 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...  The University Algebra ... - Page 382by John Fair Stoddard, William Downs Henkle - 1859 - 528 pagesFull view - About this book
 | William Enfield (M.A.) - Amusements - 1821 - 302 pages
...OF HARMONICAL PROGRESSION. Three numbers are in harmonical proportion, when the first is to the last as the difference between the first and the second...is to the difference between the second and third. Thus the numbers 6, 3, 2, are in harmonical proportion; for 6 is to 2 as 3, the difference between... | |
 | James Maginness - Arithmetic - 1821 - 378 pages
...of 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 :... | |
 | Beriah Stevens - Arithmetic - 1822 - 436 pages
...of musicaljntervals, 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... | |
 | James Ryan - Algebra - 1824 - 550 pages
...tnfinitum. Ans. 4. § III. 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. Thus, a, 6, c, are harmonically proportional,... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...infinilum, Ans. 4. § III. HARHOMCAL 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. Thus, a, 6, c, are harmonically proportional,... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...hare, in that case, a+ar+ar-+ar3+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,... | |
 | James Wood - Algebra - 1825 - 322 pages
...multiple of m and с is the least common multiple of a, b and c. (380.) Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference of the first and second is to the difference of the second and third. Any magnitudes A, B, C, D, E,... | |
 | 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... | |
 | John Bonnycastle - Algebra - 1829 - 372 pages
...shall have, "in that case, 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,... | |
 | 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 the first and second is to the difference between the second and third. Let a, b, and x be three terms in harmonical... | |
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