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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 Principles of Analytical Geometry ... - Page 14
by Henry Parr Hamilton - 1826 - 326 pages
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

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;...
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A Course of Mathematics: Designed for the Use of the Officers and ..., Volume 2

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;...
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A New, Copious and Complete System of Arithmetic: For the Use of Schools 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...
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A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

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

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...
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An Elementary Treatise on Algebra: Theoretical and Practical

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 :...
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An Elementary Treatise on Algebra, Theoretical and Practical ...

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 :...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

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...
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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 as...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

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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