 - 448 pages
...proved. 3. Examine whether any of these consequences are already known to be true, or to be false. 4. If any one of them be false, we have arrived at...theorem, proceed still further, until such are obtained. ANALYSIS OF PROBLEMS. 1. In general, any given problem will be found to depend on several problems... | |
 | Euclides - 1864 - 262 pages
...have arrived at a reductio ad abfurdum, which proves that the theorem itself is false, as in Euc. l. 25. 5. If none of the consequences so deduced be known...theorem, proceed still further, until such are obtained. ANALYSIS OF PROBLEMS. 1. In general, any given problem will be found to depend on several problems... | |
 | Robert Potts - 1868 - 434 pages
...proved. 3. Examine whether any of these consequences are already known to be true, or to be false. 4. If any one of them be false, we have arrived at...theorem, proceed still further, until such are obtained. ANALYSIS OF PROBLEMS. 1. In general, any given problem will be found to depend on several problems... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...reductio ad absurdum, which proves that the theorem itself is false, as in Book I., Prop. 4, 16, etc. 5. If none of the consequences so deduced be known...deduce other consequences from all or any of these until a result is obtained which is known to be either true or false. • 6. If we thus arrive at some... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...proved. 3. Examine whether any of these consequences are already known to be true, or to be false. • 4. If any one of them be false, we have arrived at...theorem, proceed still further, until such are obtained. ANALYSIS OF PROBLEMS. 1. In general, any given problem will be found to depend on several problems... | |
 | William Dodds - 1880 - 152 pages
...have arrived at a reductio ad absurdum, which proves that the theorem itself is false, as in Euclid i. 25. 5. If none of the consequences so deduced be...theorem, proceed still further, until such are obtained. B. In general, any given problem will be found to depend on several problems and theorems, and these... | |
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I. 25. 5. If none of the consequences so deduced be known to be either true or false, proceed to deduce other consequences from all or any of these, as in (2). 6. Examine these results, and proceed as in (3) and (4) ; and if still without any conclusive... 