 | Encyclopedias and dictionaries - 1838 - 1056 pages
...Proclus) invented this method of es haustions, which may be considered as contained in two propositions. I. If from A more than its half be taken, and from...outset (and of the same kind as A), however small. This proposition may be easily proved, and is equally true if the proportion abstracted each time be... | |
 | Society for the diffusion of useful knowledge - 1838 - 540 pages
...Proclus) invented this method of ex haustions, which may bo considered as contained in two propositions. I. If from A more than its half be taken, and from...outset (and of the same kind as A), however small. This proposition may be easily proved, and is equally true if the proportion abstracted each time be... | |
 | Encyclopedias and dictionaries - 1838 - 542 pages
...Proclus) invented this method of ex haustions, which may be considered as contained in two propositions. I. If from A more than its half be taken, and from...outset (and of the same kind as A), however small. This proposition may be easily proved, and is equally true if the proportion abstracted each time be... | |
 | 1838 - 542 pages
...Proclus) invented this method of ex haustions, which may be considered as contained in two propositions. I. If from A more than its half be taken, and from...remainder more than its half, and so on, the remainder v. ill at last become less than B, where B is any magnitude named at the outset (and of the same kind... | |
 | John Pringle Nichol - Physics - 1860 - 942 pages
...transition absolutely legitimate ; — resting it on the two following propositions. — 1. If from л, more than its half be taken, and from the remainder...half, and so on, the remainder will at last become lea than в, where в is any similar ma^rkudo named at the outset and however small. 2. Let there be... | |
 | Euclides - 1864 - 448 pages
...XII. LEMMA I. t If from the greater of two unequal majnituiles, there be taken more than i's h'df, and from the remainder more than its half; and so on: the, e shall at length remain a magnitude less than the least of the proposed magnitudes. (Book x. Prop.... | |
 | Encyclopedias and dictionaries - 1867 - 522 pages
...this method of exhaustions, which may be considered as contained in the following two propositions. I, If from A more than its half be taken, and from...so on, the remainder will at last become less than в, where в is any magnitude named at the outset (and of the same kind as A), however small. This... | |
 | Charles Knight - Encyclopedias and dictionaries - 1867 - 526 pages
...•which may be considered as contained in the following two propositions. I. If from A more than ita half be taken, and from the remainder more than its...B is any magnitude named at the outset (and of the tame kind as A), however small This proposition may be easily proved, and is equally true if the fixed... | |
 | W.R. Knorr - Mathematics - 1975 - 402 pages
...a noted convergence principle (X,l): if from a given magnitude there is removed more than its half, and from the remainder more than its half, and so on, the remainder eventually becomes smaller than any preassigned finite magnitude. It is interesting to observe here... | |
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Proclus) invented this method of ex haustions, which may be considered as contained in two propositions. I. If from A more than its half be taken, and from the remainder more than its half, and so on, the remainder will at last become less than B, where... 