 | 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... | |
 | Euclid, 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... | |
| |
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 ratio which the first of the others has to the last. NB This is... 
