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In any proportion, the product of the means is equal to the product of the extremes.
Elements of Plane Geometry: For the Use of Schools - Page 53
by Nicholas Tillinghast - 1844 - 96 pages

Higher Arithmetic: Or, The Science and Application of Numbers: Combining the ...

James Bates Thomson - Arithmetic - 1847 - 424 pages
...324 SIMPLE [SECT. XIV. fieiiviisfrat-tfin. — If four numbers are proportional, we Lave seen th:\t the product of the means is equal to the product of the i-xtrimcs ; (Art. 4!)S:) therefore the pr id let of tile acca ul and t.hv'd terms must be equal to...

Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...x= one part; then 55— £= the other. By the question, x : 55 — x : : 2 : 3. Then, since, m every proportion, the product of the means is equal to the product of the extremes, we have 3x=2(55 — x)=110 — 2x 5x=110 x=22, and 55— x=33, as before. Or thus : Let x= one part,...

Higher Arithmetic, Or, The Science and Application of Numbers: Combining the ...

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...

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...

Youth's Columbian Calculator: Being an Introductory Course on Arithmetic for ...

Almon Ticknor - Arithmetic - 1848 - 122 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...

The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ...

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...

Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 248 pages
...we have the following proportions : z+5 : y+5 : : 5 : 6 a:— 5 : y— 5 : : 3 : 4. Since, in every proportion, the product of the means is equal to the product of the extremes, we have the two equations 6(x+5)=5(y+5) 4(x-5)=3(y-5) From these equations, the values of z and y are...

Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 410 pages
...5x for the second, which fulfills the first condition. Then, Sx-\-Q : 5*+9 : : 6 : 7. But in every proportion, the product of the means is equal to the product of the extremes. (Arith. Part 3rd, Art. 209.) Hence, 6(5o:+9)=7(3;c+9). 30*4-54=2 la-l-63, 30*— 21*=63— 34, .-....