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" If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal. "
Euclid and His Modern Rivals - Page 201
by Lewis Carroll - 1885 - 275 pages
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...projections on another straight line make equal angles with that line, or are parallel to it. THEOR. 32. If there are three parallel straight lines, and the...any other straight line that cuts them are equal. COR. i. The straight line drawn through the middle point of one of the sides of a triangle parallel...
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Elementary geometry

James Maurice Wilson - 1878 - 450 pages
...(Th. 28.) and therefore ab = cd. QED Similarly the converse propositions may be proved. THEOREM 32. If there are three parallel straight lines, and the...any other straight line that cuts them are equal. Let the three parallel straight lines AD, BE, CF make equal intercepts on the straight line AC, that...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...them are equal, then the intercepts on any other straight line that cuts them are also equal. COR. 1. If there are three parallel straight lines, and the...intercepts on any other straight line that cuts them are also equal. COR. 2. The straight line drawn through the middle point of one of the sides of a triangle...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...side BK is equal to the side FL, therefore the side BD is equal to the side FH. /. 19. QED COR. 1. If there are three parallel straight lines, and the...intercepts on any other straight line that cuts them are also equal. COR. 2. The straight line drawn through the middle point of one of the sides of a triangle...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...are two pairs of straight lines all of which are parallel, and the intercepts made by each pair on a straight line that cuts them are equal, then the intercepts on any other straight line that cuts them are also equal. Let AB, CD and EF, GH be two pairs of straight lines all of which are parallel, and let...
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...=».FH. Hence AC : EG : : BD : FH. Def. 5. QED COR. i. If there are three parallel straight lines, the intercepts made by them on any straight line that cuts them are to one another in the same ratio as the corresponding intercepts on any other straight line that cuts...
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Examinations Papers

1891 - 644 pages
...two pairs of straight lines, all of" which are parallel, and the intercepts made by each pair on a straight line that cuts them are equal, then the intercepts on any other straight line that cuts them are also equal. If a quadrilateral be formed by joining the middle points of the sides of a given quadrilateral,...
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The Elements of Plane Geometry

Association for the Improvement of Geometrical Teaching - 1903 - 342 pages
...the side BK is equal to the side FL, therefore the side BD is equal to the side FH. / 19. QED COR. 1. If there are three parallel straight lines, and the...intercepts on any other straight line that cuts them are also equal. COR. 2. The straight line drawn through the middle point of one of the sides of a triangle...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...(not parallel to PQ) to cut OP, OQ, OR atp, q, r ; iapr = qr.t THKOUEM 24. If there are three or more parallel straight lines, and the intercepts made by...any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal. .< \. % 152. Data...
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The School World: A Monthly Magazine of Educational Work and Progress, Volume 5

Education - 1903 - 692 pages
...diagonal bisects the parallelogram, and the diagonals bisect one another. If there are three or more parallel straight lines, and the intercepts made by...any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal. Areas. — Parallellograms...
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