| John Playfair - Euclid's Elements - 1795 - 444 pages
...the laft definition, the ratio of A to C is compounded of the ratios of A to B, and of B to C ; but **the ratio of A to B is equal to the ratio of** B to C, becaufe A, B, C are continual proportionals ; therefore the ratio of A to C,by this definition,... | |
| Maria Gaetana Agnesi - Calculus - 1801
...proportion of three- or four terms, is thus expreffed : a . b :: b . c, when there are three terms; that is, **the ratio of a to b is equal to the ratio of** b to c. Alfo, a . b '.'. c . d means, that a is to b as c is to d. Laftly, the fign oo denotes infinite,... | |
| Charles Hutton - Mathematics - 1811
...o^ : R : : c : D. But as p and o^are equal, by supposition, they have the same ratio to R, that is, **the ratio of A to B is equal to the ratio of c to** D, or A : B : : c : D. o^ ED Corol. 1. When the two means, namely, the second and third terms, are... | |
| Charles Hutton - Mathematics - 1816
...Q : a : : c : D. But as r and q are equal, by supposition. they have the same ratio to R, that is, **the ratio of A to B is equal to the ratio of c to** D, or A - B : : c : D. q E. o. Carol. \ . When the two means, namely, the second and third terms, are... | |
| Charles Hutton - Mathematics - 1822 - 618 pages
...<l : R : : c : D. But as t and <j are equal, by supposition, they have the same ratio to R, that is, **the ratio of A to B is equal to the ratio of c to** D, or A : B : : c : DQEI). Carol. 1. When the two means, namely, the second and third terms, are equal,... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...values that —is equal to—,, then A is said to have the same ratio AC to B, th.it C has to D, or **the ratio of A to B is equal to the ratio of C 'to** D. When four quantities have this relation to .each other, they are said to be in proportion. To indicate... | |
| William Whewell - Mechanics - 1837 - 226 pages
...Ratio is the relation of quantities in respect of proportion, so that if a, b, c, d be proportional, **the ratio of a to b is equal to the ratio of c to** d. *LEMMA 1. If magnitudes be proportionals according to the algebraical definition of proportion,... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...the last definition, the ratio of A to C is compounded of the ratios of A to B, and of B to C ; hut **the ratio of A to B is equal to the ratio of** B to 0, because A, B, C, are continual proportionals ; therefore the ratio of A to C, by this definition,... | |
| Algebra - 1838 - 372 pages
...and D, having such values that BD then A is said to have the same ratio to B, that C has to D ; or, **the ratio of A to B is equal to the ratio of C to** D. When four quantities have this relation to each other, they are said to be in proportion. Hence,... | |
| Charles Davies - Algebra - 1839 - 272 pages
...other, they are said to be in proportion. Hence, proportion is an equality of ratios. To express that **the ratio of A to B is equal to the ratio of C to** D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D. The quantities which... | |
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