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" If there be 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. "
A Supplement to the Elements of Euclid - Page 92
by Daniel Cresswell - 1819 - 410 pages
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Mathematical Thought from Ancient to Modern Times: Volume 1

Morris Kline - Mathematics - 1990 - 434 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 - 347 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 - 292 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 - 200 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 - 516 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 - 408 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 - 502 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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A First Course of Geometry

130 pages
...also be used when convenient. 91. PROP. 1. If there be 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 sum of the rectangles contained by the second line and each part of the first. A c D u Let AB and X...
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Solutions of the Exercises in Tyler's Euclid

268 pages
...rects AB, CD ; AD, BC=rect. AC, BD. 137, 2. If there be two straight lines, each of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the sum of the rectangles contained by each of the parts of the first line and each of the parts of the...
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The Elements of Plane Geometry

Euclid - 1845 - 328 pages
...parallel. CHAPTER vI AREAS (CONT.) 159. PROP. 1. If there be 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 sum of the rectangles contained by the second line and each part of the first. A c DB Let AB and X...
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