 | Ferdinand Rudolph Hassler - 1826 - 224 σελίδες
...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 distant... | |
 | Jeremiah Day - 1827 - 352 σελίδες
...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 - 1830 - 278 σελίδες
...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... | |
 | Jeremiah Day - 1831 - 358 σελίδες
...necessary to give the subject a separate consideration. It will be proper, however, to observe that, if four quantities are in arithmetical proportion,...: : h.. m, then a-\-m=b-\-h For by supposition, a — b-=hm And transposing - 6 and - m, a-\-m—b-\-h So in the proportion, 12.. 10:: 11.. 9, we have... | |
 | Jeremiah Day - 1831 - 354 σελίδες
...d. It will be proper, however, to observe that, if four quantities are in arithmetical proportionate sum of the extremes is equal to the sum of the means....: h . . m, then a-\-m=b-{-h For by supposition, a - 6 = h — m And transposing - b and - m, a-\-m= 6-fA So in the proportion, 12 . . 10 : : 1 1 . .... | |
 | Ira Wanzer - 1831 - 408 σελίδες
...useful part of Arithmetical Proportions is contained in the following theorems. .THEOREM 1. — When four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the two mean terms. Thus, of the four, 2, 4, 7, 0 ; here 2+9=4+7=11. THEOREM 2. — Inany continued arithmetical... | |
 | Jeremiah Day - 1832 - 360 σελίδες
...separate consideration. The proportion a . . b : : c . . d It will be proper, however, to observe that, if four quantities are in arithmetical proportion,...: : h . . m, then a-\-m=b-\-h For by supposition, ab=h — m And transposing - b and - m, a-\-m=b-\-h So in the proportion, 12 . . 10 : : 1 1 . . 9,... | |
 | Jeremiah Day - 1832 - 354 σελίδες
...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...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 - b find - m, a-\-m=b-\-h... | |
 | John Radford Young - 1832 - 408 σελίδες
...decreasing, according as the successive terms increase or decrease. (29.) THEOREM i. If four quantities be in arithmetical proportion, the sum of the extremes is equal to the sum of the means. For let a, b, c, d, be in arithmetical proportion ; then 6 — a = d — с ; add a + с to each side... | |
 | William Smyth - 1833 - 288 σελίδες
...same with 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, b, c,... | |
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It will be proper, however, to observe that, if four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the means. Thus if a . . b : : h... 
