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" 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. "
A Collection of Problems and Examples Adapted to the "Elementary Course of ... - Página 128
de Harvey Goodwin - 1851 - 173 páginas
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 páginas
...the other part. Let AB be the given ftraight line ; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fnall be equal to the fquare of the other part. Upon AB defcribc " the fquare ABDC, bifect b AC in...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 páginas
...the other part. Let AB be the given ftraight line ; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB deferibe * the fquare ABDC ; bifect b AC in...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 páginas
...look II, k 10 i. e SI 46.".. *47-IPRO P. XI. PRO B. TO divide a given ftraight line into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight line ; it is required...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 páginas
...*• 11 B Let AB be the given ftraight line ; it is required to divide CoIK II. it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB defcribe » the fquare ABDC ; bifea b AC in...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...of the other part. Let AB be the given ftraight line; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB defcribe » the fquare ABDC, bifect b AC in...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 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...parts shall be equal to the square of the other part. Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 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...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 line ; it is required to...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 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...parts shall be equal to the square of the other part. Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...and the part produced. Prop. XI. Prob. To divide a given straight line into two parts, so that thé rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Prop. XII. Theor. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles...
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A Treatise on Algebra, in Practice and Theory: With Notes and Illustrations ...

John Bonnycastle - 1813
...It is required to divide a line, of 20 inches in length, into two such parts, that the rectangle of the whole and one of the parts shall be equal to the square of the other. Ans. 10/5 — 10 5. It is required to divide the number 60 into two such parts, that their product...
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