...fractions, we have BC = AD ; that is, Of four proportional quantities, the product of the two extremis is equal to the product of the two means. 179. If...A, B, C, and D, are so related to each other that A x D = В х С, we shall also have, — = -7-, А С and hence, A : В : : С : D; that is If the...

...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...

...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,...

...would be constant. 154. If we hav« the proportion A : B : : C : D, n T) we have ~J=~C' (Art- I45)' and by clearing the equation of fractions, we have...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...

...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;...

...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,...

...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....

...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...

...(§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...

...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...