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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 Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 346
των William Chauvenet - 1884 - 368 σελίδες
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Arithmetic: Practically Applied, for Advanced Pupils, and for Private ...

Horace Mann, Pliny Earle Chase - 1857 - 398 σελίδες
...been living when he was 500 years old ? Ans. 33554430. 9O. HARMONICAL PROGRESSION.* When three numbers are such that the first is to the third, as the difference...is to the difference between the second and third, they are said to be in HARMONICAL PROPORTION ; and a series of numbers, in continued harmonical proportion,...

Arithmetic, Practically Applied, for Advanced Pupils, and for Private ...

Horace Mann, Pliny Earle Chase - 1857 - 388 σελίδες
...been living when he was 500 years old? Ans. 33554430. >. HARMONICAL PROGRESSION.* When three numbers are such that the first is to the third, as the difference...is to the difference between the second and third, they are said to be in HARMONICAL PROPORTION ; and a series of numbers, in continued harmonical proportion,...

Arithmetic, its principles and practice

James W. Kavanagh - 1857 - 298 σελίδες
...numbers is said to form a harmonical series when of every three of its consecutive [following] terms the first is to the third, as the difference between...is to the difference between the second and third ; thus 12, 8, and 6 form a harmonical series, for 12 : 6 : : 12—8 : 8—6. 308. The middle one of...

A Treatise on Algebra

Elias Loomis - 1858 - 394 σελίδες
...are said to be in harmonical proper tion when the first is to the third as the difference between tin first and second is to the difference between the second and third. Thus, 2, 3, 6 are in harmonical proportion ; for 2:6:: 3-2 : 6—3. Let a, b, c be in harmonical proportion...

Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - 1859 - 368 σελίδες
...6—4 : 12—6. An Harmonical Proportion consists of four terms such that 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, if a : d :: a—b : c—d; or a :...

The University Algebra ...

John Fair Stoddard, William Downs Henkle - 1859 - 538 σελίδες
...: a~6 : 6~c. (4O4.) 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. The quantities a, 6, c, and d are in harmonica! proportion when a : d : : a~6 : c~<f....

A Treatise on Elementary and Higher Algebra

Theodore Strong - 1859 - 570 σελίδες
...the unknown letter enters one or more of four harmonicals, because the first must be to the fourth as the difference between the first and second is to the difference between the third and fourth, we easily (by 2) reduce the harmonicals to an equation. EXAMPLES. 1. Given, 3, 8,...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 σελίδες
...as the other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the difference between...is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression ' harmonical...

A Practical Treatise on Algebra: Designed for the Use of Students in High ...

Benjamin Greenleaf - 1860 - 490 σελίδες
...XXII. HARMONICAL PROGRESSION. ART. 280 • Three numbers are said to be in harmonical pro gression when the first is to the third as the difference between the first and second is to the diiference between the second and third. Thus the numbers 3, 4, 6, are in harmonical proportion. For...

Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 σελίδες
...names, C, D, E, F, G, A, B, c. Of these parts of a musical string, thus divided, it is the property, that the first is to the third, as the difference...is to the difference between the second and third. Thus 1 : ^ = -i : -±. Three straight lines, therefore, are said to be in Harmonical Progression, when...




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