Books Books 31 - 40 of 194 on In any proportion, the product of the means is equal to the product of the extremes.. In any proportion, the product of the means is equal to the product of the extremes. Treatise on the elements of algebra - Page 256
by James Bryce - 1837 ## Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 240 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... ## Higher Arithmetic, Or, The Science and Application of Numbers: Combining the ...

James Bates Thomson - Arithmetic - 1848 - 422 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... ## The Elements of Arithmetic...: In which Decimal and Integral ..., Part 2

Pliny Earle Chase - Arithmetic - 1848 - 240 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... ## The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ...

Zadock Thompson - Arithmetic - 1848 - 168 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... ## Ray's Algebra: Designed for High Schools and Colleges. An analytical ..., Part 2

Joseph Ray - Algebra - 1852 - 396 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... ## Key to Ray's Algebra: Parts First and Second : Containing Statements and ...

Joseph Ray - Algebra - 1852 - 343 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... ## Rational Arithmetic

Sarah Porter - Arithmetic - 1852 - 263 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... ## Stoddard's Practical Arithmetic

John Fair Stoddard - Arithmetic - 1852 - 299 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... ## Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 240 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... 