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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 so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so...
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Side 244
av Euclid, Isaac Todhunter - 1883 - 400 sider
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## A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and ...

Colin MacLaurin - 1748 - 356 sider
...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 sider
...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 sider
...lead of the propofed magnitudes. D Let AB and C be two- unequal magnitudes, of which AB is the Beater. 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 Ids than C. For C may be multiplied fo as at length...
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## Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 464 sider
...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 sider
...lefs than the lead of the 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 sider
...the leaft of the 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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## Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - 1789 - 272 sider
...continually. 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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## Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - 1795 - 400 sider
...leaft of the propofed magnitudes. r ° - , . », » .».i,-«i Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder its half, and fo on ; there fliall at length remain a magnitude...
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## A Treatise of Algebra,: In Three Parts. Containing I. The Fundamental Rules ...

Colin MacLaurin - 1796 - 504 sider
...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, Sciences ..., Volum 7,Del 1

...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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