| 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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