| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...observed, that in any magnitudes whatever of the same kind A, B, C, D, 8ec. the ratio compounded of **the ratios of the first to the second, of the second to the third,** and so on to the last, is only a name or expression by which the ratio which the first A has to the... | |
| Charles Hutton - Mathematics - 1812
...number of quantities, A, B, c, D, the ratio of the first A, to the last p, is said 10 be Compounded of **the ratios of the first to the second, of the second to the third,** and so on to the last. 84. Inverse ratio is, when the antecedent is made the consequent, and the consequent... | |
| Charles Butler - Mathematics - 1814
...any series of quantities of the same kind, the first will have to the last, the^ratio compounded of **the ratios of the first to the second, of the second to the third, of the third to the fourth, &c.** to the last quantity. 44. If two ratios of the greater inequality be compounded together, each ratio... | |
| Euclides - Geometry - 1816 - 528 pages
...observed, that in any magnitudes whatever of the same kind, A, B, C, D, &c. the ratio compounded of **the ratios of the first to the second, of the second to the third,** and so on to the last, is only a name or expression by which the ratio which the first A has to the... | |
| Jeremiah Day - Algebra - 1820 - 332 pages
...third; that is, the first divided by the second, is equal to the fourth divided by the third. 372. **When there is a series of quantities, such that the...second to the third, of the third to the fourth, &c.** arc all equal ; the quantities are said to be in continued proportion. The consequent of each preceding... | |
| Charles Hutton, Robert Adrain - Mathematics - 1822
...number of quantities, A, B, c, D, the ratio of the first, A, to the last D, is said to be Compounded of **the ratios of the first to the second, of the second to the third,** and so on to the last. 84. Inverse ratio is, when the antecedent is made the consequent, and the consequent... | |
| James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
...QED PROP. XXVI. THEOR. If there be any number of magnitudes of the same kind, the ratio compounded of **the ratios of the first to the second, of the second to the third,** and so on to the last, is equal to the ratio of the first to the last. DEMONSTRATION. Let the magnitudes... | |
| Enoch Lewis - Algebra - 1826 - 166 pages
...first of a series of quantities, of like kind, has to the last, is the same as the ratio compounded of **the ratios of the first to the second, of the second to the third,** &c. to the last. Let a, b, c, d, e,f, be quantities of a like kind, then aabcde 7=-r- X — X— y... | |
| James Ryan, Robert Adrain - Algebra - 1826 - 383 pages
...QED PROP. XXVI. THEOR. If there be any number of magnitudes of the same kind, the ratio compounded of **the ratios of the first to the second, of the second to the** thiid, and MI on to the last, is equal to the ratio of the first to the last. DEMONSTRATION. Let the... | |
| Jeremiah Day - Algebra - 1827 - 332 pages
...third; that is, the first divided by the second, is equal to the fourth divided by the third. 372. **When there is a series of quantities, such that the...The consequent of each preceding ratio is, then, the** anfecedent of the following one. — Continued proportion is also called progression, as will be seen... | |
| |