| James Elliot - 1860
...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 - 79 Seiten
...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
...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
...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
...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... | |
| John Playfair - 1855 - 317 Seiten
...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 - 400 Seiten
...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 - 400 Seiten
...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 - 141 Seiten
...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 - 410 Seiten
...is D to F. (v. def. 5.) Next, let there be four magnitudes A, B, C, Z), 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; Bio C, as Fto G; and Cto D, as .Eto F. Then A shall be to D, as E to H. by... | |
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