 | 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
...Book, arid is neceflaiy to fome of the Propofitions of this Book. IF from the greater of two unequal magnitudes there be' taken more than its half, and...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 AB and C be... | |
 | 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
...propofed magnitudes. Let AB and C be two unequal magnitudes, of which AB a the greater. If from AB there be taken more .^ than its half, and from the remainder more than ft its half, and fo on ; there fua'.l at length remain a magnitude lefs than C. For C may be multiplied... | |
 | Euclid - 1781 - 552 pages
...propofcd magnitudes. • D Let AB and C be two unequal magnitudes, of which AB i: the greater. If from AB there be taken more than its half, and from the remainder more than f its half, and fo on; there fball at length remain a magnitude lefs than C. For C may be multiplied... | |
 | 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 foundation... | |
 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...^~s*Y**J the circle in the extremities of the arch. PROP. I. THEOR *. IF from the greater of two unequal magnitudes, there be taken more than its half, and...the remainder more than its half; and fo on : There mail at length remain a magnitude lefs than the leall of the propofed magnitudes. Let AB and C be two... | |
 | Robert Simson - Trigonometry - 1804 - 530 pages
...Book, and is neceflary to fome of the Propofitions of this Book. IF from the greater of two unequal magnitudes there be taken more than its half, and...the remainder more than its half; and fo on. there mall at length remain a magnitude lefs than the leaft of the propofed magnitudes. Let AB and C be two... | |
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Lemma, if from the greater of two unequal 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. 
