 | Charles Davies - 1847 - 368 sider
...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 following examples, we have 1 : 6 : : 2 : 12; and 1x12= 2x 6; also, 4 : 12 : : 8 : 24... | |
 | Jeremiah Day - 1847 - 358 sider
...section, so far as to admit the principle that " when four quantities are in geometrical proportion, the product of the two extremes is equal to the product of the two means :" a principle which is at the foundation of the Rule of Three in arithmetic. See Arithmetic. Thus,... | |
 | Charles Davies - 1849 - 372 sider
...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 representatives;... | |
 | Jeremiah Day - 1849 - 350 sider
...ion, so rar as to admit the principle that " when four quantities are in geometrical proportion, tbe product of the two extremes is equal to the product of the two means :" a principle \vhieb is at the foundation of the Rule of Three in arithmetic. See A ri'.Umctic. Thus,... | |
 | Elias Loomis - 1849 - 252 sider
...obtain . BxC A--JP Multiplying each of these last equals by D, we have AxD=BxC. Cor. If there are three proportional quantities, the product of the two extremes is equal to the square of the mean. Thus, if A : B : : B : C ; then, by the proposition, I BOOK H. PROPOSITION ii.... | |
 | Charles Davies - 1850 - 292 sider
...would be constant. 154. If we have the proportion A : B : : C : D, D r\ we have -—=—, (Art- 145); and by clearing the equation of fractions, we have...between the numbers 2 : 10 : : 12 : 60, which gives 2x60 = 10x12 = 120. 155. If four quantities, A, B, C, D, are so related each other that we shall also... | |
 | James B. Dodd - 1850 - 278 sider
...(§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 be reduced to... | |
 | Charles Davies - 1850 - 412 sider
...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, 4 : 12 : : 8... | |
 | Oliver Byrne - 1851 - 310 sider
...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... | |
 | John Bonnycastle - 1851 - 314 sider
...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... | |
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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. 
