| 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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