| John Playfair - 1844 - 317 Seiten
...H. In the same manner is the demonstration extended to any number of magnitudes. PROP. XXIII. THEOR. **If there be any number of magnitudes, and as many...two and two, in a cross order, have the same ratio;** thefirst will have to the last of the first magnitudes the same ratio which thefirst of the others... | |
| Alexander Ingram - 1844
...= \ ... a : d : : e : h. bed fgh db PROP. XV. If there are any number of quantities more than two, **and as many others, which, taken two and two in a cross order,** are proportionals ; then ex cequo inversely are the extreme terms in the first rank, proportional to... | |
| Euclid, James Thomson - 1845 - 352 Seiten
...demonstrated in the 22d proposition of this book. 20. Ex ceguo, inversely: when there are three or more **magnitudes, and as many others, which taken two and two in a cross order, have the same ratio** ; that is, when the first magnitude is to the second in the first rank, as the last but one is to the... | |
| Euclides - 1845
...first ; that is, D is less than F. Therefore, if there be three, &c. QED PROPOSITION XXII. THEOREM. **If there be any number of magnitudes, and as many others, which taken two and two in** order, have the same ratio ; thefirst shall have to the last of thefirst magnitudes, the same ratio... | |
| Euclid - 1845 - 199 Seiten
...and therefore, D is less than F. Therefore, if there be three, &c. QBD PROPOSITION XXII. THEOB. — **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... | |
| John Playfair - 1846 - 317 Seiten
...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,...two and two, in a cross order, have the same ratio** ; thefirst will have to the last of the first magnitudes the same ratio which theJirst of the others... | |
| 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 others, 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... | |
| Dennis M'Curdy - 1846 - 138 Seiten
...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 others ; 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... | |
| Charles William Hackley - 1846 - 503 Seiten
...efg bcd=fgh' or ae , -3=5-; ie, a:d::e:h. XIV. If there be any number of quantities more than two, **and as many others, which, taken two and two in a cross order,** are proportionals (ex ;equali perturbatA), the first will have to the last of the first rank the same... | |
| Euclides - 1848
...fourth shall be greater than the sixth; and if equal, equal; and if less, less. PROP. XXII. 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... | |
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