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" In any proportion, the product of the means is equal to the product of the extremes. "
Elements of Plane Geometry: For the Use of Schools - Page 53
by Nicholas Tillinghast - 1844 - 96 pages
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - 1860 - 390 pages
...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: Combining ...

James Bates Thomson - Arithmetic - 1860 - 446 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 - 252 pages
...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 - 436 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 - 258 pages
...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 - 432 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 - 444 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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Elements of Algebra: For Colleges, Schools, and Private Students, Book 2

Joseph Ray - Algebra - 1866 - 420 pages
...as 6 to 7? 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 - 252 pages
...in proportion? Example. What is the second term called? The third ? 244. Proposition I. — In every proportion, the product of the means is equal to the product of the extremes. Let a : 6 : : c : d. Then, since this is a true proportion, we must have bd Clearing of fractions,...
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Key to Ray's New Algebras, Elementary and Higher: Containing Statements and ...

Joseph Ray - Algebra - 1867 - 240 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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