 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...  Arithmetic, Practically Applied ... - Page 289by Horace Mann - 1851Full view - About this book
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...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... | |
 | Benjamin Greenleaf - Algebra - 1860 - 490 pages
...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... | |
 | Euclides - 1861 - 464 pages
...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... | |
 | Lionel Swift (R.N.) - 1861 - 108 pages
...20 divisions. As we stated, these specific gravities are in what is called harmonic progression, ie, the first is to the third, as the difference between...is to the difference between the second and third. Now it may be shown that the reciprocals of terms in harmonic progression are in equi-different progression,... | |
 | John Mulcahy - Geometry - 1862 - 252 pages
...PROPORTION AND HARMONIC PENCILS. ART. 1. THREE quantities are said to be in harmonic proportion, when the first is to the third as the difference between...is to the difference between the second and third. Thus, 3, 4, 6, are in harmonic proportion. It follows from this definition, that the three quantities... | |
 | Encyclopedias and dictionaries - 1863 - 852 pages
...in the Greek Scholia. HARMO'NIC PROPORTION. Three numbers are said to be in harmonic proportion when the first is to the third, as the difference between...is to the difference between the second and third, otherwise harmonic proportion is that which subsists between the reciprocals of numbers which are in... | |
 | Charles Taylor - Conic sections - 1863 - 248 pages
...triangles. Therefore TP : TP = PV : P V. COR. The lines TP, TV, TP are in harmonical progression, since the first is to the third as the difference between the first and second to the difference between the second and third. Note. Any one of the last three propositions being... | |
 | Euclides - 1864 - 448 pages
...as the other extreme segment is to the middle part. 'Three lines are in harmonica! 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... | |
 | Elias Loomis - Algebra - 1864 - 386 pages
...and 8. (229.) Four quantities are said to be 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, Thus, 2, 3, 4, 8 are in harmonical proportion; for 2:8:: 3-2 : 8-4. Let a, b, c,... | |
 | Robert Potts - 1865 - 528 pages
...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... | |
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