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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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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...unequal magnitudes, there be taken SeeN. more than its half, and from the remainder more than its hay, and so on ; there shall at length remain a magnitude...less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater : if from AB there be taken more than...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more Sec N. than its half, and from the remainder more than its...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 it be so multiplied, and...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...unequal magnitudes there be taken away its half, and from the remainder its half: and so on ; there will at length remain a magnitude less than the least of the proposed magnitudes. II. Equilateral polygons, of the same number of sides, inscribed in circles, are similar, and are to...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...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 AB and C be two...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 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 it be so multiplied, and...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 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 Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...some of the propositions of this book. IF 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.* K H Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more...
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The Elements of Euclid

Euclid - 1838 - 416 sider
...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, so at length to become greater than AB. Let it be so multiplied, and let...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...manner are to be understood some things in some of the following Propositions. magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there at length remains a magnitude less than the least of the proposed magnitudes. Let then the segments...
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The elements of algebra

James Wood - 1841 - 305 sider
...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. In practice...
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