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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 ... - Página 69
por Euclides - 1846
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## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 112 páginas
...that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. 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 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 - 1837 - 410 páginas
...+ BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* 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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## Elements of Plane Geometry According to Euclid

Andrew Bell, Robert Simson - 1837 - 290 páginas
...and of the mean distance. PROPOSITION XI. PROBLEM. To divide a given straight line in medial section. Let AB be the given straight line ; it is required to divide it in medial section. Upon AB describe the square ABDC (I. 46) ; bisect AC in E (1. 10), and join BE ;...
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## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 páginas
...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,...parts, shall be equal to the square of the other part. From the point A draw* AC perpendicular and *" o™4 3' equal to AB ; bisect* AC in E, and join B,...
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## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1838 - 434 páginas
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle...
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## An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - 1840 - 634 páginas
...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 - 1841 - 378 páginas
...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...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 páginas
...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 equivalent to the square of the other part. Upon AB describe (46. 1.) the square ABDC ; bisect (10....
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 páginas
...is evident from this algebraical equality. 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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## The British Annals of Education for ...: Being The Scholastic ..., Volúmenes1-2

1844 - 688 páginas
...parts are together equal to the square of the whole line. 7. Divide a given straight line into two parts, so that the rectangle contained by the whole...parts shall be equal to the square of the other part. 8. If in a circle two straight lines cut one another, which do not both pass through the centre, they...
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