 | James Elliot - 1860 - 252 sider
...cequali, ex atquali distantta, or by direct equality. THEOREM XI. If there be any Number of Quantities, and as many others, which, taken two and two in a cross Order, have the same Ratios, the first shall have to the last ofthefirst Quantities, the same Ratio which the first of the... | |
 | George Sturton Ward - 1862 - 104 sider
...rightly said that 3 cwt. has any ratio to £1, or 6 cwt. to £8. PROP. XX. — It is further true, that if there be any number of magnitudes and as many others, which taken two and two in order, have the same ratio; if the first be greater than the last of the first magnitudes, the first... | |
 | Euclides - 1863 - 122 sider
...is to D as E is to H; EFOII I Because A, B and C are three magnitudes, and F, G and H other three, which, taken two and two in a cross order, have the same ratio. Therefore, by the first case, A is to C ~ l and so on, whatever be the number of magnitudes. ! Therefore,... | |
 | Euclides - 1864 - 448 sider
...so is D to F. (v. def. 0.) Next, let there be four magnitudes A, B, C, D, and other four E, F, G, H, which taken two and two in a cross order have the same ratio, viz. A to B, as G to H; B to C, as Fto G; and Cto D, as E to F. Then A shall be to D, as E to H. Because... | |
 | Euclides - 1865 - 402 sider
...third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less. Prop. 22. If there be any number of 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 ra'io... | |
 | Robert Potts - 1865 - 528 sider
...porturbata;" or " ex coquo porturbato." First, let there be three magnitudes A, B, C, and other three D, E, F, which taken two and two in a cross order have the same ratio, that is, such that A is to B, as E to F't and as B is to C, so is D to E. Then A shall be to C, as... | |
 | John Playfair - 1855 - 350 sider
...magnitudes. PROP. XXIII THEOR. If there be any number of magnitudes, and as many others, which, taken (to* and two, in a cross order, have the same ratio ; the. first will have to the last of the first magnitudes the same ratio which the first of the others has to the... | |
 | Euclid, Isaac Todhunter - 1867 - 426 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... | |
 | Euclid, Isaac Todhunter - 1867 - 424 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... | |
 | Euclid - 1868 - 138 sider
...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... | |
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If there be any number of 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 of the others has to the last. NB This is usually... 
