 | Edward Dingle - 1868 - 350 pagine
...grace. of Newton's first lesson, " Quantities, and ratios of quantities, which in any finite time, tend continually to equality; and before the end of that time, approach nearer to each other than by any given difference, become ultimately equal." They should have seen that the... | |
 | Catherinus Putnam Buckingham - 1875 - 374 pagine
...Newton, in the enunciation of the first lemma in the first book of the Principia. " Quantities and ratios of quantities, which in any finite time converge continually...to the other than by any given difference, become ultimately equal." The principle here stated would be applied to the solution of our problem in the... | |
 | Catherinus Putnam Buckingham - 1875 - 362 pagine
...Quantities and ratios of quantities, which in any finite time converge continually to equality, aml before the end of that time approach nearer the one to the other than by any gircn difference, become ultimately equal." The principle here stated would be applied to the solution... | |
 | James Ralston Skinner - 1875 - 354 pagine
...and the ratio of quantities, which in any finite time converge continuallv to equality, and, before that time, approach nearer the one to the other, than by any given difference, ultimately become equal." Let ABC be any triangle, and with the length AB as a radius, let the arc... | |
 | James Ralston Skinner - 1875 - 354 pagine
...regards exactitude of definition — palpably so. His " Lemma I " states : "Quantities and the ratio of quantities, which in any finite time converge continually to equality, and, before that lime, approach nearer the one to the other, than by any given difference, ultimately become equal."... | |
 | Robert Potts - 1879 - 668 pagine
...Quantities and the ratios of quantities which in any finite time continually tend to equality, and which before the end of that time approach nearer the one...to the other than by any given difference, become ultimately equal." The calculus of fluxions is founded on the idea that all magnitudes may be generated... | |
 | Robert Potts - 1879 - 672 pagine
...which in any finite timo continually tend to equality, and which before the end of that timeapproach nearer the one to the other than by any given difference, become ultimately equal." The calculus of fluxions is founded on the idea that all magnitudes may be generated... | |
 | Kansas Academy of Science - 1890 - 206 pagine
..."-Method of Limits," as enunciated by one of the discoverers of the Calculus, that "quantities, and ratios of quantities, which in any finite time converge continually...time approach nearer the one to the other than by any difference, become ultimately equal,'1 we know that dropping the higher orders will give beyond a peradventure... | |
 | Albert Taylor Bledsoe - 1886 - 253 pagine
...they all continually converge, so they continually converge toward each other, and may be made to " approach nearer the one to the other than by any given difference." If, then, it follows from this that they are all " ultimately equal," " there is only one proportion... | |
 | Kansas Academy of Science. Meeting - 1890 - 222 pagine
..."Method of Limits," as enunciated by one of the discoverers of the Calculus, that "quantities, and ratios of quantities, which in any finite time converge continually...time approach nearer the one to the other than by any difference, become ultimately equal,'' we know that dropping the higher orders will give beyond a peradventure... | |
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QUANTITIES, AND THE RATIOS OF QUANTITIES, WHICH IN ANY FINITE TIME CONVERGE CONTINUALLY TO EQUALITY, AND BEFORE THE END OF THAT TIME APPROACH NEARER THE ONE TO THE OTHER THAN BY ANY GIVEN DIFFERENCE, BECOME ULTIMATELY EQUAL. 
