 | Elias Loomis - 1855 - 356 σελίδες
...quantities is said to be in harmonical progression when, of any three consecutive terms, the first is to the third as the difference of the first and second is to the difference. of the second and third. Thus the numbers 60, 30, 20, 15, 12, 10, are in harmonical progression ; for 60 : 20 : : 60-30 : 30-20... | |
 | Isaac Todhunter - 1855 - 376 σελίδες
...that is, if we call AB, AC, AD, the first, second, and third quantities respectively, the first is to the third as the difference of the first and second is to the difference of the second and third. When the pencil is harmonic one of the three constant ratios of the pencil is equal to unity. We shall... | |
 | Horace Mann, Pliny Earle Chase - 1857 - 388 σελίδες
...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...reciprocal of a number, is the quotient of 1 by the a So called, because if a musical string be divided in harmonical proportion, the different parts will... | |
 | Horace Mann, Pliny Earle Chase, Phiny Earie Chase - 1857 - 394 σελίδες
...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...reciprocal of a number, is the quotient of 1 by the • So called, because if a musical string be divided in harmonical proportion, the different parts... | |
 | Isaac Todhunter - 1858 - 334 σελίδες
...that is, if we call AB, AC, AD, the first, second, and third quantities respectively, the first is to the third as the difference of the first and second is to the difference of the second and third. When the pencil is harmonic one of the three constant ratios of the pencil is equal to unity. We shall... | |
 | Theodore Strong - 1859 - 570 σελίδες
...quantities (of the saine kind) are said to be in harmonical proportion or progression when the first is to the third as the difference of the first and second is to the difference of the second and third. And the third term is called a third harmonical proportional to the first and second ; also, the second... | |
 | Euclid - 1859 - 150 σελίδες
...QED Definition. — Three magnitudes are said to be in Harmonical Progression, when the first is to the third as the difference of the first and second is to the difference of the second and third. С В В Definition — A straight line AB j^ is said to be cut harmonically at ' ' ' two points C,... | |
 | John Craig (F.G.S.) - 1859 - 1116 σελίδες
...mtan, ¡ч a number such, that the first and third terms being given, the first is to the third as th^ difference of the first and second is to the difference of the second and third ; — va (macnan, meni«, Sax.) Past and past jmrt. Meant ; to Ьяге in the mind, view, or contemplation... | |
 | Euclides - 1861 - 464 σελίδες
...-±. Three straight lines, therefore, are said to be in Harmonical Progression, when the first is to the third as the difference of the first and second is to the difference of the second and third. And when three lines, CO, DO, and EO are in harmonical Progression, DO is named a harmonical mean between... | |
 | Horatio Nelson Robinson - 1864 - 444 σελίδες
...2, 4, 8. 13. There are three numbers in geometrical progression; their continued product is 1, and the difference of the first and second is to the difference of the second and third as 5 to one. What aro the numbers? X< "*"1 • **/ "*" -^m. I, 1, 5. Jte.^Tliel&um of 120 dollars was... | |
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WHEN three numbers are such that the first is to the third, as the difference of the first and second is to the difference of the second and third... 
