 | Robert Potts - 1868 - 434 σελίδες
...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... | |
 | Henry William Watson - 1871 - 320 σελίδες
...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 - 376 σελίδες
...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 σελίδες
...; 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 - 80 σελίδες
...> 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 σελίδες
....•. , 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 σελίδες
...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 - 446 σελίδες
...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 - 414 σελίδες
...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 - 426 σελίδες
...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... | |
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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... 
