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" AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. "
A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI. and XI - Página 162
por Euclid, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 456 páginas
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 páginas
...because DG=DB; therefore AD2+DB2=2AC2+ 2CD2. Wherefore, if a straight line, &c, QE D, PROP. XI. PROB. TO divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other part. Let AB be the given straight...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 páginas
...double of the squares of AC, CD. Wherefore, wr a straight line, &c. QED PROP. XI. PROB. TO clivjde a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. Let AB be the given...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 554 páginas
...DB are double of the squares of AC, CD. \Vherefore, if a straight line, &c. QED PR6P. XI. PROB. TO divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. Let AB be the given...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 páginas
...double of the squares of AC, CD. Wherefore, if a straight line, £c. QED "46. 1 Ho. 1 PROP. XI. PROB. To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let AB be the given...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 páginas
...DG=DB: Therefore, AD3 +DB3=2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED . . PROP. XI. PROB. To divide a given straight line into two parts, so that the rectangle contained by the -whole, and one of the parts, may be equal to the square of the other part. Let AB be the given...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 444 páginas
...make with each other angles equal to given angles. 6. To divide a straight line into two parts such that the rectangle contained by them may be equal to the square of their difference. 7. If a straight line be divided into any two parts; -to produce it so that the...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 442 páginas
...make with each other angles equal to given angles. 6. To divide a straight line into two parts such that the rectangle contained by them may be equal to the square of their difference. 7. If a straight line be divided into any two parts; to produce it so that the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 páginas
...double of the squares of AC, CD. Wherefore, if a straight line, &c. QED Proposition Xf. Problem. To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal 'o the square of the other part. Let AB be the given...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 páginas
...being given A, B, с, a fourth proportional HF has been found. QEF Deductions. 1 . Divide a given right line into two parts, so that the rectangle contained by them may be equal to a given rectangle. 2. From a given point to draw a right line to cut a given circle, so that the distances...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 páginas
...being given A, B, c, a fourth proportional HF has been found. QEF Deductions. 1. Divide a given right line into two parts, so that the rectangle contained by them may be equal to a given rectangle. 2. From a given point to draw a right line to cut a given circle, so that the distances...
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