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" WHEN three numbers are such that the first is to the third, as the difference of the first and second is to the difference of the second and third... "
The Elements of Arithmetic ... in which Decimal and Integral Arithmetic are ... - Σελίδα 136
των Pliny Earle Chase - 1844
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Τόμος 1

1801 - 446 σελίδες
...to the difference of the second and third, 33 the first is to the third ; and, in the latter, when the difference of the first and second is to the difference of the third and fourth as the first is to the fourth. Thus, 2, 3 and 6 ; and 3, 4, 6 and 9, are harmonical...

A Course of Mathematics ...: Designed for the Use of the Officers ..., Τόμος 2

Isaac Dalby - 1806 - 526 σελίδες
...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 ............ i +«+/.. Whence,...

Mathematics: Compiled from the Best Authors, and Intended to be the ..., Τόμος 1

Samuel Webber - 1808 - 466 σελίδες
...: : 3 : 9. Three or four numbers are said to be in harmonical proportion, when, in the former case, the difference of the first and second is to the difference of the second and third, as the first is to the third ; and, in the latter, when the difference of the first and second is to...

The British encyclopedia, or, Dictionary of arts and sciences, Τόμος 3

William Nicholson - 1809 - 752 σελίδες
...with concord. HARMONICA!, proportion, or muñcal ртеportion, is that in which the first ten» is to the third, as the difference of the first and second is to the difference of Uie second and third ; or when the first, the third, and the said two differences, are in geometrical...

The British Encyclopedia: Or, Dictionary of Arts and Sciences ..., Τόμος 3

William Nicholson - 1809 - 700 σελίδες
...geometrical proportion. Or, four terms are in harmonical proportion when the first is to thcfotutk as the difference of the first and second is to the difference of the third and fourth. Tha 2, 3, 6, are in harmonical proportion, becanse 2 : 6 :: 1 : S. And the four terms...

Pocket Encyclopedia: Or, A Dictionary of Arts, Sciences, and Polite ..., Τόμος 3

Edward Augustus Kendall - 1811 - 516 σελίδες
...ordinary operation* of the musical art. HARMONICAL proportion, is that in which the first term is to the third, as the difference of the first and second, is to the difference of the second and third :-thus 2, 3, 6 are in harmonical proportion, because 2 : 6 : : 1 : 3. In four terms the 1st is to the...

A pocket encyclopædia, or library of general knowledge

Edward Augustus Kendall - 1811 - 458 σελίδες
...ordinary operations of the musical art. HABMONICAL proportion, is that in which the first term is to the third, as the difference of the first and second, is to the difference of the second and third : thus 2, 3, 6 are in harmonica! proportion, because 2 : 6 : : 1 : 3. In four terms the 1st is to the...

A System of Arithmetic: Reprinted from the Mathematical Text-book

Samuel Webber - 1812 - 260 σελίδες
...to the difference of the second and third, as the first is to the third ; and, in the latter, when the difference of the first and second is to the difference of the third and fourth, as the first is to the fourth. Thus, 2, 3, and 6 ; and 3, 4, 6, and 9, are harmonical...

The Elements of Algebra: Designed for the Use of Students in the University

James Wood - 1815 - 338 σελίδες
...of a, b and c. (380.) Three quantities are said to be in harmanical proportion, when the first is to the third, as the difference of the first and second is to the difference of the second and third. Any magnitudes A, B, C, D, E, &c. are said to be in harmonieal progression, if A : C :: A— B : BC,...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 3

John Mason Good - 1819 - 694 σελίδες
...part, contrajisiure (Winetnan). COXTRA-I-IARMOXICAL PROPORTION', tliat relation of three terms, wherein the difference of the first and second is to the difference of the second and third, as the third is to the first. To CONTRAINDÍCATE, va (contra and indico, Lat.) To point out some peculiar...




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