 | 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 of two other quantities, two of them may be made the means, and the other two the extremes of a proportion.... | |
 | Thomas W. Piper - 1874 - 352 pages
...second number, and divide the product by the first number. 100. Conversely, When the product of any two quantities is equal to the product of two others, the four quantities are proportional, the factors of either one of the products being the extremes, and those of the other... | |
 | 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.... | |
 | 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.... | |
 | 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 of a proportion.... | |
 | 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 we have... | |
 | James Bates Thomson - Algebra - 1878 - 322 pages
...e By Art. 363, | = * Clearing of fractions, at = 6s. Again, 9:6:: 6-4, and 4 xg = 62. THEOREM III. If the product of two quantities is equal to the product of two others, the four quantities are proportional j the factors of either product being taken for the extremes, and the factors of the... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...AC, we have, £ = £, or, A:B = C:DL, £ = 5, or, A:C=B:DIL, ~ = ~, or, B : A = D : C III. CA Hence, if the product of two quantities is equal to the product of two other quantities, one pair of factors may be made the extremes, and the other pair the means, of a... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...extremes equal to the product of the meaiis ia merely clearing the equation of fractions. THEOREM II. 14i 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 of a proportion.... | |
 | William James Milne - Algebra - 1881 - 360 pages
...3. What does ad, the first member of the equation, form in the proportion? What be? PRINCIPLE 3. — If the product of two quantities is equal to the product of two otlier quantities, two of them may be made the extremes, and the other two the means, of a proportion.... | |
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: b : : mx : y, For the product of the means is, in both cases, the same. And if na : b : : x : y, then a : b : : x :ny. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities... 
