 | Charles Davies - 1848 - 300 σελίδες
...and by clearing the equation of fractions, we have BC=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 : :... | |
 | Uriah Parke - 1849 - 414 σελίδες
...extremes is equal to the product of the means ; and if there be any number whatever the product of the extremes is equal to the product of any two terms equally distant from the extremes. Thus as 2 : 4 : : 8 : : 16; here 16x2=32 and 4x8=32 ; and if we extend the series, thus 2,... | |
 | Charles Davies - 1849 - 372 σελίδες
...and B, the common multiplier being m. PROPOSITION I. THEOREM. When four quantities are in proportion, the product of the two extremes is equal to the product of the two means Let A, B, C, D, be four quantities in proportion, and M : N :: P : Q be their numerical... | |
 | Elias Loomis - 1849 - 252 σελίδες
...equimultiples, are equal to each other. PROPOSITION I. THEOREM. If four quantities are proportional, the product of the two extremes is equal to the product of the two means. It has been shown that the ratio of two magnitudes, whether they are lines, surfaces,... | |
 | Uriah Parke - 1850 - 402 σελίδες
...extremes is equal to the product of the means ; and if there be any number whatever the product of the extremes is equal to the product of any two terms equally distant from the extremes. Thus as 2 : 4 : : 8 : : 16; here 16x2=32 and 4x8=32 ; and if we extend the series, thus 2,... | |
 | Charles Davies - 1850 - 412 σελίδες
...product of the divisor by the quotient is equal to the dividend, it follows, That in every proportion the product of the two extremes is equal to the product of the two means. Thus, in the example, Art. 184 we have 1 : 6 : : U : 12 ; and 1 x 12 =• 2 x 6; also,... | |
 | James B. Dodd - 1850 - 278 σελίδες
...(§216). Product of the Extremes = that of the Means. § *Jt •.;'•£. In every direct proportion, the product of the two extremes is equal to the product of the two means. In the proportion 3 : 6=4 : 8, we have two equal ratios | and | ; and if these ratios... | |
 | Oliver Byrne - 1851 - 310 σελίδες
...is the foundation and 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 is an... | |
 | John Bonnycastle - 1851 - 314 σελίδες
...product. Thus, a geometrical mean between 4 and 9 is ,/36, or 6. In any continued geometrical series, the product of the two extremes is equal to the product of any two terms that are equally distant from them, or to the square of the mean when the number of the terms is odd.... | |
 | John Bonnycastle - 1851 - 288 σελίδες
...product of the two extremes is equal to that of the two means. 6. In any continued geometrical series, the product of the two extremes is equal to the product of any two means that are equally distant from them ; or to the square of the mean, when the number of terms is... | |
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In any continued geometrical progression, the product of the two extremes is equal to the product of any two means... 
