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" It 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... "
Elements of Algebra: Being an Abridgement of Day's Algebra Adapted to the ... - Σελίδα 199
των Jeremiah Day - 1844 - 252 σελίδες
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A New System of Arithmetick Theorical and Practical: Wherein the Science of ...

Alexander Malcolm - 1730 - 627 σελίδες
...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...

A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and ...

Colin MacLaurin - 1748 - 431 σελίδες
...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}...

The New Mathematician's Guide: Containing the Elements of Universal ...

Willem Jacob 's Gravesande - 1749 - 187 σελίδες
...(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 the...

The Elements of Universal Mathematics, Or Algebra: To which is Added, A ...

Willem Jacob 's Gravesande - 1752 - 187 σελίδες
...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 the...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1814 - 303 σελίδες
...—m a-\-m=b+h So in the proportion, 12 •• 10 :: 11 •• 9,wehave 12+9 = 10+11. Again, if three quantities are in arithmetical proportion, the sum of the extremes is equal to double the mean. If a- 6:: b •• e, then a — b=b— * And transposing — b and — e, «+c=26....

The Young Man's Best Companion and Guide to Useful Knowledge

John Dougall - 1815 - 476 σελίδες
...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 means,...

Theoretic Arithmetic, in Three Books: Containing the Substance of All that ...

Thomas Taylor - 1816 - 252 σελίδες
...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...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1820 - 332 σελίδες
...however, to observe that, if four quantities are in arithmetical proportion, the sum of the extremis is equal to the sum of the means. Thus if a • • b: : h" m, then a+m=b+h For by supposition, a—b=h—m And transposing —b and — m a+m=b + h So in the proportion, 12" 10:: 11"9, we have 12+9=104...

A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

Beriah Stevens - 1822 - 423 σελίδες
...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...

A Theoretical and Practical Arithmetic: In which the Principles of that ...

Bézout - 1825 - 236 σελίδες
...plus 4. The reasoning would be the same for every other arithmetical proportion. Therefore, in every arithmetical proportion, the sum of the extremes is equal to the sum of the means. If the arithmetical proportion were continued, it is evident that the sum of the extremes would be...




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