 | 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 - 1749 - 210 pages
...(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 - Algebra - 1752 - 212 pages
...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... | |
 | Samuel Webber - Mathematics - 1808 - 466 pages
...being as their circumferences, the circumferences are also in arithmetical progression. But in such a, progression the sum of the extremes is equal to the sum of each two terms, equally distant from them ; therefore the sum of the circumferences on AC and CB is... | |
 | Jeremiah Joyce - Arithmetic - 1812 - 274 pages
...addition to the above, the learner may commit 'to memory the following facts on the subject : 1. If three numbers are in arithmetical progression, the sum of the extremes is equal to double the mean term ; as 6, 9, 12, where 6 + 12 = 2 X «f = 18. 2. If four numbers be in arithmetical... | |
 | Jeremiah Day - Algebra - 1814 - 304 pages
...a+4<7, a + 3d, a+2d, a+d, a. The sums will be Here we discover the important property, that, 428. In an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. In the series of numbers above, the sum of the... | |
 | 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. • This also is a very subtile property of... | |
 | Beriah Stevens - Arithmetic - 1822 - 436 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... | |
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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. 
