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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, the parts read in the University of Cambridge [book ...

Euclides - 1846
...THEOB. If a straight line be parallel to the base of a triangle, it shall 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. Let DE be parallel to BC, the base of the triangle ABC : BD shall be to DA as CE to EA. Join...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...^▒ ABC : I úZ7 m ABCE : i — 7 Prop. 70. : : ( ACDF. Therefore triangles, &c. PROP. LXXII. THEOR. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides proportionally: and if the sides be cut proportionally, the straight line which joins the points of...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...CD:: ^\ ABC : I d7 m ABCE : /—7 Prop. TO. :: ( ACDF. Therefore triangles, &c. PROP. LXXII. THEOR. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides proportionally: and if the sides be cut proportionally, the straight line which joins the points of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...and parallelograms that have equal altitudes, are to one another as their bases. 123 PROP. II. THEOR. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides, or the other sides produced, proportionally : And if the sides, or the sides...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...straight line be drawn parallel to one side of a triangle, it shall cut the other sides, or those sides produced proportionally : and if the sides, or the...produced, be cut proportionally, the straight line joining the sectional points, shall be parallel to the third side of the triangle. Given the triangle...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...and parallelograms that have equal altitudes, are one to another as their bases. PROP. II. 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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1849 - 317 pages
...will cut the other sides, or the other sides produced, proportionally : And if the sides, or the fides produced, be cut proportionally, the straight line which joins the points of section will be parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the...
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Minutes of the Committee of Council on Education, Volume 1

Great Britain. Committee on Education - School buildings - 1850
...contained by the segments of the other. Section 3. 1. To describe a circle about a given triangle. 2. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other two sides of the triangle proportionally ; and conversely if two sides of a triangle be cut proportionally,...
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An Epitome of Navigation and Nautical Astronomy, with Improved Lunar Tables ...

Janet Taylor - Nautical astronomy - 1851 - 621 pages
...proportional, viz : [Eu. vi. 4.] CA : AD : : CD : DE AC : CB : : DC : CB CB : BA : : CE : ED Hence if a straight line be drawn parallel to one of the sides of a plane triangle, it will cut the other two sides proportionally, [Eu. vi. 2.] or Theorem D, page 26....
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General Report on Public Instruction in the Bengal Presidency

Education - 1852
...quadrilateral figure which can be inscribed in a circle are together equal to two right angles. 4. If a straight line be drawn parallel to one of the...proportionally, the straight line which joins the point of section shall be parallel to the remaining sides of the triangle. Hence shew how a line may...
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