 | Daniel Fenning - Algebra - 1751 - 272 pages
...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 - Geometry - 1819 - 574 pages
...proportion. When B = C, the equidifference is said to be continued ; the same is said of proportion, when b = c. We have in this case that is, in continued equidifference...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 - Mathematics - 1824 - 238 pages
...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... | |
 | Bézout - Arithmetic - 1825 - 258 pages
...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 pages
...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 pages
...= - ; 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 - Algebra - 1846 - 380 pages
...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... | |
 | Samuel Alsop - Algebra - 1846 - 300 pages
...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... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...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 - Algebra - 1848 - 336 pages
...then dividing by bd, we have a с b=d Or, a : b : : 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 = b3. ab *~? Multiply by be, and ac = b*. 45. If four quantities be proportionals,... | |
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If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean. 
