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Books Books 1 - 10 of 119 on Three lines are in harmonical proportion, when the first is to the third, as the....
" 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... "
Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ... - Page 472
by Charles Davies - 1872 - 592 pages
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

Isaac Dalby - Mathematics - 1806
...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 cadets, of ...

Isaac Dalby - Mathematics - 1813
...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 ...

Arithmetic - 1821 - 372 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...is to the difference between the second and third, as the numbers 3, 4, and 6; for 3 : 6 : : 4 — 3 : 6—4. If the lengths of strings be as the numbers...
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Scientific Amusements in Philosophy and Mathematics: Including Arithmetic ...

William Enfield (M.A.) - Scientific recreations - 1821 - 276 pages
...in harmonical proportion, when the first is to the last as the difference between the first and the second is to the difference between the second and third. Thus the numbers 6, 3, 2, are in harmonical proportion; for 6 is to 2 as 3, the difference between the two first numbers,...
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The Elements of geometry [Euclid book 1-3] in general terms, with ..., Part 3

Euclides - 1821
...3 : 6, permutando 1 : 8 : : 2 : 6 *'. e . the first term of the series is to the second as the dif. between the first and second is to the difference between the second and third ; and since the second term is greater than the first, it follows that the difference between the second...
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A New, Copious and Complete System of Arithmetic: For the Use of Schools and ...

Arithmetic - 1821 - 372 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 - 423 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
...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
...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 - 516 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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