 | Alexander Malcolm - Algebra - 1730 - 702 pages
...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 - Algebra - 1748 - 490 pages
...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 - Algebra - 1752 - 212 pages
...(119), 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 Prop onion is faid to be continued -when the firft "Term differs as much from the fecond,... | |
 | Lindley Murray - Handbooks, vade-mecums, etc - 1814 - 618 pages
...as, 1, 2, 3, 4; 10, 7,4, 1 ; and a, a+b, a+2b, &c. In four quantities arithmetically proportional, the sum of the extremes is equal to the sum of the mean terms ; as in the arithmetical proportionals a, a+b, e, e+b, the sum of the extremes a+e+b=. to... | |
 | John Dougall - Encyclopedias and dictionaries - 1815 - 514 pages
...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 - Arithmetic - 1816 - 308 pages
...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. f This also is a very subtile property of this... | |
 | Jeremiah Day - Algebra - 1820 - 352 pages
...consideration. The proportion • a"b::c"d It will be proper, however, to observe that, it four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the means. Thus if a • • b: : h" m, then For by supposition, a—b=h—m And transposing —b and — m a+m=b... | |
 | Beriah Stevens - Arithmetic - 1822 - 436 pages
...proportion. 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... | |
 | George Crabb - Industrial arts - 1823 - 798 pages
...b, a + 2A, a + 34, a + 46, &c. ; *, * — b, x — 2 b, &c. This is called Arithmetical Progression. In arithmetical proportion the sum of the extremes is equal to the sum of the means, thus 3 + 16 = 7 + 12 = 19 ; and a+e+b=a+b+ e. — Geometrical Proportion denotes that relation between... | |
 | 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 be... | |
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If four quantities be in arithmetical proportion, the sum of the extremes is equal to the sum of the means. 
