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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... "
A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ... - Page 274
by Beriah Stevens - 1822 - 423 pages
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Philosophia Britannica: Or, A New & Comprehensive System of the Newtonian ...

Benjamin Martin - Science - 1747 - 574 pages
...between four Numbers is, when the Firft is to the Fourth as the Difference between the Firft and Sfcond is to the Difference between the Third and Fourth, as in the (See Annotation XXII.) alfo that the Force of moving Bodies is as the Quantity of Matter and Velocity...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

Isaac Dalby - Mathematics - 1806 - 526 pages
...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 New, Copious and Complete System of Arithmetic: For the Use of Schools and ...

James Maginness - Arithmetic - 1821 - 378 pages
...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 between the first...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 10 will sound an octave 5 to 10;...
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A New, Copious and Complete System of Arithmetic: For the Use of Schools and ...

James Maginness - Arithmetic - 1821 - 378 pages
...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...
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Arithmetic - 1822 - 536 pages
...firnt is lo the fourth, at the difference between the Jirst and lecond iğ In tlie difference betteeen the third and fourth, as in the numbers 5, 6, 8, 10 ; for strings of sjich lengths will sound an octare 5 to 10 ; u sixth greater, 6 to 10 ; a third greater 8 to 10 ; a...
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Universal Technological Dictionary: Or, Familiar Explanations of ..., Volume 2

George Crabb - Industrial arts - 1823 - 704 pages
...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 between the first...second is to the difference between the third and the fourth ; the reciprocals of an arithmetical proportion are in harmonica) proportion. Proportion...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...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...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...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...
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A Treatise on the Decorative Part of Civil Architecture, Volume 1

Sir William Chambers, Joseph Gwilt - Architecture - 1825 - 378 pages
...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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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - Algebra - 1825 - 336 pages
...1— r 9. 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, b, c, are harmonically proportional, when a:c ;;a— b : b — c, or a :...
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