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" ... 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. "
Arithmetical Spyglass and Teacher's Assistant: Intended as a Key and ... - Página 34
por Charles Waterhouse - 1842 - 166 páginas
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Philosophia Britannica: Or, A New & Comprehensive System of the Newtonian ...

Benjamin Martin - 1747
...; and of three Numbers it is, vvhen the Firjt is to the Third, as the Dif'ference between the Firfi and Second is to the Difference between the Second and Third, as the Num2. Now iince the Tending Force F acts upon the String in the Direction DB, it may be reprefented...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volumen2

Isaac Dalby - 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 ..., Volumen2

Isaac Dalby - 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 ...

James Maginness - 1821 - 372 páginas
...366503875.925. HARMONICAL PROPORTI0N. Harmonical Proportion is that, which is between those numbers that assign the lengths of musical intervals, or the lengths...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 3, 4, and 6, they...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

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 ...

James Maginness - 1821 - 372 páginas
...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 Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - 1832 - 532 páginas
...number* it is, when ¡he .first is to tlit third-, a* the difference hetwec.:. the first anil lironda to the difference between the second and third, as the numbers 3, 4, 6. Thus, if the lengths of strings be as these numbers, they will EOUII 1 an octave 3 to 6, a filth Ü to 'J, and a...
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A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

Beriah Stevens - 1822 - 423 páginas
...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 ..., Volumen2

George Crabb - 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 ..., Volumen19

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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