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" Quantities are said to be in continued proportion when the first is to the second, as the second is to the third, as the third to the fourth ; and so on. "
Robinson's Progressive Practical Arithmetic: Containing the Theory of ... - Page 282
by Horatio Nelson Robinson, Daniel W. Fish - 1874 - 372 pages
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Arithmetic - 1822 - 536 pages
...and extract the square root of the product ; which root will be the mean proportional sought. Note. When the first is to the second as the second is to the third, the second is called a mean proportional between the other two. Thus, 4 is a mean proportional between...
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A New System of Arithmetick: In which the Rules are Familiarly Demonstrated ...

William Ruger - Arithmetic - 1832 - 282 pages
...sought. EXAMPLES. 1 . What is the mean proportional between 24 aad 96 ? 24X96=^/2304= Ans. 48. NOTE. — When the first, is to the second, as the second is to the . third, the second is called a mean proportional between the other two; thus, 24 : 48 : : 96. . 2. A cheese...
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Arithmetic - 1832 - 540 pages
...and extract the square root of the product; which root will be the mean proportional sought. Note. When the first is to the second as the second is to tha third, the second is called a mean proportional between the other two. Thus, 4 is a mean proportional...
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Ruger's Arithmetick, with Questions and Answers: A New System of Arithmetick ...

William Ruger - Arithmetic - 1841 - 268 pages
...sought. EXAMPLES. 1. What is the mean proportional between 24 and 96 ? 24x96=V2304= Ans. 48. NOTE. — When the first is to the second, as the second is to the third, the second is called a mean proportional between the other two, thus. 24: 48:: 96. 2. A cheese weighed...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...That is, if the product of the first and third of two quantities, is equal to the square of a second, the first is to the second, as the second is to the third. Illustration. IT 4 : 6 : : 6 : 9, then 4X9=62=36. If 2X8=16, then 2 : /I6 : : /IB : 8 Or 2 : 4 : :...
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A plain instructor; or, A compendious view of several subjects ..., Part 2

Joseph Jones - 1849 - 370 pages
...mean proportional between the two axis of the ellipse. What do you understand by a mean proportional ? When the first is to the second as the second is to the third, (as 3 : 6 :: 6 : 12), then the second is a mean proportional between the first and third. How do find...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 250 pages
...That is, if the product of the first and third of two quantities, it equal to the square of a second, the first is to the second, as the second is to the third. Illustration. If 4 : 6 : : 6 : 9, then 4X9=62=36._ If 2X8=16, then 2: i/T6 : : /IB : 8 Or 2 : 4 : :...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...to another is defined to be the ratio which the first magnitude has to a third magnitude such that the first is to the second as the second is to the third. OBS. 1. Hence when three magnitudes are proportional (Def. 9. Obs. 2), the ratio which the first bears...
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The Progressive Practical Arithmetic: Containing the Theory of Numbers, in ...

Horatio Nelson Robinson - Arithmetic - 1859 - 362 pages
...370. The Extremes are the first and fourth terms. 371. The Means are the second and third terms. 372. Three numbers may be in proportion when the first...said to be a mean proportional between the other two. 373. In every proportion the product of the extremes is equal to the product of the means. Thus, in...
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The Progressive Higher Arithmetic, for Schools, Academies, and Mercantile ...

Horatio Nelson Robinson - Arithmetic - 1860 - 444 pages
...fourth terms ; and The Means are the second and third terms. <-I2i5. Three numbers are proportional when the first is to the second as the second is to the third. Thus, the numbers 4, 6, and 9 are proportional, since 4:6=6:9, the ratio of each couplet being |, or \\. 426. When three...
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