 | Willem Jacob 's Gravesande - 1749 - 210 σελίδες
...(127); that is, J= s *jIf we multiply each Quantity by bd, we have ad = bc; whence it follows, that in every Proportion the Product of the Extremes is equal to the Product of the Means. 135. The Inverfe of this Propofition is alfo true, T'hat Quantities are proportional^ if... | |
 | Leonhard Euler - 1821 - 380 σελίδες
...: 10; 6 : 10 = 3 5;9:6=15:10; 3:3 = 5: 5j 9: 15 = 3:5; 9:3=15: 5. 414. Shice, in every geometrical proportion, the product of the extremes is equal to the product of the means, we may, when the three first terms are known, find the fourth from them. Let the three first... | |
 | Leonhard Euler - 1822 - 640 σελίδες
...10:: 3:5; 9: 6:: 15: 10; 8:8:: 5: 5; 9: 15:: 3:5; 9 : 3 : : 15 : 5. 470. Since in every geometrical proportion the product of the extremes is equal to the product of the means, we may, when the three first terms a«' known, find the fourth from them. Thus, let the... | |
 | George Crabb - 1823 - 798 σελίδες
...Geometrical Progression, and the common multiplier or divisor is called their Common Ratio. In Geometrical Proportion the product of the extremes is equal to the product of the means, as2x 12 = 6 x 4 = 24 ; and ax br = ar x b. This sort of Proportion is moreover distinguished... | |
 | Charles Tayler - 1824 - 350 σελίδες
...10:;S : 5 9 : 6::15 : 10 3:3::5: 5; 9:1.5::3:S 9: 3:: 15: 5, &C. 346. Now since in every geometrical proportion the product of the extremes is equal to the product of the means, if three terms of a proportion be given, we are enabled from the same theorem to find the... | |
 | Silvestre François Lacroix - 1825 - 404 σελίδες
...5 : 10; 6 : 10 = 3 5;9:6=15:10; , 3:3 = 5: 5;9:15 = 3:5;9:3=15: 5. 414. Since, in every geometrical proportion, the product of the extremes is equal to the product of the means, we may, when the three first terms are known, find the fourth from them. Let the three first... | |
 | Jeremiah Day - 1827 - 352 σελίδες
...- 6 and — c, ' o+c— 26. GEOMETRICAL PROPORTION. 374. But if four quantities are in geometrical proportion, the PRODUCT of the extremes is equal to the product of the meant. If a : b'. '.c : d, ad=bc For by supposition, (Arts. 346, 364.) -=bd Multiplying by bd,... | |
 | George Peacock - 1830 - 732 σελίδες
...omitting the common denominator, ad = be. It appears, therefore, that if four quantities constitute a proportion, the product of the extremes is equal to the product of the means. lu con- 371 . Conversely, if the product of any two quantities be equal to the product of... | |
 | Jeremiah Day - 1831 - 358 σελίδες
...transposing - b and - c, «+c=26. GEOMETRICAL PROPORTION. 374. But if four quantities are in geomeirkal proportion, the PRODUCT of the extremes is equal to the product of the. means. If a: b :: c: d, ad=bc For by supposition, (Arts. 346, 364.) -=1 bd Multiplying by bd,... | |
 | Silvestre François Lacroix - 1831 - 324 σελίδες
...follows, that, in equidifference, the sum of the extreme terms is equal to that of the means ^ and in proportion, the product of the extremes is equal to the product of the means, as has been shown in Arithmetic (127, 113), by reasonings, of which the above equations... | |
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In any proportion the product of the extremes is equal to the product of the means. 
