 | Euclid - Euclid's Elements - 1833 - 216 pages
...substituted for the following : When of the equi-multiples of four magnitudes the multiple of thejirst is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth : then the first is said to have to the second a greater ratio than the... | |
 | Perry Fairfax Nursey - Industrial arts - 1833 - 502 pages
...of clerer contemporaries, for his proficiency and skill. He asserts that when, of the equimultiples of four magnitudes, taken as in the fifth definition, the multiple of the first is equal to the multiple of U\e second, but the multiple of the third less than the multiple of the fourth,... | |
 | Euclid - 1835 - 540 pages
...by saying the first is to the second, as • the third to the fourth. VII. When of the equimultiples of four magnitudes (taken as in the fifth definition,)...but the multiple of the third is not greater than the multiple of the fourth ; then, the first is said to have to the second a greater ratio than the... | |
 | Mathematics - 1836 - 488 pages
...which the fililí has to the sixth, and soon whatever be their number. 7. When of the equimultiples of four magnitudes, taken as in the fifth definition,...but the multiple of the third is not greater than the multiple of the fourth; then the first is said to have to the second a greater ratio than the third... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...a proportion or an analogy. 14. When of the equimultiples of four magnitudes, taken as in the tenth definition, the multiple of the first is greater than...but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the... | |
 | Euclides - 1840 - 192 pages
...A is to B as C to D, which is thus briefly written, A : B : : C : D.] 7. When, of the equimultiples of four magnitudes, taken as in the fifth definition,...but the multiple of the third is not greater than the multiple of the fourth ; then the first magnitude is said to have to the second a greater ratio... | |
 | Oliver Byrne - Mathematics - 1841 - 144 pages
...••• D : О = D : 0 (5> def- v). . Equal magnitudes, &c. DEFINITION VII When of the equimultiples of four magnitudes (taken as in the fifth definition),...but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the... | |
 | Euclides - Geometry - 1841 - 378 pages
...the second and fourth take equimultiples 14 and S4; then these multiples are 20, 14, 120, S4. Here the multiple of the first is greater than that of the second, and the multiple of the third is also greater than that of the fourth; therefore the three conditions... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...to D, and to write them thus, A : B :: C : D, or " thus, A : B=C : D." 7. When of the equimultiples of four magnitudes, taken as in the fifth definition,...greater than that of the second, but the multiple of the jhird is not greater than the multiple of the fourth : then the first is said to have to the second... | |
 | George Peacock - Algebra - 1842 - 426 pages
...there exists any multiple of the first which is greater than that of the second, but the corresponding multiple of the third is not greater than that of the fourth ; or that the multiple of the first is equal to that of the second, but the multiple of the third not... | |
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When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth; then the first is said to have... 
