 ... magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.  The Element of Geometry - Σελίδα 87των John Playfair - 1836 - 114 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Colin MacLaurin - 1748 - 490 σελίδες
...is lefs than the half of that which preceded it next but one. Now if from any Quantity you take away more than its half, and from the Remainder, more than its half, and proceed in this Manner, you will come at a Remainder lefs rhan any allignable Quantity. It appears... | |
 | Colin MacLaurin - 1756 - 538 σελίδες
...is lefs than the half of that which preceded it next but one. Now if from any quantity you take away more than its half, and from the remainder more than its half, and proceed in this manner, you will come at a remainder lefs than any affignable quantity. It appears... | |
 | Robert Simson - 1762 - 488 σελίδες
...fome of the Propofitions of this Book. IF from the greater of two unequal magnitudes there be' taken more than its half, and from the remainder more than its half ; and fo on. there fhall at length remain a magnitude lefs than the lead of the propofed magnitudes. D Let... | |
 | Euclid - 1765 - 492 σελίδες
...the tenth book* that if there be two propufed unequal magnitudes, and from the greater he taken away more than its half, and from the remainder more than its half, and this be continually done, there will at laft remain fome magnitude that is lefs than the leaft of the... | |
 | Robert Simson - 1775 - 534 σελίδες
...fome of the propofitions of this book. TF from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than its half; and fo on: There lhall at length remain a magnitude lefs than the lead of the propofed magnitudes. Let... | |
 | Euclid - 1781 - 552 σελίδες
...feme of the propofitions of this book. TF from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than its half ; and fo on : There fhall at length remain a magnitude lefs than the leaft of the propofcd magnitudes. •... | |
 | Euclid - 1789 - 296 σελίδες
...Since, therefore, the circle ABCD is greater than the fpace s, and from the former there has been taken more than its half, and from the remainder more than its half, &c. there will at length remain fegments which, taken together, fhall be lefs than the excefs of the... | |
 | Colin MacLaurin - 1796 - 554 σελίδες
...is lefs than the half of that which preceded it next but one. Now if from any quantity you take away more than its half, and from the remainder more than its half, and proceed in this manner, you will come at a remainder lefs (Euclid Prop. i. Book 10) than any aflignable... | |
 | Colin Macfarquhar, George Gleig - 1797 - 446 σελίδες
...in the proof of prop. I. bookx. which imports, that if, from the greater of two quantities, you take more than its half, and from the remainder more than its half, and fo continually, there will, at length, remain a quantity lefs than cither of thofe propofed. On this... | |
 | Alexander Ingram - 1799 - 374 σελίδες
...magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and fo on ; there fhall at length remain a magnitude lefs than C. For C may be multiplied fo, as at length... | |
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