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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, containing the first six books, with a selection of ...

Euclides - 1874
...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 these produced, proportionally ; and conversely, if the sides, or the sides produced, be cut proportionally,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 403 pages
...square. 12. If a straight line be parallel to the 'base of a triangle it will cut the sides, or the sides produced, proportionally, and if the sides, or the...joins the points of section shall be parallel to the base. 13, To find a mean proportional between two given straight lines. JUNIOB AND SENIOB MATBICULATION,...
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The Madras University Calendar, Volume 1

University of Madras - 1876
...straight lines. III. Explain the terms " homologous sides," " duplicate ratio," and "ex equali." IV. (a) If a straight line be drawn parallel to one of the sides of a triangle, it shall Rut the other sides proportionally, (b) ABCD is a parallelogram, a point E is taken in BD the diagonal,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 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, il must cut the other side*, or those sides produced, proportionally. Let DE be drawn || to BC, a side...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 372 pages
...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
...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 - 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...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 ..., Volume 23

1879
...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, Volume 22

Great Britain. Parliament. House of Commons - Great Britain - 1879
...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 - Geometry - 1879 - 266 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...
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