 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...locus of the vertex. *** (530) DBF. — Three magnitudes are said to be 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. *#* (531) DBF. — A right line AB is said to be cut... | |
 | Thomas Curtis - Aeronautics - 1829 - 798 pages
...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...is to the difference between the second and third. Let a, b, and x be three terms in harmonical proportion ; then a ; x '. '. a — b '. Ь — x. whence... | |
 | John Bonnycastle - Algebra - 1829 - 372 pages
...when nb ~2a— b' 10. Four quantities are in harmonica] proportion, when the first is to the fourth, as the difference between the first and second is to the difference between the third and fourth. Thus, a, b, c, d, are in harmonical proportion, when a = d ; : a— 6 : c — rf,... | |
 | Nicolas Pike - Arithmetic - 1832 - 540 pages
...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 be... | |
 | Nicolas Pike - Arithmetic - 1832 - 544 pages
...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 lie... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...bisecting 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 - Euclid's Elements - 1837 - 290 pages
...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 a harmonic... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...1, $, and '. , produce the sounds of a certain note, its fifth, and its octave ; and these lengths are such that the first is to the third, as the difference of the first and second to the difference of the second and third. By the insertion of other harmonical... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...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 pages
...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...second is to the difference between the second and the third. Thus, if a, b, с be the consecutive terms in a series, then if a : с :: a — b : b —... | |
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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... 
