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When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c.
Elements of Algebra: Being an Abridgement of Day's Algebra Adapted to the ... - Σελίδα 198
των Jeremiah Day - 1844 - 252 σελίδες
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 σελίδες
...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...

A Course of Mathematics: For the Use of Academies as Well as ..., Τόμος 1

Charles Hutton - 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...

An Easy Introduction to the Mathematics: In which the Theory and ..., Τόμος 2

Charles Butler - 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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 σελίδες
...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...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1820 - 332 σελίδες
...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...

A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 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...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...:FROP. 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 lost, ie, equal to the ratio of the first to the last. DEMONSTRATION. Let the magnitudes...

An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...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...

The Practical Analyst: Or, A Treatise on Algebra, Containing the Most Useful ...

Enoch Lewis - 1826 - 166 σελίδες
...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...

An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - 1826 - 383 σελίδες
...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...