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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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION 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...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 pages
...BC: Base 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...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 pages
...CD : : ^▒ 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1847 - 340 pages
...another. Then, if the same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. If a straight line be drawn parallel to one of the sides of a triangle, it mil cut the other sides, or the other sides produced, proportionally : And if the sides, or the sides...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...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...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1849 - 332 pages
...another. Then, if the same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. If a straight line be drawn parallel...produced, proportionally : And if the sides, or the fides produced, be cut proportionally, the straight line which joins the points of section will be...
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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...
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An Epitome of Navigation and Nautical Astronomy, with Improved Lunar Tables ...

Janet Taylor - Nautical astronomy - 1851 - 702 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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Five Years in an English University, Volume 2

Charles Astor Bristed - 1852
...a right angle : and the angle in a segment less than a semicircle is greater than a right angle. 6. If a straight line be drawn parallel to one of the...sides of a triangle, it will cut the other sides, or these produced, proportionally ; and if the sides, or these produced, be cut proportionally, the straight...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pages
...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 sides of a triangle, it shall cut the other sides or those produced proportionally, and if the sides or the sides produced...
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