| William Whewell - 1837
...GEOMETRY. ELEMENTS or GEOMETRY. EUCLID, Books *i, *II, *III, IV. Book v. *Definition of Proportion. **The first of four magnitudes is said to have the same ratio to the second** which the third has to the fourth, when^ — any eq'wi-multiples whatsoever of the Jirst and third... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 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 Hind - Arithmetic - 1840 - 224 pages
...in iheJifth Book of Euclid's Elements, that " Proportion is the Similitude of Ratios; and theJirst **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^rst and third being taken,... | |
| Oliver Byrne - Ratio and proportion - 1841 - 98 pages
...of the four magnitudes, taken in the same manner. Euclid expresses this definition as follows : — **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 whatsoever of the first and third being taken,... | |
| Euclides - 1841
...mutual relation of two magnitudes of the " same kind to one another, in respect of quantity." IV. 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 whatsoever of the first and third being taken,... | |
| Euclides - 1842
...the ratio of the third to the fourth. Definition of proportion according to Euclid, (Def. V., Book " **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 whatsoever of the first and third being... | |
| Wales Christopher Hotson - 1842
...:: a + c + e ... : 6 + d +/... 149. Geometrical Definition of Proportion. (Euclid, book v. def. 5). **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 whatsoever of the first and third being taken,... | |
| John Playfair - Euclid's Elements - 1842 - 317 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,... | |
| Robert Potts - 1845
...said to have a ratio to one another, when the less can be multiplied so as to 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 whatsoever of the first and third being taken,... | |
| Euclid - Geometry - 1845 - 199 pages
...said to have a ratio to one another, when the less can be multiplied so as to 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 whatsoever of the first and third being taken,... | |
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