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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. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 70
by Euclides - 1838
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 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...parts, shall be equal to the square of the other part. e 47. 1. Upon AB describe the square ABDC ; bisect5 AC in E, Book ir. and join BE ; produce CA to...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...square of the other part. Let AB be the given straight Hue; it is required to divide it into two part", so that the rectangle contained by the whole, and...parts, shall be equal to the square of the other part. c 3. ']. ' e 47. 1. Upon AB describe * the square ABDC ; bisect b AC in E, Book II and join BE ; produce...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 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...parts shall be equal to the square of the other part. Upon AB describe (16. 2.) the square ABDC; bisect (8. 1.) AC in E, and join BE ; produce CA to F, and...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...that this = AC* + CE* + EF! + FG", and that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. To divide a given straight line into two parts, so...and one of the parts shall be equal to the square of c KT~i the other part. Steps of the Demonstration. 1. Prove that CF x FA + AE* = EF*, and that this...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...HB, AD are equal. Then c B (II. 9.) HB2 + BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* 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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An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - Algebra - 1840 - 634 pages
...required to divide a line of 20 inches in length, into two such parts that the rectangle of the whple and one- of the parts shall be equal to the square of the other. Let one part — x ; then the other will be 20 — x. And by the question 20(20 — х)=з?, or ^+20^=400...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 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...parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; bisect* AC * 46. 1. in E, and join BE; produce CA to F, making*...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...are equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. XI. PROB. To divide a given straight line into two parts, so...contained by the whole, and one of the parts, shall be equivalent to the square of the other part. Let AB be the given straight line : it is required to divide...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...(2a-f*)2+*2=2a2+2(a+i)2, and the proposition is evident from this algebraical equality. 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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Proceedings

Scotland free church, gen. assembly - 1847 - 554 pages
...the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle...
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