 | Daniel Fenning - 1751 - 272 σελίδες
...perfectly well. • Phi. Then you are to obferve as follows. OBS ERv. i. Any three Numbers in Geometrical Proportion, the Product of the Extremes is equal to the Square of the Mean ; that is, equal to the middle Term multiplied by or into itfelf. Let the 3 Numbers be 4, 16, and 64.... | |
 | Adrien Marie Legendre - 1819 - 574 σελίδες
...quantities are such, that two among them give the same sum, or the same product, as the other two, tht Jirst are the means and the second the extremes (or the...extremes is equal to double the mean ; and in proportion, tlie product of liie extremes is equal to the square of the mean. From this we deduce the quantity... | |
 | Etienne Bézout - 1824 - 238 σελίδες
...product of the extremes and means may then be taken reciprocally for each other. And in a continued proportion, the product of the extremes is equal to the square of the mean term: because, the two mean terms being equal, their product is the square of either. Then, to find... | |
 | Adrien Marie Legendre - 1825 - 570 σελίδες
...quantities are such, that two among them give the same sum, or the same product, as the other too, the firsl are the means and the second the extremes (or the...said of proportion, when b = c. We have in this case A + D = 2B, ad — b3 : that is, in continued equidifference, the sum of the extremes is equal to double... | |
 | Bézout - 1825 - 258 σελίδες
...take the product of the extremes for that of the means, and reciprocally. Therefore, in the continued proportion, the product of the extremes is equal to the square of the mean term; for the two means being equal, their product is the square of one of them. Therefore, to have... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 σελίδες
...proportion, the other two are means, and conversely. (359.) COR. 4. — If three quantities be in continued proportion,' the product of the extremes is equal to the square of the mean.1 Let а:Ъ — Ъ:с, then ac = bb = № (360.) Hence when the extremes are known, the square... | |
 | Alexander Ingram - 1844 - 262 σελίδες
...= - ; whence a : b : : c : d or c : d : : a : b. ao PROP. II. If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean, and conversely. Let a:b::b:c; then axc = bxb or ac — b*. Conversely. If the product of any two quantities... | |
 | Elias Loomis - 1846 - 380 σελίδες
...numbers are proportional ; that is, 5 : 6 : : 10 : 12. (215.) If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean. If a:b::b:c. Then, by Art. 212, ac = bb = b\ Conversely, if the product of two quantities is equal... | |
 | Elias Loomis - 1846 - 376 σελίδες
...numbers are proportional ; that is, 5 : 6 : : 10 : 12. (215.) If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean. If a:b::b:c. Then, by Art. 212, ac — bb= V. Conversely, if the product of two quantities is equal... | |
 | Samuel Alsop - 1846 - 300 σελίδες
...dividing by bd, we have a с . b=d Or, • , в : 6 : : с : d. 44. If three magnitudes be in continual proportion, the product of the extremes is equal to the square of the mean. If a : b : : b : c, then ac = ¿>3. ab *-? Multiply by be, and ac = №. 45. If four quantities be... | |
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If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean. 
