 | Euclid, Isaac Todhunter - 1867 - 426 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 - 138 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... | |
 | Henry William Watson - 1871 - 320 Seiten
...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...ratio, the first shall have to the last of the first set of magnitudes the same ratio as the first has to the last of the second set of magnitudes. Fig.... | |
 | Euclides, James Hamblin Smith - 1872 - 376 Seiten
...is greater than FV 9. Similarly the other cases may bo proved. Q. nn PROPOSITION XXI. (Eucl. v. 22.) If there be any number of magnitudes, and as many others, which have the same ratio taken two and two in order, the first must have to the last of the first magnitudes... | |
 | Euclides - 1874 - 342 Seiten
...be the number of magnitudes. Therefore, if there be any number, &o. QED PROPOSITION 23. — 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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 Seiten
...proportion will be B+A:BA::D + C:DG PHOP. XI.— THEOREM. (Euc. V. 22, 23). Tf there be three or more magnitudes, and as many others which, taken two and two in order, have the same ratio, then by equality, the first IMS to the last of the first rank the same ratio that the first has to... | |
 | Euclid, Lewis Carroll - 1874 - 80 Seiten
...> l ; С .-. , xn« by с, а>с. Similarly, if А=С, а=с; and if А<С, а< с. QED PROP. XXII. If there be any number of magnitudes, and as many others which, taken two and two, have the same ratio : the first of the first rank shall have to the last the same ratio as the first... | |
 | Charles Lutwidge Dodgson - 1874 - 96 Seiten
....•. , substituting, - > 1 ; QED by c, a>c. Similarly, if A=C, a — c; and if A<C, a< c. PROP. XXII. If there be any number of magnitudes, and as many others which, taken two and two, have the same ratio : the first of the first rank shall have to the last the same ratio as the first... | |
 | Euclid - 1876 - 240 Seiten
...follows that if A is > C, D is > F; and if equal, equal ; if less, less. PROPOSITION XXII. THEOREM. — If there be any number of magnitudes, and as many...and two in order, have the same ratio ; the first has to the last of the first magnitudes the same ratio which the first has to the last of the others.... | |
 | University of Oxford - 1879 - 414 Seiten
...rectilineal figure and equal to another given rectilineal figure. 8. Inscribe a square in a given circle. 9. 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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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... 
