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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 - Side 87
av John Playfair - 1836 - 114 sider
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...PROP. A. IF from the greater of two unequal magnitudes there be taken its half, and from the remainder its half, and so on : there shall at length remain...magnitude less than the least of the proposed magnitudes, how small soever it may be. Let A, B, c, D, &c. be a series of magnitudes such that в is half of A,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied so as, at length, to become greater than AB. Let DE, therefore, be a -g\...
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Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - 1843 - 147 sider
...difference between any two unequal magnitudes being diminished by more than its half, and the remainder by more than its half, and so on ; there shall at length remain a magnitude less than any that may be assigned." It is by this process that Archimedes demonstrates the equality of the area...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...Prop. 1.) 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...there shall at length remain a magnitude less than C. BCE For C may be multiplied so as at length to become greater than AB. Let it be so multiplied,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...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 will at length remain a magnitude less than C. For C may be multiplied so as at length to become greater...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...given line. For it has been shown in the proposition that this is equivalent to taking away from EC more than its half, and from the remainder more than its half, and so on continually ; .-. (Prop. 73, Cor.) the quantity ultimately left is less than any given quantity. PROPOSITION...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...given magnitude there be taken a greater than its half, and from the remainder a magnitude greater than its half, and so on, there shall at length remain a magnitude less than any other given magnitude less than the former. Let AB and C be the two given magnitudes, of which...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 sider
...magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied so as, at length, to become greater than AB. Let DE, therefore, be a multiple...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...another. BOOK XII. PROPOSITIONS. LEMMA I. IP from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than...magnitude less than the least of the proposed magnitudes. (Book x. Prop, i.) PROP. I. THEOREM. Similar polygons inscribed in circles, are to one another as the...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...this Book. LEMMA I. If from the greater of two unequal magnitudes of the same kind, 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 AB and C be two...
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