 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...the number of magnitudes. Therefore, if there be any number of 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... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...: A : : F : E, therefore, by this first case, since C 7 A, F 7 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... | |
 | Euclid - Geometry - 1838 - 470 pages
...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 same jatio which the first of the others has to the last. NB This is usually cited by the words " ex sequali... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...whatever be the number of magnitudes. Therefore, if there be any number, &c. QED 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 shall have to the last of the first magnitudes the same... | |
 | Euclides - 1840 - 192 pages
...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 others, which, taken two and two, irregularly, have the same ratio ; the first will have to the last of the first series of magnitudes... | |
 | Euclides - Geometry - 1841 - 378 pages
...greater than D, that is, D is less than F. Therefore, if there be three, &c. QED PROP. XXII. THEOR. If there be any number of magnitudes, and as many...of the first magnitudes, the same ratio which the fi'..*t has to th . last of the others. N. 13. This is usually cited by the words " ex aequali," or... | |
 | Oliver Byrne - Mathematics - 1841 - 140 pages
...THEO. 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...the first magnitudes the same ratio which the first of the others has to the last of the same. NB — This is usually cited by the words "ex œquali in... | |
 | Oliver Byrne - Mathematics - 1841 - 144 pages
...d' e' f a' V U * c' 1/ 7' > a ' 7 * ? ' d' a' ( r У Of Ь edefg Ь' tí ОГ y g PROP. XXIII. THEO. 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... | |
 | Euclides - 1842 - 316 pages
...proportion. The proposition is usually cited by the words, ex cequali (sc. distantia), or ex &quo. PROP. XI. 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 of the one set of magnitudes will have to the last,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...: A : : F : E, therefore, by this first case, since Cy A, F "7 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... | |
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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... 
