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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, may be equal to the square of the other part.
The Elements of Euclid, the parts read in the University of Cambridge [book ... - Pagina 69
di Euclides - 1846
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 pagine
...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 pagine
...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 pagine
...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 Young Geometrician's Companion: Being A New and Comprehensive ..., Volume 6

Richard Turner - 1787 - 240 pagine
...Proportion ; that is, to cut a Line fo that the Product of the whole Line and one of the Parts fhall be equal to the Square of the other Part. Let AB be the Right Line given to be fo divided. 11 «L AC Cbnftruflion. Firft, on the Point A, ere£ the Perpeniicukr...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 pagine
...*• 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: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 pagine
...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 contained by the whole...parts shall be equal to the square of the other part. a 46. 1. Upon AB describe a the square ABDC ; bisect 1• AC in E, ami b 10. 1. jo1n BE ; produce CA...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 pagine
...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 line ; it is required to...
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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 - 428 pagine
...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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