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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. "
The Elements of Plane Geometry - Side 79
av Charles Austin Hobbs - 1899 - 240 sider
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1814 - 303 sider
...=-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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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1827 - 332 sider
...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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Elements of Algebra

1838 - 358 sider
...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 - 252 sider
...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 - 324 sider
...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 - 252 sider
...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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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1842 - 258 sider
...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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Elements of Algebra

Charles Davies - 1842 - 358 sider
...related to each other that we shall also have — =— ., jfi 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. we have -=^; , BC...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - 1842 - 300 sider
...Suppose we have ad = bc. Dividing both members by 6 and d, we have r = -, or a : b = c : d. Hence, oa If the product of two quantities is equal to the product of ttca other quantities, the two factors of either product may be made the means, and the two factors...
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

James Bates Thomson - 1844 - 252 sider
...the means in both cases is the same. So if na:b::x:y, then a : b : : x : ny. 339. 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 if they are so arranged, that those on one side...
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