....if., either continued or interrupted (provided the interruption be between the 2d and 3d term), the product of the means is equal to the product of the extremes. EXAMPLE. Let the 4 numbers be 5, 15, 26, and 78 interrupted; then 5 x 78 = 15 x 26= 390. It will be...

...thus, since - z= -. • ba and f = > therefore 1=7. hdbh 68. If 4 quantities are proportional, the product of the means is equal to the product of the extremes. Thus suppose a : b : : c : d Then ad = he. For ? = ^ (s+)i and multiplying both fractions by W we have...

...product of the first and fourth equals the product of the second and third, or in other words, that the product of the means is equal to the •product of the extremes. 194. In the proportion, 4 : 6 : : 12 : 18, the order of the terms may he altered without destroying...

...proportion. Thus 6 : 9 : : 10 : 15 : : 8 : 12 , is a continued proportion. 63. In every proportion, the product of the means is equal to the product of the extremes. For if two equal fractions be reduced to a common denominator, their numerators must be equal. Thus...

...product of the first and fourth equals the product of the second and third, or, in other words, that the product of the means is equal to the product of the extremes. 194. In the proportion, 4 : 6 : : 12 : 18, the order of the terms may be altered without destroying...

...other principles of the doctrine of proportion may also be demonstrated ; as the proposition that the product of the means is equal to the product of the extremes, proportion by alternation, or that if the first term be to the second as the third is to the fourth,...

...(because 450 — г is A's gain, and 450 — (500 — x) = — 50 -f- x is B's gain,) and because the product of the means is equal to the product of the extremes, 450,000 — 900 x — 1,000 x -j- 2 x2 = 5 z2 — 250 *. This equation, when reduced, may be written...

...proportion, the sum of the extremes is equal to that of the means, and, in geometrical proportions, the product of the means is equal to the product of the extremes, either extreme (or mean) may be found in the former, by subtracting the given extreme (or mean) from...

...numerator of the second is the product of the mean terms ; hence, in every geometrical proportion, the product of the means is equal to the product of the extremes. The proof is independent of the particular numbers which enter into the proportion, as maybe shown...

...whence we easily find 4. Given, — £— : — ^ — : : 7 : 4, to find ». Since, in a proportion, the product of the means is equal to the product of the extremes (Eue. VI. 16), it follows that 126—7х 10х+8= - 4 - O2 By multiplication, 40 x +32 =126— 7x. whence,...