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" If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. "
The first and second books of Euclid explained to beginners, by C.P. Mason - Page 144
by Euclid, Charles Peter Mason - 1872
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Galois' Theory of Algebraic Equations

Jean-Pierre Tignol - Mathematics - 2001 - 360 pages
...the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half. Л С D В к H M F On the figure above, the straight line AB has been cut into equal segments...
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Apollonius of Perga's Conica: Text, Context, Subtext

Michael N. Fried - History - 2001 - 516 pages
...the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half."21 It will be easy for the attentive reader to note Abu Kamil's use (for a Greek, this is...
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From Discrete to Continuous: The Broadening of Number Concepts in Early ...

K. Neal - Mathematics - 2002 - 194 pages
...the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half."" Instead of a construction of rectangles and squares, he constructs nothing at all.14 He...
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Classics in the History of Greek Mathematics

Jean Christianidis - Mathematics - 2004 - 502 pages
...the rectangle contained by the unequal segments ofthe whole together with the square on the straight line between the points of section is equal to the square on the half.' 58 EUCLID'S proof advances through the following stages: Let AB be given and bisected at...
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Developing Thinking in Algebra

John Mason, Alan Graham, Sue Johnston-Wilder - Business & Economics - 2005 - 342 pages
...contained by the two parts. Euclid Book ll Prop 5 if a straight line is divided equally and also unequally, the rectangle contained by the unequal parts, together...section, is equal to the square on half the line. 1 t Task 1 5.3.1 b Diagramming Text and Texting Diagrams For the two diagrams, produce a text which...
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