| William Frederick Greenfield - 1853 - 228 pages
...product of the extremes is equal to that of the meam, and conversely. Four numbers are proportionals **when the ratio of the first to the second is equal to** that of the third to the fourth. Hence these ratios must be compared, which is effected by comparing... | |
| William Somerville Orr - Science - 1854 - 534 pages
...is of course the same as the ratio 4 : 2, or the ratio 2:1. When there are four quantities such that **the ratio of the first to the second is equal to the ratio of the third to the fourth, the** four quantities are said tobe in proportion: thus, if the four quantities a, b, c, d, be euch that... | |
| Barnard Smith - Arithmetic - 1854 - 368 pages
...and thus those numbers are proportionals. 149. When proportion exists among four numbers, that is, **when the ratio of the first to the second is equal to** that of the third to the fourth, this proportion or equality is often denoted by writing down the two... | |
| 1855 - 424 pages
...that the first divided by the second is equal to the third divided by the fourth — in other words, **when the ratio of the first to the second is equal to the ratio of the third to the fourth, the** four are said to be in direct proportion. From this definition it will be seen, that proportion is... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...the measured quantity ; hence, the measure of proportion is ratio. Four quantities are in proportion **when the ratio of the first to the second is equal to the ratio of the third to the fourth** ; this relation is expressed algebraically thus, a : b :: с : d. This expression is called a proportion... | |
| Charles Davies - Algebra - 1857 - 408 pages
...undergo changes of value, then a is said to be proportional to 6. 183i four quantities are in proportion, **when the ratio of the first to the second, is equal to the ratio of the third to the fourth.** Thus, if b_ d_ ~^~~' the quantities a, b, c and d, are said to be in proportion. We generally express... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...than its consequent ; if equal, equal ; and if less, less. Def. 3. Three quantities are said to be **proportional, when the ratio of the first to the second is equal to the ratio of the** second to the third ; thus, if A, B, and C are in proportion, then A : B : : B : C. In this case the... | |
| James B. Dodd - Arithmetic - 1859 - 368 pages
...PROPORTION. (141.) PROPORTION consists in an equality of ratios. Four quantities are in proportion **when the ratio of the first to the second is equal to the ratio of the third to the fourth.** Thus the numbers 6, 3, 8, 4 are in proportion, since — » —IThe first and third terms are the antecedents,... | |
| James B. Dodd - Algebra - 1859 - 368 pages
...in order ; thus 4 is a fourth proportional to 6, 3, and 8. (138.) Three quantities are in Proportion **when the ratio of the first to the second is equal to the ratio of the** second to the third, — the second term being called a mean proportional between the other two. Thus... | |
| John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...called the antecedent, and the second term the consequent . (379.) Three quantities are in proportion **when the ratio of the first to the second is equal to the ratio of the** second to the third. (38O.) The second quantity is called a mean proportional between the other two,... | |
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