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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 on the other part. "
The definitions, postulates, axioms, and enunciations of the propositions of ... - Page 12
by Euclides - 1848 - 42 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 488 pages
...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 - Trigonometry - 1775 - 534 pages
...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 - 552 pages
...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 - Trigonometry - 1799 - 374 pages
...*• 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 - Trigonometry - 1804 - 530 pages
...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...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...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 ...

Euclides - 1816 - 588 pages
...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 contained by...the whole, and one of the parts, shall be equal to thcsquare of the other part. Upon AB describe* the square ABDC ; bisect b AC in E, and join BE ; produce,...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...tangents to the two circles, drawn from any point of the line, shall be equal to one another. (LXXV.) To divide a given straight line into two parts, so that the square of the one shall be equal to the rectangle contained by the other and a given straight line....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...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...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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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...squares may be equal to a given square, and their rectangle equal to a given rectangle. 9. To divide a 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 a given line, which is less than the line to be divided. 10. To divide...
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