 | Robert Potts - 1865 - 528 σελίδες
...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... | |
 | Paul Allen Towne - 1865 - 314 σελίδες
...is one in which several ratios are equal. Thus, a : b : : c : d : : m : u : : p : q, &c. 8. Three or four quantities are in harmonical proportion when the first is to the last, as the difference between the first two ia to the difference between the last two. Thus, a, b,... | |
 | Rolla Rouse - 1867 - 228 σελίδες
...and third and the said two differences are in geometric proportion — or, four terms are in harmonic proportion when the first is to the fourth as the difference between the first and second to the difference between the third and fourth. J (117.) Triangles and parallelograms of the same height... | |
 | George Whitefield Samson - 1867 - 842 σελίδες
...octave, and the 5th of the second octave, are in the following proportion; "the first is to the third as the difference between the first and second is to the difference between the second and third ;" or 24 : 72 : : 36—24 : 72—36 ; ie 1 : 3 : : 12 : 36. These proportions coming... | |
 | 1868 - 872 σελίδες
...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... | |
 | Robert Potts - 1868 - 434 σελίδες
...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 betwe en the first and third. The expression... | |
 | William Henry Besant - 1869 - 304 σελίδες
...conic. DEP. Three magnitudes are said to be in harmonic progression 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 magnitude is said to be an harmonic mean between the first and third.... | |
 | William Chauvenet - 1871 - 380 σελίδες
...written thug, AC : AD = AB — AC : AD — AB, or, AC, AB, AD, 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 ; that is, they are in harmonic progression, according to the definition commonly... | |
 | William Chauvenet - 1872 - 382 σελίδες
...written thus, AC : AD = AB — AC : AD — AB, or, AC, AB, AD, 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 ; that is, they are in harmonic progression, according to the definition commonly... | |
 | Thomas Steadman Aldis - 1872 - 84 σελίδες
...transversal be drawn.) DEP. When we have three straight lines 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, the second is said to be the harmome mean between the first and third. AB a harmonic... | |
| |
C = 2^V 10. 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. 
