 ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.  The boys' algebra - Page 199by James Cahill (of Dublin.) - 1875 - 209 pagesFull view - About this book
 | James B. Dodd - Algebra - 1859 - 368 pages
...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 :... | |
 | Theodore Strong - Algebra - 1859 - 570 pages
...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,... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...extreme segments, 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...the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression ' harmonical proportion'... | |
 | Euclides - 1860 - 288 pages
...segment. C. Three straight lines are said to be in harmonical progression or harmonical progressionals, when the first is to the third, as the difference...is to the difference between the second and third. 7. The second of three lines in this progression is called a harmonic mean between 'the other two;... | |
 | 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... | |
 | Lionel Swift (R.N.) - 1861 - 104 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,... | |
 | Euclides - 1861 - 464 pages
...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 between...is to the difference between the second and third. Thus 1 : ^ = -i : -±. Three straight lines, therefore, are said to be in Harmonical Progression, when... | |
 | John Mulcahy - Geometry - 1862 - 252 pages
...CHAPTER I. HARMONIC PROPORTION AND HARMONIC PENCILS. ART. 1. THREE quantities are said to be in harmonic proportion, when the first is to the third as the...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
...come down to us 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...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... | |
| |
