 | Charles Davies - Algebra - 1866 - 314 pages
...clearing the equation of fractions, we have, BC = AD. That is : Of four proportional quantities, tl4e product of the two extremes is equal to the product of the two means. This general principle is apparent in the proportion between the numbers, 2 : 10 : : 12 : 60, which... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...— D : C, or A — B : B : : C — D : D. PROPOSITION I. — THEOREM. 135. If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. and reducing the fractions of this equation to a common denominator, we have A_X_D BXC BXD "= BX D'... | |
 | Richard Wormell - Arithmetic - 1868 - 184 pages
...means. 207. It follows from what is stated in 203 and 206, that when four numbers are in proportion.the product of the two extremes is equal to the product of the two meansThus, since the proportion 5:9 '•'• 10 : 18 may be written 5 = }i ; if each of these fractions... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...— D : C, or A — B : B : : C — D : D. PROPOSITION I. — THEOREM. 136. If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. Let A : B : : C : D ; then will AXD = BX C. For, since the magnitudes are in proportion, A C. and reducing... | |
 | Ezra S. Winslow - Business mathematics - 1872 - 256 pages
...and in the last, or in the progression 2, 10, 50, 250, 5 is the ratio. In a geometrical progression, the product of the two extremes is equal to the product of any two. means that are equally distant from the extremes, and, also, equal to the square of the middle... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...A — B : A : . C—D : C, or A — B : B : : C—D : D. THEOREM I. 104. If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. LetA:B::C:D; then will AXD = BX C. For, since the magnitudes are in proportion, A _ C ~B~T)' and reducing... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...division, A — B: A : : C—D: C, or A — B: B : : C—D: D. THEOREM I. 104. If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. LetA:B::C:D; then will AXD = BX C. For, since the magnitudes are in proportion, A _ C B~ D' and reducing... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...equimultiples are equal to one another. PROPOSITION I. THEOREM. If four quantities are proportional, the product of the two extremes is equal to the product of the two means. Let A, B, C, D be the numerical representatives of four proportional quantities, so that A : B : :... | |
 | Homeopathy - 1881 - 628 pages
...is based upon a corollarv from the geometrical proposition: "If four quantities .ire proportional, the product of the two extremes is equal to the product of the two means." In like manner the practical surveyor mav, from his field notes, determine the contents of his survey... | |
 | James Morton - Circle-squaring - 1881 - 236 pages
...equivp alent to double the area of the diagonal. When four magnitudes are in proportion, the product _ of the two extremes is equal to the product of the two means. If four magnitudes are in proportion, they will be in proportion if taken inversely. Equimultiples... | |
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If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. 
