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" 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 the square of the other part. "
The First Six Books: Together with the Eleventh and Twelfth - Page 61
by Euclid - 1781 - 520 pages
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The Elements of Euclid: The errors, by which Theon, or others, have long ago ...

Robert Simson, Euclid - Trigonometry - 1762 - 466 pages
...equal to the fquare 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, 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, Euclid - Trigonometry - 1775 - 520 pages
..."Wherefore, if a ftraight line, &c. Q^ED t 47. r. PROP, Book IT. B4. i. b lo. i. c 3. i. c. . fi 47. PRO P. XI. PRO B. •"TO divide a given ftraight line into two parts, fo that the reftangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part....
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1781 - 466 pages
...equal to the fquare 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...parts, fhall be equal to the fquare of the other part. Upon AB delcribe * the fquare ABDC, bifcct "> AC in E, and join BE ; produce CA to F, and make c EF...
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The elements of Euclid: with dissertations intended to assist and ..., Volume 1

James Williamson - Mathematics - 1781
...part produced, as upon one line. Which was to be demonftrated. PROP. XI. To cut a given ftraight line, fo that the rectangle contained by the whole and one of the fegments may be equal to the fquare of the remaining fegment. Let AB be the given ftraight line ; it...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - Euclid's Elements - 1795 - 400 pages
...fquares of AD, DB are double of the fquares of AC, CD i Wherefore, if a ftraight line, &c. Q^ ED PROP. TO divide a given ftraight line into two parts, fo that the redtangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part....
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The elements of Euclid: viz. the first six books, with the eleventh and ...

Alexander Ingram, Robert Simson - Trigonometry - 1799 - 351 pages
...together double of the fquares of CD half their fum, and AC half their difference. PROP. XI. PROB. TO divide a given ftraight line into two parts, fo that the reel-angle contained by the whole, and one of the parts, lhall be equal to the fquare of the pther...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - Euclid's Elements - 1803 - 279 pages
...to the fum qf the fquareg of AS, Bg, CD and DA. Q..ED PROP. XXII, PROBLEM. To divide a given right line into two parts, fo that the rectangle contained by the whole line and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given right...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...C^,E, D. h. 34. a. i. 47. i. i. 47. i. a. 46. t. b. 10. i. c. 3. l. <L 6. 3. e. 47. PROP. XI. PR OB. TO divide a given ftraight line into two parts, fo that the rectangle contained by the whale, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight...
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Trigonometry - 1806 - 311 pages
...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 the square of the other part, e 47. 1. Upon AB describe" the square ABDC ; bisectb...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...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 straight line ; it is required...
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