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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: Designed for the Use of Students - Page 14
by Henry Parr Hamilton - 1826 - 326 pages
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A Universal Key to the Science of Algebra: In which Some New Modes of ...

Horatio Nelson Robinson - Algebra - 1844 - 184 pages
...product equal to 576, to find the numbers. NB Three numbers 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, x, b, are in harmonical proportion, when a ; b...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...as the other extreme segment is to the middle part. 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...
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Watson's Tutor's assistant; or, Complete school arithmetic

William Watson (of Beverley.) - 1845 - 188 pages
...Progression is formed by multiplication or division. 13. Harmonical Proportion, is when 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, when the first is to the fourth as...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...Harmonical Proportion. (Art. 124.) When three magnitudes, a,b,c, have the relation of a:c::a — b:b — c; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonica I...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...Art. 213, ae : bf : : eg : dh. (228.) 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, 2, 3, 6 are in harmonical proportion, for 2:6::3...
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An Elementary Treatise on Algebra: In which the Principles of the Science ...

Samuel Alsop - Algebra - 1846 - 300 pages
...Harmorącal Proportion. . J • . - » 68. Three quantities are said to be in harmonical proportion, if the first is to the third as the difference between the first and second is to the difference between the second and third. Thus, if a : с : : a — -b : b — c; the magnitudes...
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Arithmetic, Its Principles and Practice

James W. Kavanagh - 1846 - 304 pages
...said to form a harmonica! series when of every three of its consecutive [following] terms the iirst is to the third, as the difference between the first and second is to the difference between the second and third ; thus 12, 8, and 6 form a harmonica1 series, for 12 :...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - Mathematics - 1846 - 500 pages
...quantities are said to be in harmonical progression, when any three successive terms are so related, that the first is to the third as the difference between the first and the second is to the difference between the second and third. Thus if a, b, c are in harmonical progression,...
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A Theoretical and Practical Treatise on Algebra ...

Horatio Nelson Robinson - Algebra - 1848 - 354 pages
...PROPORTION. (Art. 124.) When three magnitudes, a, b, c, have the relation of a: c : : a — b : b — c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion....
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A Treatise on Algebra: In which the Principles of the Science are Familiarly ...

Samuel Alsop - Algebra - 1848 - 336 pages
...SECTION IV. . Harmonical Proportion. 68. Three quantities are said to be in harmonical proportion, if the first is to the third as the difference between the first and second is to the difference between the second and third. Thus, if a : с : : a -- о : b — с ; the magnitudes...
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