| Euclid - Geometry - 1810 - 518 pages
...Therefore, if there be three, &c. QED Beis to B : but A is A D B E C F A D B E PROP. XXII. THEOR. seeNote. **IF there be any number of magnitudes, and as many others, which,** takcn two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes... | |
| John Mason Good - 1813 - 722 pages
...fourth shall be greater than the sixth; and if equal, equal; and if less, less. Prop. XXII. Theor. **If there be any number of magnitudes, and as many...which, taken two and two in order, have the same ratio;** the first shall have to the last of the first magnitudes the «ame ratio which the first of the others... | |
| Euclides - 1816 - 528 pages
...Boon V. ,. • I ' -I . . * " / ' . t . •>!« ' . l:i •! : . I. I .1 * . PROP. XXIII. THEOR. SeeN. **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... | |
| John Mason Good - 1819 - 740 pages
...fourth shall be greater than the sixth ; and if equal, equal ; and if less, less. Prop. XXII. Theor. **If there be any number of magnitudes, and as many others, which, taken two and** t«m in order, have the same ratio ; the first shall have to the last of the flrst magnitudes the same... | |
| John Playfair - 1819 - 317 pages
...sited by the words'' ex sequali," or " A, D, B, E, c, F. A, E, B, F, c, D, H. G, PROP. XXIII. THEOR. **If there be any number of magnitudes, and as many others, which, taken** twoand two, in a cross order, have the same ratio ; the first will have to the last of the first magnitudes... | |
| Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...words " ex xquali," or " ex xquo." A, D, B, c, i E, F. A, B, F, c, D, H. E, G, PROP. XXIII. THEOR. Tf **there be any number of magnitudes, and as many others, which, taken** twoand two, in a cross order, have the same ratio ; the first will have to the last of the first magnitudes... | |
| Rev. John Allen - Astronomy - 1822 - 508 pages
...that, if A be equal to Ci D is equal to F; and if Jess, less. ' 20 ••• .-/' PROP. XXII. THEOR. **If there be any number of magnitudes, and as many others, which, taken two and two in order,** are in the same ratio ; by ordinate equality, the ratio of the first, of the Jlrst magnitudes, to the... | |
| Rev. John Allen - Astronomy - 1822 - 516 pages
...of A to B and of D to E being equal (Hyp.), A is to G, as D is to H (22. 5). PROP. XXIII. THEOR. ff **there be any number of magnitudes, and as many others, which, taken two and two in** perturbate order, are in the same ratio ; the ratio of the first, of tiie first magnitudes, to the... | |
| Euclid - 1822 - 179 pages
...(i)JPrep£6. bate (1), and therefore if a be greater than c, d greater than/(2). PROP. XXXVIII. THEOR. **If there be any number of magnitudes, and as many others, which taken two** by two are in the same ratio but perturbate, they are ex aequali in the same ratio. First, let there... | |
| James Ryan - Algebra - 1824 - 552 pages
...of the proposition may be shown, whatever be the number of magnitudes. QED 3«J PROP. XXIII. THEOR. **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 6rst shall have to the last of the first magnitudes the same... | |
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