| Henry William Watson - 1871 - 285 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 others, 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... | |
| Euclides, James Hamblin Smith - 1872 - 349 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
...; that is, 1. D is less than F. Therefore, if there be three, &c. QED PROPOSITION 22. — Theorem. **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... | |
| Euclid, Lewis Carroll - 1874 - 62 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
....•. , 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... | |
| Euclides - 1876
...G' G H' &c. ThenA or_ E - F E H' F G G H' therefore A : D :: E : H. PROPOSITION XXIIL THEOREM. — **If there be any number of magnitudes, and as many...in a cross 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.... | |
| Robert Potts - 1876 - 403 Seiten
...first; that is, 1) is less than F. Therefore, if there be three, Sic. QED, PROPOSITION XXII. THEOKEM. **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... | |
| University of Oxford - 1879
...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... | |
| Isaac Todhunter - 1880 - 400 Seiten
...is greater oD; t is, D is less than F. Wherefore, if there be three &c. QED PROPOSITION 22. THEOREM. **If there be any number of magnitudes, and as many others, which** have the same ratio, taken two and two in order, the first shall fiave to the last of the first magnitudes... | |
| Euclides - 1881
...* ex aquali," or * ex ayuo," that it, from equality of distance U'ff. \9). PROP. XXIII. THEOREM. y **there be any number of magnitudes, and as many others,...in a cross order, have the same ratio ; the first** shatt havt to the last of the first magnitudes the same ratio which the first hat to the last of the... | |
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