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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 figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 54
by Euclides - 1840
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...ABC to ACD and CD to DL as ACD to ADL • But BC to DL as ABC to ADL. TROP. xvii. THEOREM. (E. 6. 2). If- a straight line be drawn parallel to one of the sides of a triangle, it cuts the other two sides, or these sides produced proportionally, so that the segments between the...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...Corollary 2.—Triangles of equal altitude are proportional to their bases. 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, or the sides produced, be ad proportionally,...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879
...Describe an isosceles triangle, having each of the angles at the base double of the third angle. 6. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides...
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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 sides of a triangle, it shall cut the other sides or those produced proportionally. Construct a triangle similar to a given...
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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 sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 292 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, or the sides produced, be cut...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 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 sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides...
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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 sides of a triangle, it shall cut the other sides, or those sides produced, proportionally. Shew that two straight lines drawn...
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Knowledge: An Illustrated Magazine of Science, Volume 5

Science - 1884 - 536 pages
...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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