Books Books In any proportion, the product of the means is equal to the product of the extremes. The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ... - Page 73
by Zadock Thompson - 1832 - 168 pages ## Smith and Duke's The American Statistical Arithmetic: Designed for Academies ...

Francis Henney Smith - Arithmetic - 1845 - 300 pages
...fourth by multiplying the second and third terms together, and dividing by thefirst. For, by Art. 178, the product of the means is equal to the product of the first term by the fourth. The fourth term must therefore be equal to the product of the means divided... ## North American Arithmetic: Part Second and Part Third, Part 2

Frederick Emerson - Arithmetic - 1846 - 268 pages
...Since. the product of the extremes m every proportion is equal to the product of the means, one product may be taken for the other. Now, if we divide the product of the extremes by one extreme, the quotient is the other extreme ; therefore, if we divide the product of... ## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...dividing the antecedent by the consequent is called the ratio. If four quantities are proportional, the product of the means is equal to the product of the extremes; in the proportion a : 6 ; ; c : d, a and d are the extremes, b and c the means. Wherefore, in order... ## Higher Arithmetic: Or, The Science and Application of Numbers; Combining the ...

James Bates Thomson - Arithmetic - 1847 - 434 pages
...the work is right. (Art. 500.) 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 prDcliict of the second and third terms must be equal to that of the first... ## 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 - 252 pages
...Ans< Or thus: Let x= one part; then 55— x= the other. By the question, x : 55 — x : : 2 : 3. Then, since, in every proportion, the product of the means is equal to the product of the extremes, we have 3z=2(55 — z)=110 — 2x 5*=110 z=22, and 55— x=33, as before. Or thus : Let x= one part,... ## Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...Let 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,... ## 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... ## 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... 