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" PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 50
by Euclides - 1841 - 351 pages
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Introduction and books 1,2

Euclid - Mathematics, Greek - 1908
...PROPOSITION i. If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments. Let A, BC be two straight lines, and let BC be cut at...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908
...line AB is the sum of the segments AX, XB. THEOREM 50. [Euclid II. 1.] If of two straight lines, one is divided into any number of parts, the rectangle contained by the two lines is equal to the sum of the rectangles contained by the undivided line and the several parts of...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 339 pages
...follows : If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments. This amounts to saying that \lx=p + q + r-\ , then ax...
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Mathematical Thought from Ancient to Modern Times: Volume 1

Morris Kline - Mathematics - 1990 - 428 pages
...there be two straight lines (Fig. 4.8) and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments. Propositions 2 and 3 are really special cases of Proposition...
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The Heritage of Thales

W.S. Anglin, J. Lambek - Science - 1998 - 331 pages
...thus: If there are two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments (Elements II 1). The law (a + b)2 = a2 + lab + b2 is illustrated...
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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 278 pages
...(Proposition 1): If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments. Translated into algebraic notation, this corresponds...
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The Beginnings and Evolution of Algebra

I. G. Bashmakova, G. S. Smirnova - Mathematics - 2000 - 179 pages
...that: If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments (note that by "straight line" Euclid always means a bounded...
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Apollonius of Perga's Conica: Text, Context, Subtext

Michael N. Fried - History - 2001 - 499 pages
...reads: "If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments". Though mathematically equivalent, historically and epistemologically...
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Geometry: Our Cultural Heritage

Audun Holme - Mathematics - 2002 - 378 pages
...Formula 1 If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the (sum of the) rectangles contained by the uncut straight line and each of the segments. Again, the parenthesis...
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Classics in the History of Greek Mathematics

Jean Christianidis - Mathematics - 2004 - 474 pages
...translation of HEATH: If there be two straight lines, and one of them be cut into any number of segments, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments. Fig. 2. Diagram to EUCLJDS Prop. II. 1. Geometrically,...
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