 If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = bc, then, divide by bd. т~, - г~;« bd bd а с 01 6 = 5  New School Algebra - Σελίδα 310των G. A. Wentworth - 1898Πλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | William Frothingham Bradbury - 1872 - 262 σελίδες
...extremes equal to the product of the means is merely clearing the equation of fractions. THEOREM II. 14, If the product of two quantities is equal to the product of two others, the factors of eiIher product may be made the extremes, and the factors of the other the means of a... | |
 | Charles Davies - 1872 - 464 σελίδες
...this case, the square of the mean w equal to the product of the extremes. PROPOSITION II. THEOREM. If the product of two quantities is equal to the product of two other quantit1es, two nf them may be made the means, and the other two the extremes of a proportion.... | |
 | Daniel Barnard Hagar - 1873 - 278 σελίδες
...Theorem II. 332. If the product of two quantities be equal to the product of two other quantities, either two may be made the extremes of a proportion, and the other two the means. Let ad = bc; Dividing by bd, — = — ; bd Theorem III. 333. In a proportion, either extreme is equal... | |
 | Elias Loomis - 1873 - 396 σελίδες
...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.... | |
 | Adrien Marie Legendre - 1874 - 500 σελίδες
...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.... | |
 | William Guy Peck - 1875 - 348 σελίδες
...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 - 1876 - 412 σελίδες
...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.... | |
 | George Albert Wentworth - 1877 - 436 σελίδες
...extracting the square root, b = \ac7 QED PROPOSITION III. 261. If ihe product of two quantities be equal to the product of two others, either two may be made the extremes of a proportion in which the other two are made the means. Let ad = be. We are to prove a : b : : с : d. Divide both... | |
 | George Albert Wentworth - 1877 - 426 σελίδες
...means). Whence, extracting the square root, PROPOSITION III. 261. lf the product of two quantities be equal to the product of two others, either two may be made the extremes nf a proportion in which the other two are made the means. Let ad = be. We are to prove a : b : : с... | |
 | William Frothingham Bradbury - 1877 - 302 σελίδες
...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... | |
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