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Books Books 11 - 20 of 189 on AB be the given straight line ; it is required to divide it into two parts, so that....  
" 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. "
Introduction and books 1,2 - Page 402
by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908
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The Element of Geometry

John Playfair - Trigonometry - 1836 - 114 pages
...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 the square of the other part. Upon AB describe (16. 2.) the square ABDC; bisect...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Mathematics - 1837 - 390 pages
...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...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837
...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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - History - 1838
...Wherefore, if a straight line, &c. QED PROP. XI. PROS. 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 the other part. Let AB be the given straight line: it is required...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...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 the square of the other part. Upon AB describe* the square ABDC; bisect* AC...
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Mathematics - 1842 - 317 pages
...equilateral and equiangular pentagon has been inscribed. Otherwise. " Divide the radius of the given circle, so that the rectangle contained " by the whole and one of the parts may be equal to the square of the other " (11. 2.). . Apply in the circle, on each side of a...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - History - 1842
...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...
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The British Annals of Education for ...: Being The Scholastic ..., Volume 1

Education - 1844
...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 and one of the parts shall be equal to the square of the other part. 8. If in a circle two straight lines cut one...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley, William Henry Johnstone - 1845
...these points. (Euclid, iii. 18. Cape, ii. 38.) 59. 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 a given line, which is less than the line to be divided. (Euclid,...
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The first six and the eleventh and twelfth books of Euclid's Elements; with ...

Euclides - Mathematics - 1845
...are, by the same curolla'y, tli» 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...
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