 | Isaac Dalby - Mathematics - 1813 - 538 pages
...that of the second and third by b. • If three numbers are in musical proportion, the first will be to the third. as the difference between the first and second, is to the difference of the second and third. Let the first number be x; Then the second will be x + a; And... | |
 | James Maginness - Arithmetic - 1821 - 378 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 difference between the second and third, as the numbers 3, 4, and 6; for 3 : 6 :: 4—3 : 6—4.... | |
 | Beriah Stevens - Arithmetic - 1822 - 436 pages
...rousicaljntervals, 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 lengths of strings... | |
 | Encyclopedias and dictionaries - 1823 - 936 pages
...geometrical series. 3. Harmonic Series is that in which the first of any three of its consecutive terms is to the third, as the difference between the first and second to the difference between the second and third : hence we readily find that putting a and 6 for its... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...HARMONICAL PROPORTION AND PROGRESSION. 490. 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. 491. Four quantities are in harmonica! proportion, when... | |
 | James Ryan - Algebra - 1824 - 550 pages
...HARMONICAL PROPORTION AND PROGRESSION. 490. 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. a : c : : a—b : b—c, or a : c : : b—a : c—b. And... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...+ar*, &c. ad infinitum-^—. 1—r 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:c... | |
 | James Ryan - Algebra - 1826 - 430 pages
...HARMONICAL PROPORTION AND PROGRESSION. 490. Three quantities are said to be in harmonical proportion, w-hori 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 :... | |
 | 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... | |
 | John Bonnycastle - Algebra - 1829 - 372 pages
...+ar 3 +ar t , &c. ad infinitum . 9. Three quantities are said to be in harmonica! 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, o, 6, c, are harmonically proportional, when a:... | |
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the first is to the third as the difference between the first and second is to 
