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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... "
Text book of geometry - Page 180
by Thomas Steadman Aldis - 1872
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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; And the third ...............
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A Course of Mathematics: Designed for the Use of the Officers and ..., Volume 2

Isaac Dalby - Mathematics - 1813 - 538 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; And the third ...............
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A New, Copious and Complete System of Arithmetic: For the Use of Schools and ...

James Maginness - Arithmetic - 1821 - 378 pages
...a fifth 2 to 3, and a fourth 3 to 4. Again, between four numbers, when the first is to the fourth, as the difference between the first and second, is to the difference between the third and fourth, as in the numbers 5, 6, 8, 10; for 5 : 10 :: 6—5 : 10—8, and strings of the lengths...
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A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

Beriah Stevens - Arithmetic - 1822 - 436 pages
...a fifth 2 to 3, and a fourth 3 to 4. Again, between four numbers, when the first ie to the fourth, as the difference between the first and second, is to the difference between the third and fourth, as in the numbers 5, 6, 8, 10 : For strings of such lengths will sound an octave...
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Universal Technological Dictionary: Or, Familiar Explanations of ..., Volume 2

George Crabb - Industrial arts - 1823 - 704 pages
...as the difference between the second and third ; or in four terms, when the first is to the fourth as the difference between the first and second is to the difference between the third and the fourth ; the reciprocals of an arithmetical proportion are in harmonica) proportion....
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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 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, Robert Adrain - Algebra - 1824 - 542 pages
...and 6, when c= ah 491. Four quantities are in harmonica! proportion, when the first is to the fourth, as the difference between the first and second is to the difference between the third and fourth. Thus, a, b, c, d, are in harmonical proportion, when a : d : : a — 6 : c — d,...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...and b, when c= ab 491. Four quantities are in harmonica! proportion, when the first is to the fourth, as the difference between the first and second is to the difference between the third and fourth. Thus, n, 4, c, </, are in harmonica! proportion, when aid:: a — 6 : c — d, or...
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A Treatise on the Decorative Part of Civil Architecture, Volume 1

Sir William Chambers, Joseph Gwilt - Architecture - 1825 - 378 pages
...to the difference between the second and third, or in four terms, where the first is to the fourth as the difference between the first and second is to the difference between the third and fourth, as 6, 4, 3, or with four terms 24, 16, 12, 9; a sesquialteral ratio is that wherein...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - Algebra - 1825 - 336 pages
...when C~2a— 6' „ 10. Four quantities are in harmonical proportion, when the first is to the fourth, as the difference between the first and Second is to the difference between the third and fourth. Thus, a, b, c, d, are in harmonica] proportion, when « : d ;: 0 — 6: c— d, or...
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