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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. "
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... - Σελίδα 188
των Jeremiah Day - 1831 - 332 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

A Treatise on the Elements of Algebra

James Bryce - 1837 - 80 σελίδες
...product of the means is equal to the product of the extremes; and if the product of two quantitles be equal to the product of two others, the four quantities will form a proportion. ft f, Let the proportion be a:b::c:d; then -=- = -; and о а clearing of fractions, ad=bc. Again,...

Elements of algebra

Bourdon (Louis Pierre Marie, M.) - 1838 - 355 σελίδες
...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....

First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - 1839 - 252 σελίδες
...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....

Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1842 - 258 σελίδες
...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,...

Elements of Algebra

Charles Davies - 1842 - 358 σελίδες
...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....

An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - 1842 - 300 σελίδες
...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...

Elements of Algebra: Being an Abridgement of Day's Algebra Adapted to the ...

Jeremiah Day - 1844 - 252 σελίδες
...for the product of 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...others, the four quantities will form a proportion if they are so arranged, that those on one side of the equation shall constitute the means, and those...

Elements of Arithmetic and Algebra: For the Use of the Royal Military College

William Scott - 1844 - 500 σελίδες
...products, and each is divided by irf, ad be acc _ a that is, a : b::c : d, or c '. d:'.a '. b. Wherefore, if the product of two quantities is equal to the product of two others, the four quantities are convertible into a proportion of which the multiplicand and multiplier of either product form the...

Elements of Algebra: Including Sturm's Theorem

1845 - 368 σελίδες
...other that A x D — B x C, 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 other quantities, two of them may be made the extremes, and the other two the means of a proportion....

A Treatise on Algebra

Elias Loomis - 1846 - 346 σελίδες
...becomes abd bed T=T or ad — be. Thus, if 3 : 4 : : 9 : 12, then 3 x 12 = 4 x 9. (213.) Conversely, if the product of two quantities is equal to the product of two others, the first two quantities may be made the extremes, and the other two the means of a proportion. Let ad...




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