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" IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section... "
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 138
by Euclid, James Thomson - 1837 - 390 pages
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Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

Euclides, James Hamblin Smith - Euclid's Elements - 1879 - 349 pages
...parallel to either of them, shall cut the other sides, or these produced, proportionally. And Conversely, If the sides, or the sides produced, be cut proportionally, the straight line which joini the points of section must be parallel to the remaining side of the triangle. Let the sides AB,...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...the triangle will bisect that angle. 8. Find a point in the diagonal of a square produced, from which if a straight line be drawn parallel to one of the sides, and meeting another side produced, it will form with the produced diagonal and produced side a triangle...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880
...square, prove 3AD3 = 2AB2. 5. Inscribe a circle in a given equilateral and equiangular pentagon. 6. If a straight line be drawn parallel to one of the...the other sides or those produced proportionally. Construct a triangle similar to a given triangle, such that each of its sides shall be one-fourth of...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION 2. THEOREM. If a straight line be drawn parallel to one of the...a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 266 pages
...of equal altitude are proportional to their bases. GEOMETRY— BOOK V. Proposition 2. Theorem. — If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides, or those sides produced proportionally ; and if the sides of a triangle,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION 2. THEOREM. If a straight line be drawn parallel to one of the...a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the...
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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884
...given circle. Shew that any equilateral figure inscribed in a circle must also be equiangular. 10. If a straight line be drawn parallel to one of the...a triangle, it shall cut the other sides, or those sides produced, proportionally. Shew that two straight lines drawn from two angular points of a triangle...
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Knowledge: An Illustrated Magazine of Science, Volume 5

Science - 1884
...В Q are drawn ; PQ meets the circumferences again at P and S show that AR is parallel to B S. 79. If a straight line be drawn parallel to one of the sides of an equilateral triangle, it will form with the other sides, produced ii necessary, another equilateral...
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First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - Geometry - 1887 - 180 pages
...triangle, it will form with the other sides, produced if necessary, another equilateral triangle. 80. If a straight line be drawn parallel to one of the sides of a triangle, it will form with the other sides, produced if necessary, a triangle equiangular to the first. 81. Two...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889
...equiangular pentagon include between them a pentagon which is itself equilateral and equiangular. 9. If a straight line be drawn parallel to one of the...sides of a triangle, it shall cut the other sides, or these produced, proportionally; and, conversely, if two sides, or these produced, be cut proportionally,...
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