| Euclides - 1845
...be the number of magnitudes. Therefore, if there be any number, &c. QED PROPOSITION XXIII. 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 Jirsl shall have to the last of the first magnitudes the same... | |
| Euclid - 1845 - 199 sider
...number of magnitudes. Therefore, if there be any number, &c. QED ABCD EFGH PROPOSITION 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 first shall have to the last of the first magnitudes, the... | |
| Euclid, James Thomson - 1845 - 352 sider
...the number of magnitudes. Therefore, if there be any numberof magnitudes, &c. 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 first has to the last of the first magnitudes the same ratio... | |
| Euclides - 1846
...greater than D, that is, D is less than F. Wherefore, If there be three %c. QED PROP. XXII. THEOS. **If there be any number of magnitudes, and as many...which, taken two and two in order, have the same ratio,** then the first shall have to the last of the first magnitudes the same ratio which the first of the... | |
| Dennis M'Curdy - 1846 - 138 sider
...be greater than Recite (a) def. 10, 5 ; (b) p. 15, 5; (c) Note 3, page 32; (d) p. A of b. 5. 22 Th. **If there be any number of magnitudes, and as many...which, taken two and two in order, have the same ratio:** then the first is to the last of one rank, as the first is to the last of the other rank. G, H, in... | |
| John Playfair - 1846 - 317 sider
...the same manner is the demonstration extended to any number of magnitudes. PROP. XXIII. THEOR. iff **there be any number of magnitudes, and as many others, which, taken two and two, in** a cross order, have the same ratio ; thefirst will have to the last of the first magnitudes the same... | |
| Euclides - 1848
...others. • NB This is usually cited by the words "ex tequali," or "ex aguo." PROP. XXIII. 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... | |
| John Playfair - 1849 - 317 sider
...and B : A : : F : E, therefore, by this first case, since CyA, F7 D, that is, D/F. PROP. XXII. THEOR. **If there be any number of magnitudes, and as many others, which, taken two** ana two in order, have the same ratio ; the first will have to the last of the first magnitudes, the... | |
| Royal Military Academy, Woolwich - 1853
...less than F. Therefore, if there be three, etc. QED c • EUCLID S ELEMENTS. PROPOSITION XXII. THEOR. **If there be any number of magnitudes, and as many...the first magnitudes, the same ratio which the first** of tke others has to the last. NB This is usually cited by the words " ex sequali," or " ex sequo.".... | |
| Euclides - 1853 - 147 sider
...number of magnitudes. Therefore, if there be any number, <fec. QED PROPOSITION XXIII. — 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 sliall have to the last of the first magnitudes the... | |
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