| James Bates Thomson - Arithmetic - 1848 - 432 pages
...is simple proportion proved ? Demonstration.—If four numbers are proportional, we have seen that the product of the means is equal to the product of the extremes; (Art. 498;) therefore the product of the second and third terms must be equal to that of the first... | |
| Joseph Ray - Algebra - 1848 - 250 pages
...c is called a third proportional to a and b. ART. 244. — PROPOSITION I. — In every proportion, the product of the means is equal to the product of the extremes. Let a : b : : c : d. Then, since this is a true proportion, the quotient of the second divided by the... | |
| Pliny Earle Chase - Arithmetic - 1848 - 244 pages
...consequents may, therefore, change places in a variety of ways, the proportion always continuing so long as the product of the means is equal to the product of the extremes. Then, whenever one of the extremes and the two means are given, to find the other extreme, Divide the... | |
| Almon Ticknor - Arithmetic - 1848 - 124 pages
...means, and the first and fourth terms the extremes : 2 : (4 : : 8) : 16 _4X _2X 32 32 Here we see that the product of the means is equal to the product of the extremes. If 2 pounds of tea cost 4 dollars, •what will 8 pounds cost 1 6. Here the price of the tea is 2 dollars... | |
| Zadock Thompson - Arithmetic - 1848 - 184 pages
...product rr the first and fourth equals the product of the second and third, or, m other words, that tlie 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... | |
| Joseph Ray - Algebra - 1852 - 408 pages
...consecutive, they are said to form a continued proportion. ART. 267. PROPOSITION I. — In every proportion, the product of the means is equal to the product of the extremes. Let a : 6 : : c : d. Since this is a true proportion, the ratio of the first term to the second, is... | |
| Joseph Ray - Algebra - 1852 - 366 pages
...100 — 3x= B's gain, and 40x — 200= A's stock. .-. 40ж— 200 : 20ж : ; 3ж : 100— 3ж. Since the product of the means is equal to the product of the extremes, 60x2=(40x — 200)(100— 3x) ; reducing ж'— ïfi!3=— 'Лр- • Whence x=20, hence 3x=60= A's... | |
| Joseph Ray - Algebra - 1848 - 250 pages
...c is called a third proportional to a and &. ART. 244. — PROPOSITION I. — In every proportion, the product of the means is equal to the product of the extremes. Let a : b : : c : d. Then, since this is a true proportion, the quotient of the second divided by the... | |
| John Fair Stoddard - Arithmetic - 1852 - 320 pages
...obtained by dividing the third term by the fourth, we can readily deduce the following PROPOSITIONS. , 1. The product of the means is equal to the product of the extremes. Therefore. 2. If the product of the means be divided by one extreme, the quotient will be the other... | |
| Sarah Porter - Arithmetic - 1852 - 286 pages
...multiplied by the third term : ji 1 fi for as 7 : 8 : : 14 : 16, therefore - = — = 8x14=16x7, or the product of the means is equal to the product of the extremes. Hence if any three numbers be given, a fourth proportional to them may be found, such as, this 4th... | |
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