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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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 155
av Euclid, Robert Simson - 1821 - 516 sider
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 408 sider
...648=2-81157501, log. 864=2'93651374, find log. 108. GEOMETRY, TRIGONOMETRY, CONICS. Afternoon Paper, 1. 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 the sides, or the sides produced, be cut proportionally,...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 sider
...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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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879 - 414 sider
...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...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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Report of Her Majesty's Civil Service Commissioners: Together with ..., Volum 23

1879 - 636 sider
...produced, proportionally; PAT-KIT am* ^ tne s'^es> or tne sides produced, be cut proportionately, OFFICE the straight line which joins the points of section...be parallel to the remaining side of the triangle. 10. If from the three angles of a triangle lines be drawn to the points of bisection of the opposite...
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Parliamentary Papers, Volum 22

Great Britain. Parliament. House of Commons - 1879 - 632 sider
...proportionally ; r^Tira8' an(^ ^ t'ie s'^es> or the sides produced, be cut proportionately, OFFICE the straight line which joins the points of section...be parallel to the remaining side of the triangle. 10. If from the three angles of a triangle lines be drawn to the points of bisection of the opposite...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 282 sider
...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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1879 - 376 sider
...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 - 146 sider
...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 - 68 sider
...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 - 1880 - 426 sider
...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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