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 Principles of Analytical Geometry ... - Page 14by Henry Parr Hamilton - 1826 - 326 pagesFull view - About this book
| Isaac Dalby - Mathematics - 1806 - 526 pages
...and that of the second and third by b. If 3 numbers are in musical proportion, the first wilt he (o **the third, as the difference between the first and second, is to** the difference of the second and third. Let the first number be i ; Then the second will be * + a;... | |
| Isaac Dalby - Mathematics - 1813 - 532 pages
...that of the second and third by b. m If three numbers are ia 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 * ; Then the second will be x + a;... | |
| 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... | |
| Beriah Stevens - Arithmetic - 1822 - 423 pages
...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 of strings... | |
| Encyclopedias and dictionaries - 1823
...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 - Algebra - 1824 - 516 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. Thus, a, 6, c, are harmonically proportional, when a :... | |
| James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
...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, when a :... | |
| John Bonnycastle - Algebra - 1825 - 312 pages
...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, when a:c... | |
| Sir William Chambers, Joseph Gwilt - Architecture - 1825 - 378 pages
...for 9 divided by 6 is the same as 6 divided by 4, each being 1£ ; harmonical, wherein the first term **is to the third as the difference between the first and second is to** the difference between the second and third, or in four terms, where the first is to the fourth as... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 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... | |
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