| Euclid - 1810 - 518 sider
...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
...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...shall have to the last of the first magnitudes the** «ame ratio which the first of the others has to the last. NB This is usually cited by the words "... | |
| Euclides - 1814
...&c. QED BC ABC PROP. XXII. THEOR. DEF See N. IF there be any number of magnitudes, and as many other, **which, taken two and two in order, have the same ratio...the first magnitudes the same ratio which the first** of the others has to the last. NB This is usually cited by the words " ex tequali" or " ex j£qiu>"... | |
| Euclides - 1816 - 528 sider
...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
...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 sider
...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... | |
| John Playfair - 1819 - 333 sider
...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... | |
| Euclid, Rev. John Allen - 1822 - 494 sider
...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... | |
| Euclid, Rev. John Allen - 1822 - 494 sider
...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 sider
...(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... | |
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