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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 Treatise on Arithmetic ...

Noble Heath - 1855 - 468 pages
...proportion. The proportion is written thus : a . b : c . d, and is read a is to b, as c is to d. In an arithmetical proportion, the sum of the extremes is equal to the sum of the meuns : and this, which is called the fundamental property, may be thus demonstrated : Let a .6 : c...

## The Popular Educator, Volume 6

1855 - 424 pages
...— m, o+»i=o+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--b : :b" c, then, a — fc;J с And transposing — Ь and — e, e+£=2¿. Quantities,...

## Treatise on Algebra, for the Use of Schools and Colleges

William Smyth - Algebra - 1855 - 370 pages
...with the equation b — a = d — c, from which we deduce a -j- d = b -\- c. Thus in an equidifference the sum of the extremes is equal to the sum of the means. This is the leading property of equidifferences. Reciprocally, let there be four quantities...

## Arithmetic on the Productive System: Accompanied by a Key and Cubical Blocks

Roswell Chamberlain Smith - Arithmetic - 1856 - 334 pages
...extremes 7 and 6 added together are equal to the means 5 and 8 added together, and universally — 23. 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...

## A Treatise on Arithmetic: Through which the Entire Science Can be Most ...

Noble Heath - Arithmetic - 1856 - 472 pages
...a-(-d=6-|-c, as before. Thus, in the proportion 5 . 2 : 7 . 4, we have 5 -|- 4 = 7 + 2. Wherefore, in every arithmetical proportion the sum of the extremes is equal to the sum of the means. 453. From this fundamental property, it is evident, that we may change the places of the means...

## A Treatise on Algebra

Benedict Sestini - Algebra - 1857 - 258 pages
...= a' — b', we have Properties. ™. . 7 ., a -f b' = a' + b, so also in arithmetical proportions, The sum of the extremes is equal to the sum of the mean terms. And since from any equation, like a + b' = a' + b, we deduce a — b = a' — b', so, vice...

## A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - Algebra - 1858 - 344 pages
...the equation b — a =• d — c, from which we deduce a -\- d = b -\- c. Thus in an equidifference the sum of the extremes is equal to the sum of the means. This is the leading property of equidifferences. Reciprocally, let there be four quantities...

## A Treatise on Elementary and Higher Algebra

Theodore Strong - Algebra - 1859 - 570 pages
...decrease, the progression is said to be decreasing. (4.) If four numbers or quantities of the same kind are in arithmetical proportion, the sum of the extremes is equal to the sum of the means. For, let a, 5, c, d denote four numbers or quantities, such that we have a — b = c — d,...