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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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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volumen9

1816
...flumes in the proof of prop. i. book x. which imports, that if, from the grc.Uer of two quantities, be taken more than its half, and from the remainder more than its half, and fo continually, there will, at length, remain a quantity Icfs than either of thole propofed. On th;s foundation...
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Encyclopaedia Britannica; Or A Dictionary of Arts, Sciences, and ..., Volumen8

1823
...the proof of Prob. I. book x. 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 so continually, there will, at length, remain a quantity less than either of those proposed. On this...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 páginas
...book, and is necessary to tome of the propositions of lias book. If from the greater afino 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 Itss than the least of the proposed magnitudes. Let...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 páginas
...the circle EFGH above the space S; because by the preceding 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. Let...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...circle EFGH, above the space S: Because, by the preceding 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. Let...
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The Element of Geometry

John Playfair - 1836 - 114 páginas
...proposed 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 so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 páginas
...Wherefore, if there be two triangular prisms, &c. BOOK XII. LEMMA I.* 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 will at length remain a magnitude less than the least of the proposed magnitudes. Let...
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The Elements of Euclid

Euclid - 1838 - 416 páginas
...proposed 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 D than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied,...
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The elements of algebra

James Wood - 1841 - 305 páginas
...manner, when с is the dividend, more than its half is taken away, and so on ; but if from any quantity there be taken more than its half, and from the remainder more than its half, and so on, there will, at length, remain a quantity less than any that can be asigned (Eue. x. I.) [109....
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 páginas
...&c. QED THE ELEMENTS OF EUCLID. BOOK XII. LEMMA I. 1 I f from the greater of ttno unequal magnitude*, there be taken more than its half, and from the remainder more than Us half; and 10 on: there shall at length remain a magnitude less than the least of the proposed magnitudes....
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