 Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on whatever be their number. " When four magnitudes,...  High School Arithmetic - Page 163by James B. Dodd - 1853Full view - About this book
 | John Playfair - Mathematics - 1806 - 320 pages
...second the same ratio that the third has to the fourth. VI. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on, whatever... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...second the same ratio that the third has to the fourth. VI. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth Las to the sixth, and so OD, whatever... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclid - 1835 - 540 pages
...the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Mathematics - 1836 - 488 pages
...the same ratio that the third has to the fourth. 6. Magnitudes are said to be proportionals, wheti the first has the same ratio to the second that the third has to the fourth ; and the third to the fouitii the same ratio which the fililí has to the sixth, and soon whatever... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...third quantity be contained in a fourth an equal number of times exactly, — then the first quantity has the same ratio to the second that the third has to the fourth. Thus, if the right line j± _ B o ___ JJ AB be contained, say 4 times exactly in CD, and if the triangle... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...second the same ratio that the third has to the fourth. 11. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on, whatever... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...like multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or lie first has the same ratio to the second that the third has to the fourth. We are now arrived very nearly at Euclid's definition ; for, let A, B, C, D be four proportionals,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...second the same ratio that the third has to the fourth. 6. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on whatever be... | |
 | Scottish school-book assoc - 1845 - 444 pages
...necessary to substitute another, which is as follows: — Def. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatever of the first and third being taken, and any equimultiples whatever... | |
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