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When four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the two mean terms.
A New and Easy Introduction to the Mathematics: Containing. A system of ... - Page 272
by Ira Wanzer - 1831 - 396 pages

A Course of Mathematics: In Two Volumes. For the Use of Academies ..., Volume 1

Charles Hutton - Arithmetic - 1818 - 646 pages
...terms of a Progression, are called the Extremes ; and the other terms, lying between them, the Means. The most useful part of arithmetical proportions,...quantities are in arithmetical proportion, the sum uf the two extremes is equal to the sum of the two means. Thus, of the four 2, 4, 6, 8, here 2 48 =...

A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...Progression the numbers or terms have all the same multiplier or divisor. The most useful part of Proportion, is contained in the following theorems. THEOREM 1. When four quantities are in proportion, the product of the two extremes is equal to the product of the two mean?. Thus, in the...

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

Beriah Stevens - Arithmetic - 1822 - 434 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...

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

Bézout - Arithmetic - 1825 - 258 pages
...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...

A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

Charles Hutton - Mathematics - 1825 - 608 pages
...terms of a Progression, are called the Extremes ; and the other terms, lying between them, the Means. The most useful part of arithmetical proportions, is contained in the following theorems : THEOREM I. When four quantities are in arithmetical proportion, the sum of the two extremes is equal to the...

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...

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

Jeremiah Day - Algebra - 1827 - 352 pages
...transposing— b and —m, a+m=6+A So in the proportion, 12..10: ;11..9, we have 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 .. c, then, a — b=b — c S And transposing - 6 and — c, ' o+c—...

Elements of Algebra

William Smyth - Algebra - 1830 - 280 pages
...with the equation 6 — o = d — c, from which we deduce a -f- d = 6 -f- c Thus in an equidifference the sum of the extremes is equal to the sum of the meant. This is the leading property of equi•differences. Reciprocally, let there be four quantities...