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" 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. "
Manual of Algebra - Página 239
por William Guy Peck - 1875 - 331 páginas
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1814 - 304 páginas
...=-jtyeducing the fractions, ad=bc. Thus 12: 8:: IS: 10, therefore 12x10=8x15. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion, when they are so arranged, that those .on one side...
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A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

Beriah Stevens - 1822 - 436 páginas
...ad, (2X 12) whether they are continued, or discontinued, and if three quantities, a, b, c, (2, 4, 8') the square of the mean is equal to the product of the two extremes. THEOREM 2. If four quantities, a, b, c, d, (2, 6, '4, 12.) are such that the product...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1827 - 352 páginas
...is, in both cases the same. And if no : b'. '.x : yy then a : b'.'.x : ny. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion, when they are so arranged, that those on one side...
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The Tutor's Assistant: Being a Compendium of Practical Arithmetic, for the ...

Francis Walkingame - 1833 - 204 páginas
...ratio 3. It is evident that either of these may be continued without end. In an odd number of terms, the square of the mean is equal to the product of the extremes, or of any two terms equidistant from the mean. Thus, in 3, 6, 12, 24, 48 ; 12 X 12 = 3 X 48 =6X24 =...
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Elements of Algebra

1838 - 372 páginas
...other that AxD=B*C, i „ , , BD we shall also have ~T=~r' A. O and hence, A : B : : C : D; that is, if the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion. 180. If we have...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - 1839 - 272 páginas
...each other that AxD=BxC, we shall also have — =— ; A. L> , and hence, A : B : : C : D. That is : If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion. Thus, if we have...
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Elements of Algebra

Bourdon (M., Louis Pierre Marie) - 1839 - 368 páginas
...so related to each other that we shall also have — =— , AC/ and hence, A : B : : C : D; that is, if the product of two quantities is equal to the product of two otter quantities, two of them may be made the extremes, and the other two the means of a proportion....
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - 1840 - 264 páginas
...each other that ta.ll.!! BD we shall also have — =— ; AO and hence, A : B : : C : D. That is : If the product of two quantities is equal to the product of two otlier quantities, two of them may be made the extremes, and the other two the means of a proportion....
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - 1841 - 314 páginas
...transposition we obtain a — b = c — d. Therefore, if the+sum of two quantities is equal to the sum of two other quantities, the first two may be made the means, and the last two the extremes, or the reverse, of an equidifference. When three quantities, a, b, c, either...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1842 - 284 páginas
...Thus, if we have the proportion 3 : 6 : : 6 : 12, t we shall also have = 62 = 3xl2=36. QUEST. — 155. If the product of two quantities is equal to the product of two other quantities, may the four be placed in a proportion 1 How ? — 156. If three quantities are proportional, what...
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