 | 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... | |
 | 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,... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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,... | |
 | Cadmus Marcellus Wilcox - Rifle practice - 1859 - 308 pages
...5, or between 12 and 10, is called the ratio of the proportion. In every proportion by difference, the sum of the extremes is equal to the sum of the means. PROPORTIONS BY QUOTIENTS, OR SIMPLY PROPORTIONS. "We give the name of proportion by quotient... | |
 | James Bates Thomson - Arithmetic - 1860 - 440 pages
...series is called descending ; as, 11,9, 7,5, &c. 598. When four numbers are in arithmetical progression the sum of the extremes is equal to the sum of the means. Thus, if 5—3 = 9 — 7, then will 5 + 7 = 3 + 9. Again, if three numbers are in arithmetical... | |
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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. 
