| James Elliot - 1860 - 252 pages
...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... | |
| Euclides - 1861 - 464 pages
...to the last of the first magnitudes, the same ratio which the first has to the last of the others. ' **If there be any number of magnitudes, and as many others, which taken two and two,** have the same ratio, they shall have the same ratio by equality. "— EUCLID. CON. Pst. 1, V. DEM.... | |
| George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...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 - 1864 - 448 pages
...than F. Therefore, if there be three, &c. QED PROPOSITION XXII. THEOREM. If there be any number nf **magnitudes, and as many others, which taken two and two in order, have the same ratio** ; the first shall have to the last of the first magnitudes, the same ratio which the first has to the... | |
| Euclides - 1865 - 402 pages
...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 - Euclid's Elements - 1867 - 424 pages
...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... | |
| Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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... | |
| Euclid - 1868 - 138 pages
...то irX^боc, avvSvo \afißavofiiva Kai ¿v тф avry Xóy^* кaí Siîaov iv Tif avru \oyil> iarai. **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... | |
| Robert Potts - 1868 - 434 pages
...greater than D, by case first ; PROPOSITION XXII. THEOREM. If there be any number of magnitudes, and a3 **many others, which taken two and two in order, have the same ratio** ; the first shall have to the last of the first magnitudes, the same ratio which the first has to the... | |
| Henry William Watson - Geometry - 1871 - 320 pages
...true whatever be the number of equal ratios and whatever be the magnitudes considered. PROPOSITION 12. **If there be any number of magnitudes, and as many...which taken two and two in order have the same ratio,** the first shall have to the last of the first set of magnitudes the same ratio as the first has to... | |
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