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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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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...these two sides is a right angle. BOOK II. 1. If there be two straight lines, one of which is divided into any number of parts, the rectangle contained...lines is equal to the rectangles contained by the undivided line and the several parts of the divided line. 2. If a straight line be divided into any...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 504 pages
...AD, BC is equal to the rectangle AC, BD. 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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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - Euclid's Elements - 1895 - 657 pages
...there be two straight lines &c. COROLLARY 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 undivided line and each of the parts of the divided line. If...
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Book 1

Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 304 pages
...expressed arithmetically. PROPOSITION 1. THEOREM. If there are 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 undivided straight line and the several parts of the divided...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 355 pages
...one of which is divided into any number of parts (x, y, z say) while the other is of length a, then the rectangle contained by the two straight lines is equal to the sum of the rectangles contained by the undivided straight line and the several parts of the divided...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 456 pages
...EUCLID-S ELEMENTS. PROPOSITION 1. THEOREM. If there are 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 undivided straight line and the several parts of the divided...
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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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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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The Teaching of Geometry in Schools: A Report Prepared for the Mathematical ...

Mathematical Association - Geometry - 1923 - 74 pages
...II. 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. III. 15 : Of straight lines in a circle the diameter...
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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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