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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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 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 Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...cut the other tides, or thect produced, proportionally : and conversely, if the sides, or the tides produced, be cut proportionally, the straight line...points of section shall be parallel to the remaining siae of the triangle. Let DE be drawn parallel to EC, one of the sides of the triangle .4 .BC. Then...
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Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI

Euclid - 1868 - 141 pages
...ij firi т TOfi iriiwy/ivq ivoiia trapa TijV Xotirijv IOTUI TOV Tpiyivov irXivpv. If a straight line be drawn parallel to one of the sides of a triangle, it cuts t he other two sides proportionally ; and if the two sides he cut proportionally, the straight...
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The Edinburgh university calendar

Edinburgh univ - 1868
...lines drawn from the angles of a triangle to the bisections of the opposite sides meet in a point. 9. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sideSi or the other sides produced, proportionally ; and if the sides, or the sides...
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Examination for women. Examination papers, with lists of syndics and examiners

Cambridge univ, exam. papers - 1870
...in AB, QP is equal to the length of the tangent from Q. proportionally; and if the sides or the side produced, be cut proportionally, the straight line...be parallel to the remaining side of the triangle. Show that the straight lines joining the middle points of the opposite sides of any quadrilateral bisect...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 285 pages
...between the same parallels, therefore D is equal to E, AC therefore - is equal to =-. BL) PROPOSITION 5. If a straight line be drawn parallel to one of the sides of a triangle it shall cut the other two sides or those sides produced proportionally; and if two of the sides, or the sides produced, of...
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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
...into which the parallelogram is then divided, must be equal, two and two. PROPOSITION II. THEOREM. If a straight line be drawn parallel to one of the sides of a triangle, it must cut the other sides, or those sides produced, proportionally. Let DE be drawn II to BC, a side...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...rect. (/, k); (v. 12) .-. A : H as c : k. (v.3> BOOK VI. COMPARISON OF STRAIGHT LINES. PROPOSITION I. 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. D Let DE be drawn || to BC, one of the sides of the A ABC. Then AD...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...of the square inscribed in any circle is half that of the square described about the same circle. 6. 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. 7. Equal parallelograms, which have one angle of the one equal to one...
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