 | Euclid - 1835 - 540 pages
...taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth ; or, if the multiple of the first be equal to that of the second, the... | |
 | James Ryan - Algebra - 1838 - 412 pages
...the third is also less than that of the fourth ; or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal...the multiple of the third is also greater than that ofs the fourth. SCHOLIUM. We shall demonstrate towards the close of this essay, that this definition... | |
 | Euclid - Geometry - 1838 - 470 pages
...multiple of the first be equal to that of the second, the multiple of the third is also equal to tl&t of the fourth ; or, if the multiple of the first be...the third is also greater than that of the fourth. VI. Magnitudes which [have the same ratio are called proportionals. NB ' When four magnitudes are proportionals,... | |
 | John Hind - Arithmetic - 1840 - 252 pages
...being taken, and any equimultiples whatever of the second anA fourth ; if the multiple of thejirst be greater than that of the second, the multiple of...the third is also greater than that of the fourth ; if equal, equal ; and if less, less." This conclusion has been established in the text with respect... | |
 | Euclides - Geometry - 1841 - 378 pages
...taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth; or, if the multiple of the first be equal to that of the second, the... | |
 | Oliver Byrne - Mathematics - 1841 - 144 pages
...taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth ; or, if the multiple of the first be equal to that of the second, the... | |
 | Wales Christopher Hotson - 1842 - 306 pages
...taken, and any equimultiples whatsover of the second and fourth ; if the multiple of the first, be less than that of the second, the multiple of the third is also less than that of the fourth ; or if the multiple of the first be equal to that of the second, the... | |
 | Philip Kelland - Algebra - 1843 - 168 pages
...certain multiples, the definition appeared to be satisfied, inasmuch as the multiple of the first, being greater than that of the second, the multiple of the third is greater than that of the fourth, and similarly for less ; yet for another set of multiples, we find... | |
 | Scottish school-book assoc - 1845 - 444 pages
...than unity, which can only be by me being less than nd; hence, when the multiple of the first is less than that of the second, the multiple of the third is also less than that of the fourth. Therefore, if four quantities be proportional by the algebraical definition,... | |
 | Euclides - 1845 - 546 pages
...taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the... | |
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... if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of... 
