 | Horace Mann, Pliny Earle Chase, Phiny Earie Chase - Arithmetic - 1857 - 394 pages
...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 between the first and second is to the difference between the second and third, they are said to be in HARMONICAL PROPORTION ; and a series... | |
 | James W. Kavanagh - Arithmetic - 1857 - 298 pages
...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 the first and second is to the difference between the second and third ; thus 12, 8, and 6 form a harmonical series, for 12 :... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...cirfcn. (a:c ::m:n ) HARMONICAL PROPORTION. (4O3.) Three quantities are in harmonical proportion, when the first is to the third, as the difference between the first and the second is to the difference between the second and third. The quantities a, 6, and e aro in karmonical... | |
 | Theodore Strong - Algebra - 1859 - 570 pages
...letter entera one 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.... | |
 | 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 the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the... | |
 | 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 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... | |
 | 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 the first and second is to the difference between the second and third. Thus 1 : ^ = -i : -±. Three straight lines, therefore,... | |
 | 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 the first and second is to the difference between the second and third. Thus, 3, 4, 6, are in harmonic proportion. It follows... | |
 | 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 the first and second is to the difference between the second and third, otherwise harmonic proportion is that which subsists between... | |
 | 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... | |
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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... 
