 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...extremes equal to the product of the means is merely clearing the equation of fractions. THEOREM II. 141 If the product of two quantities is equal to the product of two others, the factors of either product may be made the extremes, and the factors of the other the means... | |
 | Charles Davies - Algebra - 1873 - 322 pages
...related to each other, that A x D = B x C, we shall also have, -r = -^; A (j and hence, A : _B :: C : J). That is: If the product of two quantities is equal...extremes, and the other two the means of a proportion. 195. If four quantities are proportional, what is the product of the two means equal to? Tims, if we... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...c : d. Then | = |,Art.292. Multiplying each of these equals by bd, we have ad=bc. 300. Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion. Let ad— be.... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...this case, the square of the mean is equal to the product of the extremes. PROPOSITION n. THEOREM. If the product of two quantities is equal to the product...two other quantities, two of them may be made the means, and the other two the extremes of a proportion. If we have, AD = BC, by changing the members... | |
 | Charles Davies - Algebra - 1875 - 318 pages
...have, -j = -^ ; and hence, u4 : -Z? : : C : D. That is: If the product of two quantities is eqital to the product of two other quantities, two of them...extremes, and the other two the means of a proportion, 195. If four quantities are proportional, what is the product of the two means equal to ? 276 ELEMENTARY... | |
 | William Guy Peck - Algebra - 1875 - 348 pages
...extremes. Conversely, if we divide both members of (2) by ca, we have, - = -; or, a : b :: c : d; hence, ac If the product of two quantities is equal to the product of two other quantities, the first two may be made the means, and the second two the extremes, of a proportion. It follows,... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...we then have the square of the mean equal to the product of the extremes. PROPOSITION III. THEOREM. If the product of two quantities is equal to the product of two other quantities, the first two may be made the means and the other two the extremes of a proportion. Assume the equation,... | |
 | Benjamin Greenleaf - 1876 - 332 pages
...THEOREM n. 316i If the product of two quantities befyual to the product of two others, two of them way be made the extremes and the other two the means of a proportion. Let ad = be. Dividing by bd and reducing, =- = ^, or, a : b : : c : d. THEOREM III. /317i If three... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...this proposition, A x C=B x B, which is equal to B'. PROPOSITION ii. THEOREM. (Converse of Prop. I.) If the product of two quantities is equal to the product of two others, the one pair may be made the extremes, and the other t/ie means of a proportion. Thus, suppose... | |
 | William Frothingham Bradbury - Algebra - 1877 - 302 pages
...product of the extremes is equal to the product of the means. Let a : 6 = c : d i=5 THEOREM II. 203. If the product of two quantities is equal to the product of two others, the factors of either product may be made the extremes, and the factors of the other the means... | |
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If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion. 
