 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...  College Algebra - Page 524by James Harrington Boyd - 1901 - 777 pagesFull view - About this book
 | John Playfair - Mathematics - 1806 - 320 pages
...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
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the 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,... | |
 | Euclid - 1835 - 540 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same...the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same...the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...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... | |
 | Mathematics - 1836 - 488 pages
...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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 - 1842 - 332 pages
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the 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,... | |
 | Scottish school-book assoc - 1845 - 444 pages
...geometrical magnitudes, and therefore it is necessary to substitute another, which is as follows: — Def. The first of four magnitudes is said to have the same...fourth, when any equimultiples whatever of the first and third being taken, and any equimultiples whatever of the second and fourth — if the multiple of the... | |
 | Euclides - 1846 - 292 pages
...exceed the other. v. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when, any equimultiples whatever of the first and third being taken, and any whatever of the second and fourth, if the multiple of the first be equal... | |
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