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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. "
Elements of Geometry: Containing the Principal Propositions in the First Six ... - Página 213
por Euclid - 1789 - 272 páginas
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A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and ...

Colin MacLaurin - 1748 - 431 páginas
...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...
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A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules ...

Colin MacLaurin - 1756 - 432 páginas
...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 páginas
...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...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 464 páginas
...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...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 páginas
...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...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 páginas
...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...
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A Treatise of Algebra,: In Three Parts. Containing I. The Fundamental Rules ...

Colin MacLaurin - 1796 - 504 páginas
...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...
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Encyclopædia Britannica: Or, A Dictionary of Arts ..., Volumen7,Parte1

Colin Macfarquhar, George Gleig - 1797
...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...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 páginas
...^~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...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...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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