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" In any proportion, the product of the means is equal to the product of the extremes. "
The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ... - Page 67
by Zadock Thompson - 1848 - 168 pages
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - 1860
...to the quotient obtained by dividing the product of the extremes by the oiher mean. (6.) Hence, in a proportion — The product of the means is equal to the product of the extremes. 161. Practical Problems. (a.) The forming of a proportion from the conditions of a probiem is called...
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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
...6 d b and 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

Robert Johnston (F.R.G.S.) - 1863
...proportion are 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 ...

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 ...

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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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 240 pages
...thus : Let a;= one part ; 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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Ray's Algebra, First Book: Primary Elements of Algebra, for Common Schools ...

Joseph Ray - Algebra - 1866 - 240 pages
...are the first and last terms of a proportion called ? The second and third? 244. Proposition I. — In every proportion, the product of the means is equal to the product of the extremes. Let a : b • : c : d. Then, since this is a true proportion, we must hnve bd Clearing of fractions,...
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Key to Ray's New Algebras, Elementary and Higher: Containing Statements and ...

Joseph Ray - Algebra - 1867 - 224 pages
...100—3z= B's gain, and 40z — 200= A's stock. Therefore, 4te— 200 : 20a; : : 3x : 100—3z. Since the product of the means is equal to the product of the extremes, 60z2=(40z— 200)(100— 3). Reducing, z2— J{x=— io. Whence, z=20; hence, &c=60= A's gain,...
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