 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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 fractious of this equation to a common denominator, we have AJ<J> BXC BXD == BX D'... | |
 | Oliver Byrne - Engineering - 1863 - 600 pages
...reason of the practice in the Rule of Three. THEOREM 2. — In any continued geometrical progression, the product of the two extremes is equal to the product of any two means that are equally distant from them, or equal to the square of the middle term when there... | |
 | 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...between the numbers, 2 : 10 : : 12 : 60, which gives, 2 X 60 = 10 X 12 = 120. 196. If four quantities, A, B, (7, Z>, are so related to each other, that AXD... | |
 | Charles Davies - Algebra - 1867 - 316 pages
...equation of fractions, we have, SC = AD. That is : Of four proportional quantities, the product of tlie two extremes is equal to the product of the two means....between the numbers, 2 : 10 : : 12 : 60, which gives, 2 X 60 •— 10 X 12 = 120. 196. If four quantities, A, B, C, D, are so related to each other, that... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...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
...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
...: . 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
...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... | |
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AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means. 
