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" C = 2^V 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. "
An Introduction to Algebra: With Notes and Observations, Designed for the ... - Σελίδα 97
των John Bonnycastle - 1825 - 312 σελίδες
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Τόμος 2

Isaac Dalby - 1806
...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 ...............

Easy Introduction to Mathematics, Τόμος 2

Charles Butler - 1814
...difference of the first and second to the difference of the second and third ; and four terms are said to be in harmonical proportion, when the first is to the fourth, as the difference of the first and second to the. difference of the third and fourth. Thus, if a : c :: a—b : b—c,...

American Edition of the British Encyclopedia: Or, Dictionary of ..., Τόμος 6

William Nicholson - 1819
...wlu-n the first, the third, and the said two differences, are in geometrical proportion. Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth. Thus 2, 3, 6, are in harmonicaI...

A New, Copious and Complete System of Arithmetic: For the Use of Schools and ...

James Maginness - 1821 - 372 σελίδες
...they will sound an octave S to 6, 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...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 5, 6, 8, and...

A New, Copious and Complete System of Arithmetic: For the Use of Schools and ...

James Maginness - 1821 - 372 σελίδες
...lengths of strings sounding musical notes; and of three numbers it is, 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, and 6; for 3 : 6 : : 4 — 3 : 6 — 4. If the lengths of strings...

A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

Beriah Stevens - 1822 - 423 σελίδες
...lengths of strings sounding musical notes ; and of three numbers it is, 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. Thus, if the lengths of strings be as these numbers, they...

Universal Technological Dictionary: Or, Familiar Explanations of ..., Τόμος 2

George Crabb - 1823
...when the first term is to the third as the difference between the second and third ; or in four terms, when the first is to the fourth as the difference...second is to the difference between the third and the fourth ; the reciprocals of an arithmetical proportion are in harmonica) proportion. Proportion...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...PROGRESSION. 490. 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, a, 6, c, are harmonically proportional, when a : c : : a — b : b — c, or...

An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...PROGRESSION. 490. 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, a, 6, c, are harmonically proportional, when a : c : : a — b : b — c, or...

A Treatise on the Decorative Part of Civil Architecture, Τόμος 1

Sir William Chambers, Joseph Gwilt - 1825 - 514 σελίδες
...is the same as 6 divided by 4, each being 1£ ; harmonical, wherein 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, where the first is to the fourth as the difference between the...




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