 | Sir John Leslie - Geometry, Analytic - 1809 - 542 pages
...the terms. Thus A : B denotes the ratio of A to B, and the compound symbols A : B : : C : D, signify that the ratio of A to B is the same as that of C to D, or that A is to B as C to D. PROP. I. THEOR. The product of a number into the sum or difference of... | |
 | Sir John Leslie - Geometry - 1817 - 456 pages
...the terms. Thus A : B denotes the ratio of A to B ; and the compound symbols A : B : : C : D, signify that the ratio of A to B is the same as that of C to D, or that A is to B as C to D. PROP. I. THEOR. The product of a number into the sum or dif* ference of... | |
 | James Mitchell - Mathematics - 1823 - 666 pages
...conjugate diameter. PROPORTION, in Mathematics, is an equality or similitude of ratio ; thus if the ratio a to b is the same as that of c to d ; that is, if ac — = — then a, bt ct d, are in pro6 d J portion, which is denoted by placing the... | |
 | Downside sch - 1844 - 384 pages
...coexisting relations of A to B and of B to A, then — supposing that words are to keep their meaning the ratio of A to B is the same as that of B to A, quod est absurdum. Even DeMorgan, who is usually so cautious in the choice of terms, writes... | |
 | Stephen Chase - Algebra - 1849 - 348 pages
...the ratio (§ 113. 3). Thus, the ratio of 2 to 3 is the same as that of 2x5 to 3X5, or of % to f . So the ratio of a to b is the same as that of am to bm, or of — to — . That is, mm (/c) Lat., relation. a 2_2X5 _| a_am_yT ~ 5 b~bm~!T m or,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...cubic inch as the unit of measure, and we find it to be contained 9 times in A, and 13 times in B, then the ratio of A to B is the same as that of 9 to 13. And even if there is no unit which is contained an exact number of times in both solids, still,... | |
 | Euclides - Geometry - 1853 - 334 pages
...is the ratio compounded of the two ratios of A to B, and of B to C. And in the particular case when the ratio of A to B is the same as that of B to C, the ratio of A to C is called the duplicate ratio of that of A to B, or of B to C. Ex. 2. If... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...cubic inch as the unit of measure, and we find it to be contained 9 times in A, and 13 times in B, then the ratio of A to B is the same as that of 9 to 13. And even if there is no unit which is contained an exact number of times in both solids, still,... | |
 | Mathematics - 1874 - 240 pages
...of ratios, except in its simplest form, I should propose to defer until later. Theorem 7 is that "If the ratio of A to B is the same as that of C to 2), then the ratio of mA to B will be the same as that of mC to D, where mA, mC are any equimultiples... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...cubic inch as the unit of measure, and we find it to be contained 9 times in A, and 13 times in B, then the ratio of A to B is the same as that of 9 to 13. And even if there is no unit which is contained an exact number of times in both solids, still,... | |
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... required. Again, if we wish to find the ratio of two solids, A and B, we seek some unit of measure which is contained an exact number of times in each of them. If we take a cubic inch as the unit of measure, and we find it to be contained 9 times... 
