 | John Bonnycastle - 1829 - 372 pągines
...a+ar+ar3+ar3-r-ar«, &c. ad infinitum ° 9. Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference between the first and second is to the difference between the second and third. Thus, a, b, c, are harmonically proportional, when a :... | |
 | Thomas Curtis - 1829 - 798 pągines
...proportion. It has been observed in the article PROPORTION, that if three numbers be in harmonical proportion the first is to the third as the difference between the first and second is to the difference between the second and third. Let a, b, and x be three terms in harmonical proportion... | |
 | Nicolas Pike - 1832 - 540 pągines
...musical intervals, or the lengths of strings sounding musical notes : and of three numbers it is, when the first is to the third as the difference between the first and second is to the diflerencc between the second and third, as the numbers 3, 4, 6. Thus, if the lengths of strings... | |
 | Nicolas Pike - 1832 - 544 pągines
...intervals, or the lengths of strings sounding musical mites : and of three numbers it is, when thejirst iu to the third as the difference between the first and second is to the diilerence between the second and third, as the numbers 3, 4, 6. Thus, if the lengths of strings... | |
 | Euclid - 1833 - 216 pągines
...the internal and external angles divide the base produced in harmonical proportion, that is, so that the first is to the third as the difference between the first and second to the difference between the second and third. BE is to EC as BD is to CD, therefore by alternation... | |
 | Andrew Bell - 1837 - 290 pągines
...segment, as the other extreme segment to the middle segment. gression or harmonical progressionals, when the first is to the third, as the difference between the first and second is to the difference hetween the second and third. 7. The second of three lines in this progression, is called... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pągines
...HARMONICAL PROGRESSION. DEFINITIONS. (434.) 1 Three quantities are said to he in harmonical progression when the first is to the third as the difference between the first and second to the difference between the second and third ; and the three quantities are called harmonical professional»?... | |
 | Thomas Grainger Hall - 1840 - 266 pągines
...146. Quantities are said to be in harmonic progression •when any 3 consecutive terms being taken ; the first is to the third as the difference between the first and second is to the difference between the second and the third. Thus, if a, b, с be the consecutive terms in a series,... | |
 | Charles Waterhouse - 1842 - 178 pągines
...musical intervals, or the lengths of strings sounding musical notes ; and of three numbers it is, when the first is to the third, as the difference between the first and second is to the difference between the second and third, as the numbers, 3, 4, 6. Thus, if the length of strings... | |
 | Wales Christopher Hotson - 1842 - 306 pągines
...Harmonical Progression is a series of quantities of which, if any three consecutive terms be taken, the first is to the third as the difference between the first and second is to the difference between the second and third. Thus, if a,, a.2, a3, a4, &c. be the consecutive terms... | |
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Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression... 
