... 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 - Page 87by John Playfair - 1836 - 114 pagesFull view - About this book
| Colin MacLaurin - Algebra - 1748 - 490 pages
...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 - Algebra - 1756 - 538 pages
...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 - Trigonometry - 1762 - 488 pages
...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 - Geometry - 1765 - 492 pages
...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 - Trigonometry - 1775 - 534 pages
...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 pages
...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 - Euclid's Elements - 1789 - 296 pages
...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 - Algebra - 1796 - 554 pages
...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 - Encyclopedias and dictionaries - 1797 - 446 pages
...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 - Trigonometry - 1799 - 374 pages
...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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