| 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 =... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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—... | |
| 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... | |
| Charles Hutton - Mathematics - 1831 - 662 pages
...and the other terms, lying between them, the Means. The moat useful part of arithmetical proportion, **is contained in the following theorems : THEOREM 1....quantities are in arithmetical proportion, the sum of the** two extremes is equal to the sum of the two means. Thus, of the four 2, 4, 6, 8, here 2 48 = 4 + 6=10.... | |
| Jeremiah Day - Algebra - 1832 - 354 pages
...separate consideration. The proportion a..b::c..d It will be proper, however, to observe that, if fowr **quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the** means. Thus if a . . b : : h . . in, then ,a-\-m= b-\-h For by supposition, a - b = h - m And transposing... | |
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