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" ... 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 87
by John Playfair - 1836 - 114 pages
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A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and ...

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

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

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

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

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

Euclid - 1781 - 520 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. •...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - Euclid's Elements - 1789 - 272 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...
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A Treatise of Algebra,: In Three Parts. Containing I. The Fundamental Rules ...

Colin MacLaurin - Algebra - 1796 - 504 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...
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Encyclopędia Britannica: Or, A Dictionary of Arts ..., Volume 7, Part 1

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

Alexander Ingram - Trigonometry - 1799 - 351 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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