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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. "
The Elements of Euclid, the parts read in the University of Cambridge [book ... - Page 58
by Euclides - 1846
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...sometimes "the rectangle ABC." To this proposition may be added the corollary : If two straight lines be divided into any number of parts, the rectangle contained...lines, is equal to the rectangles contained by the several parts of one line and the several parts of the other respectively. The method of reasoning...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...to £ (AB+CD)xEF. Hence the theorem; the area of a trapezoid, etc. THEOREM XXXV. If one of two lines is divided into any number of parts, the rectangle contained by the two lines is equal to the sum of the several rectangles contained by the undivided line and the several...
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The Edinburgh university calendar

Edinburgh univ - 1871 - 392 pages
...described upon the other two sides of it; the angle contained by these two sides is a right angle. 3. If there be two straight lines, one of which is divided...number of parts, the rectangle contained by the two lines is equal to the rectangles contained by the undivided line and the several parts of the divided...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...same parallels, the area of the triangle will be half the area of the parallelogram. PROPOSITION 1r. If there be two straight lines, one of which is divided into any number of farts, the rectangle of the two straight lines shall be equal to tJ1e sum of tJ1e rectangles of the...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...AB, CD = sum of reet. AB, CE and rect. AB, EF and rect. AB, FD. QED Ex. If two straight lines be each divided into any number of parts, the rectangle contained by the two lines is equal to the rectangles contained] by all the parts of the one taken separately with all the...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...the signs +, — , and =. They will accordingly be occasionally employed. PBOPOSITION I. If there are two straight lines one of which is divided into any...contained by the two straight lines is equal* to the sum of the rectangles contained by the undivided line and the several parts of che divided line. For...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...AB, CE and rect. AB, EF .: rect. AB, 6'/> = and rect. AB, FD. QED Ex. If two straight lines be each divided into any number of parts, the rectangle contained by the two lines is equal to •'he rectangles contained^ by all the parts of the one taken '.rn.t.ely with nil...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 580 pages
...together with the complements AF, FC, is the gnomon AGK, or EHC. I. — If there be two straight linns, one of which is divided into any number of parts;...and the several parts of the divided line. Let A and BO be two straight lines ; of which BC is divided into any parts in the points D, E. Then the rectangle...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...equal to A ABC = square-Xy; /. square on AB - squares on AC, CB. BOOK II. RECTANGLES. PROPOSITION I. If there be two straight lines, one of which is divided...undivided line and the several parts of the divided line. a Let A and BC be two straight lines, and let BC be divided into any parts BP, PQ, QC. Then shall the...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...are at the opposite angles of the parallelograms which make the gnomon." PROPOSITION 1.. — Theorem. If there be two straight lines, one of which is divided...the rectangle contained by the two straight lines ^s equal to the rectangles contained by the undivided line, and the several parts of the divided line....
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