 | Benjamin Greenleaf - 1860 - 456 σελίδες
...will be equal. The effect is the same when the terms are multiplied by the same number. 336. In every proportion the product of the two extremes is equal to the product of the two means. Thus, the proportion 16 : 8 : : 20 : .10 may be expressed Jg4 = f g. Now, if we reduce these fractions... | |
 | Charles Davies - 1861 - 322 σελίδες
...»nd 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. This general principle is apparent in the proportion between the numbers 2 : 10 : : 12 : 60, which... | |
 | Benjamin Greenleaf - 1861 - 638 σελίδες
...B:A::C — 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. Let A : B : : C : D ; then will AXD = BX C. For, since the magnitudes are in proportion, AC and reducing... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...B:A::C — 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. Let A : B : : C : D ; then will AXD = BX C. For, since the magnitudes are in proportion, and reducing... | |
 | Elias Loomis - 1862 - 312 σελίδες
...2:4::4:8, where 4 is a mean proportional between 2 and 8. (183.) 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; then will ad=bc. For, since the four quantities are proportional, a_c A~d' and, by clearing... | |
 | Benjamin Greenleaf - 1863 - 504 σελίδες
...— 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 fractious of this equation to a common denominator, we have AJ<J> BXC BXD == BX D'... | |
 | Oliver Byrne - 1863 - 600 σελίδες
...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 - 1866 - 314 σελίδες
...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 - 1868 - 340 σελίδες
...— 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 - 1868 - 184 σελίδες
...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... | |
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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. 
