 | Euclides - 1845 - 546 sider
...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 - 218 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 - 382 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 - 292 sider
...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 - 168 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... | |
 | Euclid, John Playfair - 1846 - 334 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 - 52 sider
...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 - 332 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 - 400 sider
...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 - 176 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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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 ratio which the first of the others has to the last. NB This is... 
