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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... "
The elements of algebra - Page 317
by Andrew Bell (writer on mathematics.) - 1839
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 304 pages
...389. 6. Then a:ar::ar—a:arz—ar::arx—ar:ar'—ar*, &c. That is, the first term is Ui liu- second, as the difference between the first and second, to the difference between the second and third; and as tn« difference between the second and third, to the difference between the third and fourth, &c....
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A New, Copious and Complete System of Arithmetic: For the Use of Schools and ...

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 : : 4 —...
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A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

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 of...
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Encyclopaedia Britannica; Or A Dictionary of Arts, Sciences, and ..., Volume 19

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...second to the difference between the second and third : hence we readily find that putting a and 6 for its two first terme, its general form will be n /i...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 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...
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An Elementary Treatise on Algebra: Theoretical and Practical

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. Thus, a, 6, c, are harmonically proportional, when...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - Algebra - 1825 - 336 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...
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A Treatise on the Decorative Part of Civil Architecture, Volume 1

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...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 352 pages
...'.ar — a : ar3 —ar'.-'.ar3 — ar : ar3 — ar3, &c. That is, the first term is to the second, as the difference between the first and second, to the difference between the second and third ; and as the difference between the second and third, to the difference betAveen the third and fourth, &c....
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...given, this circumference is the locus of the vertex. *** (530) DBF. — Three magnitudes are said to be in harmonical progression, when the first is to the...second to the difference between the second and third. *#* (531) DBF. — A right line AB is said to be cut harmonically at two points CD, when AC, AD, AB...
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