 | John Craig (F.G.S.) - 1849 - 1148 páginas
...three terms ; the harmonic mean, i~ a number such, that the first and third terms being given, tho first is to the third as the difference of the first and second is to the diSerencc of the second and third ; — г. а. (таелап, тепал, Sax.) Past and pott jmrt.... | |
 | James Haddon - 1850 - 210 páginas
...「 ・ イ S ' 丁 ・ 辞 十 神 HARMONICAL PROGRESSION. XXIV. When the first of three quantities is to the third as the difference of the first and...second is to the difference of the second and third， the three quantities are in hannonical proportion. 二 1 ム 一 な arithme 杜 c Ⅰfa @ Ⅰ @ @... | |
 | Joseph Ray - 1852 - 408 páginas
...such that the sum of the first and second is to the sum of the second and third, as 4 is to 5; and the difference of the first and second, is to the difference of the first and third, as 2 to 3 1 Ans. 0, 7, and 8. 3. Find four numbers, such that the sum of the first,... | |
 | Samuel Maunder - 1853 - 852 páginas
...1'ROl'OR'TION, in arithmetic and algebra, is that in which the first term is to the third, as tlie difference of the first and second is to the difference of the second and third: thus 2, 3, 6, are in harmonical proportion, because 2 : C : : 1 i 3. In four terras the 1st is to the... | |
 | Isaac Todhunter - 1855 - 376 páginas
...harmonic pencil is so called because it divides any transversal harmonically. For since AB.DC= AD.BC, ABBC that is, if we call AB, AC, AD, the first, second,...equal to unity. We shall sometimes select one of the anhannonic ratios of a pencil, and confine our attention to it, and shall then speak of the selected... | |
 | Elias Loomis - 1855 - 356 páginas
...series of 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...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... | |
 | Euclid - 1859 - 150 páginas
...number of parallels. QED Definition. — Three magnitudes are said to be in Harmonical Progression, when the first is to the third as the difference of the...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,... | |
 | Theodore Strong - 1859 - 570 páginas
...numbers or 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...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... | |
 | John Craig (F.G.S.) - 1859 - 1116 páginas
...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... | |
 | James Elliot - 1860 - 252 páginas
...the numbers ? Ans. f, f , i, f. THEOREM. Of any three consecutive Terms in a Harmonical Progression, the first is to the third as the Difference of the first and second to the Difference of the second and third. DEM. Let a, b, c represent the three terms. Then their reciprocals,... | |
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Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth. 
