| John Playfair - 1855 - 318 sider
...demonstration extended to any number of magnitudes. nF(11.5.). Again, PROP. XXIII THEOR. If there le **any number of magnitudes, and as many others, which, taken two and two, in** a cross order, have the same ratio ; the first will have to the last of the first magnitudes the same... | |
| Euclides - 1855
...Therefore, if there be three, &c. QED PROP. XXII. THEOREM. If there be any number of magnitudes, andas **many others, which taken two and two in order, have the same ratio** ; (he first shall have to the last of the first magnitudes, the same ratio which the first has to the... | |
| Euclides - 1855
...3 KMHLN ABC_EFG lhen B ' C ' DF ' G ' H' therefore A : D :: E : H. PROPOSITION XXIII. THEOREM.—Jf **there be any number of magnitudes, and as many others, which, taken** tivo and two, in a cross order, have tlie same ratio; the first has to the last of the first magnitudes... | |
| Euclides - 1859
...laa rо irXqöOç, aiivSvo \apßavoptva Kai iv rif avrif \oyif Kai Stîffov iv ry avru Xóyy Éffrai. **If there be any number of magnitudes, and as many others, which, taken two and two,** have the same ratio; they shall be in the same ratio by equality. Statement — Let there be three... | |
| Euclides - 1860
...same manner the demonstration is extended to any number of magnitudes. PROPOSITION XXIII. THEOREM. **If there be any number of magnitudes, and as many others, which, taken two and two in** a cross order, have the same ratio ; the first shall have to the last of the first magnitudes the same... | |
| Eucleides - 1860
...any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio. **If there be any number of magnitudes, and as many others, which, taken two and two, in** a cross order, have the same ratio. If magnitudes are equal . . If two magnitudes are unequal. If a... | |
| James Elliot - 1860
...greatest and consequently c the least, b + c > a + d. THEOREM X. If there be any Number of Quantities, **and as many others, which, taken two and two in Order, have the same** Ratios, tlie first shall have to the last ofthefirst Quantities the same Ratio which the first of the... | |
| George Sturton Ward - 1862 - 79 sider
...n : : p : z. PROPOSITION XXIII. " Ex jEQUALI IN PROPORTIONS PERTURBATA," OR " Ex jEQUO PERTURBATO." **If there be any number of magnitudes, and as many others, which, taken two and two in** a cross order, have the same ratio ; the first shall have to the last of the first magnitudes the same... | |
| Euclides - 1865
...whatever be the number of magnitudes. Therefore, if there be any number, &c. QED PROP. XXm.— THEOREM. // **there be any number of magnitudes, and as many others, which taken two and two in** a cross order, have the same ratio ; then the first shall have to the last of the first magnitudes... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...whatever be the number of magnitudes. Wherefore, if there be any number &c. QED PROPOSITION 23. THEOREM. **If there be any number of magnitudes, and as many others, which** have the same ratio, taken two and two in a cross order, the first shall have to the last of the first... | |
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