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" IN ARITHMETICAL PROPORTION THE SUM OF THE EXTREMES is EQUAL TO THE SUM OF THE MEANS. 24. GEOMETRICAL' PROPORTION is AN EQUALITY OF GEOMETRICAL RATIOS, AND ARITHMETICAL PROPORTION AN EQUALITY OF ARITHMETICAL RATIOS. "
A Treatise on Algebra - Page 144
by Benedict Sestini - 1857 - 216 pages
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A New System of Arithmetick Theorical and Practical: Wherein the Science of ...

Alexander Malcolm - Algebra - 1730 - 702 pages
...then we begin with the Addition. Example : 1"Н Í¿ 0 REM I. IF fouï Numbers are :/, thus, *.b:td, the Sum of the Extremes is equal to the Sum of the middle Terms, a-\~d = b-\-e. DEMON. If the Difference were o, the thing would be evident ; and if it...
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A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and ...

Colin MacLaurin - Algebra - 1748 - 490 pages
...7> 4» i> — 2-> — 5» — 8, &c. • § 60. In four Quantities Arithmetically pro~ porlional, " the Sum of the Extremes is equal to the Sum of the meanTerms." Thus, a, a+b, e, e-\-b, are Arithmetical Proportionals, and the Sum of the Extremes (a-\-e+b}...
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The New Mathematician's Guide: Containing the Elements of Universal ...

Willem Jacob 's Gravesande - Algebra - 1749 - 210 pages
...(119), if to both we add b-\- d, we do not deftroy the Equality ; and then a -\- d = cf- b, that is, the Sum of the Extremes is equal to the Sum of the Means. 123. Arithmetic Proportion is faid to be continued •when the fir ft Term differs as much from...
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The Elements of Universal Mathematics, Or Algebra: To which is Added, A ...

Willem Jacob 's Gravesande - Algebra - 1752 - 212 pages
...19), if to both we add b-\- d, we do not deftroy the Equality ; and then a -f- d = c-\-b, that is, the Sum of the Extremes is equal to the Sum of the Means. 123. Arithmetic Proportion is faid to be continued -when the fir ft "Term differs as much from...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 304 pages
...d. ft will be proper, however, to observe that, if four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the means. •, ... Thus if a ~b::h ••*», then n+m.=6+A For by supposition , a-rb=h — m And transp.—...
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The Young Man's Best Companion and Guide to Useful Knowledge

John Dougall - Encyclopedias and dictionaries - 1815 - 514 pages
...and the 2nd and 3rd the means. The fondamental property of numbers in arithmetical proportion is that the sum of the extremes is equal to the sum of the means ! tims in 5, 10, 8, 13, the sum of the extremes § and 13, or 18, is equal to the sum of the...
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Theoretic Arithmetic, in Three Books: Containing the Substance of All that ...

Thomas Taylor - Arithmetic - 1816 - 308 pages
...the sum of the extremes is double the mean; as in 1. 2. 3, 1 +3=4=; 2x2. But if there are four terms, the sum of the extremes is equal to the sum of the two means. Thus if the terms are 1 . 2.3.4., 1+4= 2+3. • This also is a very subtile property of...
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A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

Beriah Stevens - Arithmetic - 1822 - 436 pages
...proportions. THEOREM 3. In an arithmetical series, consisting of 4, 6, or any even number of terms, the sum of the extremes is equal to the sum of the two cciddle terms, or to the sum of any two means equally distant from the extremes. Thus, in the series...
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A Theoretical and Practical Arithmetic: In which the Principles of that ...

Bézout - Arithmetic - 1825 - 258 pages
...the sum 22, 1 have 1 1 for the mean term, so that -r-7 .11 .15. * In every arithmetical proportion, the sum of the extremes is equal to the sum of the means. Let us take, for example, the arithmetical proportion 5.3:6.4. Since the difference between...
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Elements of Arithmetic, Theoretical and Practical: Adapted to the Use of ...

Ferdinand Rudolph Hassler - Arithmetic - 1826 - 224 pages
...deduced from the nature of the series, in the following manner. As we found in arithmetic proportion that the sum of the extremes is equal to the sum of the means, so it is evident that here the sum of the extremes is equal to the sum of any two terms equally...
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