 | James B. Dodd - Algebra - 1859 - 368 pages
...4—3 : 6—4, and 4 : 12 :I 6—4 : 12—6. An Harmonical Proportion consists of four terms such that the first is to the fourth as the difference between...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 : d :: b — a : d — c.... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...karmonical proportion when ' о : с : a~6 : 6~c. (4O4.) Four quantities are in harmonical proportion, when the first is to the fourth, as the difference between...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. PROBLEM. (4O5.)... | |
 | Charles Davies, William Guy Peck - Mathematics - 1859 - 622 pages
...HARMONÍA!.. Four quantities are in harmonial proportion when the first is to the fourth as the différence between the first and second is to the difference between the third and fourth. Thus 24, 16, 12, and 9 arc in hannonial proportion, because 24 : 9 : : 8 : 3. Three quantities are in hannonial... | |
 | Theodore Strong - Algebra - 1859 - 570 pages
...or more of three expressions in harmonical proportion, then since tJie first miist be to the third as the difference between the first and second is to the difference between the second and third, we easily (by 2) reduce the harmonicals to an equation. Similarly, if the unknown... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...segment is to the middle part. 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... | |
 | Alexander Henry - English language - 1861 - 226 pages
...concordant. Harmonical Proportion. In arithmetic, that relation of four quantities to each other, in which the first is to the fourth as the difference between the first and second is to the diiference between the third and fourth. Har'mony (Gr. аppо(ш, harmozu, I fit together). A proper... | |
 | Euclides - 1861 - 464 pages
...these parts of a musical string, thus divided, it is the property, that the first is to the third, as the difference between the first and second is to the difference between the second and third. Thus 1 : ^ = -i : -±. Three straight lines, therefore, are said to be in Harmonical... | |
 | Lionel Swift (R.N.) - 1861 - 104 pages
...these specific gravities are in what is called harmonic progression, ie, the first is to the third, as the difference between the first and second is to the difference between the second and third. Now it may be shown that the reciprocals of terms in harmonic progression are in... | |
 | John Mulcahy - Geometry - 1862 - 252 pages
...PENCILS. ART. 1. THREE quantities are said to be in harmonic 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, 3, 4, 6, are in harmonic proportion. It follows from this definition, that... | |
 | Encyclopedias and dictionaries - 1863 - 852 pages
...HARMO'NIC PROPORTION. Three numbers are said to be in harmonic 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, otherwise harmonic proportion is that which subsists between the reciprocals of numbers... | |
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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... 
