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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. "
The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... - Pagina 353
door Isaac Todhunter - 1880 - 400 pagina’s
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 pagina’s
...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: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 pagina’s
...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 - 518 pagina’s
...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 - 528 pagina’s
...double of the squares of AC, CD. Wherefore, if a straight line, úc. 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 - 333 pagina’s
...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 - 377 pagina’s
...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 - 377 pagina’s
...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 - 372 pagina’s
...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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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...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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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pagina’s
...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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