...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...

...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...

...ratio to the quantity 6 yards, as $12, the coat of 3 yards, to x dollars, the cost of 1 3 yards. Since the product of the two extremes is equal to the product of the two means, (Art. 225), 3xz=6xl2; and if 3xx=6x12, * must be equal to this product divided by 3 : that is, " The...

...other, and their product is constant. PROPOSITION I. THEOEEM. When four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. Let A, B, Cj D, be any four magnitudes, and M, N, P, Q, their numerical representatives; then, if'....

...and 3. (§216). Product of the Extremes — that of the Means. § 228. In every direct proportion, the product of the two extremes is equal to the product of the two means. In the proportion 3 : fi=4 : 8, we have two equal ratios f and J ; and if these ratios be reduced to...

...6 and 3. (§ 216). Product of the Extremes = that of the Means. § 223. 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 f- ; and if these ratios be reduced to...

...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...

...their product is constant. BOOK II. 61 PROPOSITION I. THEOREM. When four magnitudes are in proport'on, the product of the two extremes is equal to the product of the two means. Let A, If, C, D, be any four magnitudes, and M} N, P, Q, their numerical representatives ; then, if...

...Proportion contains the following theorems. THEOREM 1. — 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. When the number of terms are odd it is equal to the...

...equal to the half sum of the extremes multiplied by the number of terms. In a geometrical progression, the product of the two extremes is equal to the product of any two means equally distant from the extremes. In a geometrical progression, any term is a mean proportional...