 | 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... | |
 | 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... | |
 | Charles Hutton - Mathematics - 1811 - 406 pages
...difference being d. The mqst useful part of arithmetical proportion is contained in the following theorems : 1. When four quantities are in Arithmetical Proportion, the sum of the two extremes is equal to the sum of the two means. Thus, in the arithmeticals 4, 6, 7, 9, the sum 4... | |
 | Charles Hutton - Mathematics - 1812 - 620 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,...following theorems : THEOREM 1. When four quantities arc in arithmetical proportion, the sum of the two extremes is equal to the sum of the two means. Thus,... | |
 | Jeremiah Day - Algebra - 1814 - 304 pages
...—m a-\-m=b+h So in the proportion, 12 •• 10 :: 11 •• 9,wehave 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 •• e, then a — b=b— * And transposing — b and — e, «+c=26.... | |
 | 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... | |
 | Charles Hutton - Mathematics - 1816 - 610 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 of the two extremes is equal to the sura of the two means. Thus, of the four 2, 4, 6, 8, here 2 -j8 = 4 +... | |
 | 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... | |
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When four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the two mean terms. 
