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Books Books 51 - 60 of 192 on In any proportion, the product of the means is equal to the product of the extremes..
" In any proportion, the product of the means is equal to the product of the extremes. "
Treatise on the elements of algebra - Page 256
by James Bryce - 1837
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University Algebra : Embracing a Logical Development of the Science with ...

Charles Davies - Algebra - 1860 - 320 pages
...(1.) ac Clearing of fractions, we have, bc = ad (2.) Hence, 1 . If four quantities are in proportion, the product of the means is equal to the product of the extremes. Conversely, if we divide both members of ( 2 ) by ca, we shall have, - — - ; or, a : b : : c : d....
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Higher Arithmetic : Or, The Science and Application of Numbers ..., Book 6

James Bates Thomson - Arithmetic - 1860 - 422 pages
...the work is right. (Art. 500.) Demtrmtral'ian. -If four numbers are proportional, we have seen that the product of the means is equal to the product of the extremes ; (Art. 498 ;) therefore the priduct of the second and thin/ terms must be equal to that of the first...
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Common School Algebra

Thomas Sherwin - 1862
...d, we have ad=bc. But a and d are the extremes, and 6 and c are the means. Hence, In any proportion, the product of the means is equal to the product of the extremes. (n). Suppose we have the equation ad—be. If we divide both members by 6 and d, we have — = —,...
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Higher Arithmetic, Or, the Science and Application of Numbers: Combining the ...

James Bates Thomson - Arithmetic - 1862 - 422 pages
...work is right. (Art. 500.) Demmatratian. -If four numbers are proportional, we have seen that th« product of the means is equal to the product of the extremes ; (Art. 498 ;} therefore the prxiict of the second and third terms must be equal to that of the first...
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The civil service arithmetic. [With] A key, Book 1

1863
...called means (9 and 10); the first and fourth extremes (15 and 6). When four numbers form a proportion, the product of the means is equal to the product of the extremes. Thus, 6 : 3 : : 8 : 4 ; here, 6x4, the extremes, = 8x3, the means, = 24. If the product of any two...
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New University Algebra: A Theoretical and Practical Treatise Containing Many ...

Horatio Nelson Robinson - Algebra - 1863 - 420 pages
...the extremes is equal to the square of the mean. 2d. When four terms are in geometrical progression, the product of the means is equal to the product of the extremes. APPLICATION OF THE FORMULAS. 364. The two primitive equations, ,««. ,given, the other two may be...
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New University Algebra: A Theoretical and Practical Treatise Containing Many ...

Horatio Nelson Robinson - Algebra - 1864 - 420 pages
...the. extremes is equal to the square of the mean. 2d. When four terms are in geometrical progression, the product of the means is equal to the product of the extremes. APPLICATION OF THE FOKMULAS. 364. The two primitive equations, contain the five quantities, a, r, l,...
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Ray's Algebra, First Book: Primary Elements of Algebra, for Common ..., Book 1

Joseph Ray - Algebra - 1866 - 240 pages
...then, 55 — x= the other. By the question, x : 55 — x : : 2 : 3. Then, since, in every proportion, the product of the means is equal to the product of the extremes, we have 3x=2(55 — x)=H0 — 2x. 5z=110 3x Or, thus : Let x= one part; then, -^-= the other. ' ' I'...
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Elements of Algebra: For Colleges, Schools, and Private Students, Book 2

Joseph Ray - Algebra - 1866 - 406 pages
...Let 3a;= the first, and 5x= the second number. Then, 3a;+9 : 5z+9 : : 6 : 7. But in every proportion, the product of the means is equal to the product of the extremes. (RAY'S ARITH., 3d Book, Art. 200.) Hence, 6(5a;+9)=7(3a;+9). From which the answer is readily found....
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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 240 pages
...then, 55 — £= the other. By the question, x : 55 — x : : 2 : 3. Then, since, in every proportion, the product of the means is equal to the product of the extremes, we have 3a;=2(55 — 2)=110 — 2x. 5z=110 3=22, and 55— 3=33, as before. Or, thus : Let x= one part;...
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