 | Alexander Malcolm - 1730 - 702 σελίδες
...then we begin with the Addition. Example : 1"Н Í¿ 0 REM I. IF fouï Numbers are :/, thus, *.b:td, the Sum of the Extremes is equal to the Sum of the middle Terms, a-\~d = b-\-e. DEMON. If the Difference were o, the thing would be evident ; and if it... | |
 | Colin MacLaurin - 1748 - 490 σελίδες
...7> 4» i> — 2-> — 5» — 8, &c. • § 60. In four Quantities Arithmetically pro~ porlional, " the Sum of the Extremes is equal to the Sum of the meanTerms." Thus, a, a+b, e, e-\-b, are Arithmetical Proportionals, and the Sum of the Extremes (a-\-e+b}... | |
 | Willem Jacob 's Gravesande - 1749 - 210 σελίδες
...(119), if to both we add b-\- d, we do not deftroy the Equality ; and then a -\- d = cf- b, that is, the Sum of the Extremes is equal to the Sum of the Means. 123. Arithmetic Proportion is faid to be continued •when the fir ft Term differs as much from the... | |
 | Willem Jacob 's Gravesande - 1752 - 212 σελίδες
...19), if to both we add b-\- d, we do not deftroy the Equality ; and then a -f- d = c-\-b, that is, the Sum of the Extremes is equal to the Sum of the Means. 123. Arithmetic Proportion is faid to be continued -when the fir ft "Term differs as much from the... | |
 | Jeremiah Day - 1814 - 304 σελίδες
...d. ft 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 ••*», then n+m.=6+A For by supposition , a-rb=h — m And transp.—... | |
 | John Dougall - 1815 - 514 σελίδες
...extremes, and the 2nd and 3rd the means. The fondamental property of numbers in arithmetical proportion is that the sum of the extremes is equal to the sum of the means ! tims in 5, 10, 8, 13, the sum of the extremes § and 13, or 18, is equal to the sum of the means,... | |
 | Thomas Taylor - 1816 - 308 σελίδες
...the sum of the extremes is double the mean; as in 1. 2. 3, 1 +3=4=; 2x2. But if there are four terms, the sum of the extremes is equal to the sum of the two means. Thus if the terms are 1 . 2.3.4., 1+4= 2+3. • This also is a very subtile property of... | |
 | Beriah Stevens - 1822 - 436 σελίδες
...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 - 1825 - 258 σελίδες
...PROPERTIES OF ARITHMETICAL PROPORTION. 176. The fundamental property of arithmetical proportion, is that the sum of -the extremes is equal to the sum of the •means : for example, in this proportion 3.7:8.12, the sum 3 and 12 of the extremes, and that 7 and 8 of the... | |
 | Jeremiah Day - 1827 - 352 σελίδες
...d. 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 . . 6: '.h , . m, then a+m=/.+& For by supposition, a—b=h—m And transposing— b and... | |
| |
When four numbers are in arithmetical progression t/te • sum of the extremes is equal to the sum of the means. 
