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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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The Edinburgh university calendar

Edinburgh univ - 1871
...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 into any...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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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871
...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 Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 285 pages
...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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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872
...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 - 349 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
...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 - 349 pages
...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 into any...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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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...g. 1. — t BOOK II. PROPOSITION I. — THEOREM. (Euc. II. 1.) Jf there be two straight lines, oiie of which is divided into any number of parts, the...contained by the two straight lines is equal to the sum of the rectangles contained by the undivided line, and the several parts of the divided line. Let...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...opposite angles of the parallelograms which make the gnomon." PROPOSITION 1.. — Theorem. If there be two straight lines, one of which is divided into any...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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Pure mathematics, Volume 1

Edward Atkins - 1874
...opposite angles of the parallelograms which make the gnomon. Proposition 1. — Theorem. If t/iere be two straight lines, one of which is divided into any number of parts, t/ie rectangle contained by the two straight lines is equal to t/ie rectangles contained by the undivided...
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