 | 1867 - 964 σελίδες
...12 X 3 = 4 x 9. Sow, 12 and 3 are the extremes, and 4 and 9 are the means, oí tie given proportion. Conversely, if the product of two numbers is equal to the product of any other two numbers, the four numbers will form a proportion. Thus, since — 8 x 3 = « x 4 or,... | |
 | Nicholas Tillinghast - 1844 - 108 σελίδες
...the means is equal to the product of the extremes ; as, 6 : 4 : : 15 : 10, hence 10.6=15.4. Prop. 2. If the product of two numbers is equal to the product of two other numbers, the four may be arranged in a proportion; as, 8.3=12.2, hence 8: 12: : 2 : 3. Scholium.... | |
 | Bourdon (M., Louis Pierre Marie) - 1858 - 262 σελίδες
...multiplication, they must have been equal at first. Hence the property is proved. 161. Reciprocally. — If the product of two numbers is equal to the product of two other numbers, these four numbers form a proportion of which either pair of factors will constitute... | |
 | Eli Todd Tappan - 1864 - 288 σελίδες
...quantities is the square root of their product. * 18. Proposition — When the product of two quantities is equal to the product of two others, either two may be the extremes and the other two the means of a proportion. Let aXd = bXc represent the equal products.... | |
 | Thomas Percy Hudson - 1866 - 268 σελίδες
...4 X 9. 48 45 ' Now, 12 and 3 are the extremes, and 4 and 9 are the means, of the given proportion. Conversely, if the product of two numbers is equal to the product of any other two numbers, the four numbers will form a proportion. Thus, since 8X3 = 6X4, 8, 4, 6, 3 form... | |
 | Eli Todd Tappan - 1868 - 444 σελίδες
...quantities is the square root of their product. 18. Proposition.- — When the product of two quantities is equal to the product, of two others, either two may be the extremes and the other two the means of a proportion. Let aXd=bXc represent the equal products.... | |
 | William Chauvenet - 1871 - 380 σελίδες
...; that is, a mean proportional between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal...of two others, either two may be made the extremes, and the other two the means, of a proportion. For, if we have given ab' = a'b, then, dividing by bb',... | |
 | William Chauvenet - 1872 - 382 σελίδες
...; that is, a mean proportional between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal...of two others, either two may be made the extremes, and the other two the means, of a proportion. For, if we have given ab' = a'b, then, dividing by bb',... | |
 | 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... | |
 | Richard Wormell - 1876 - 268 σελίδες
...mark the fourth term by x — 12 : 108 : : n : x. And from what has already been said — («). When the product of two numbers is equal to the product of two othtrs they form a proportion in four different ways. Thus the four numbers (5, 54, 6, 45) form a proportion... | |
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If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. 
