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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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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 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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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,...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION II. TIIEOR. 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 if the sides, or the sides produced, be cut proportionally, the...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 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 shaU cut tlie other sides, or these produced, proportionally ; and if the sides, or the sides produced,...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - Science - 1854
...(DE) be drawn parallel to one of the sides (BC) of a triangle, it shall cut the other sides, or these produced, proportionally ; and if the sides, or the...produced, be cut proportionally, the straight line which ioins the noints of section shall be parallel to the remaining side of the triangle. For draw BE, CD....
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 318 pages
...that have equal altitudes, are to one another as their bases. PROP. II. THEOR. 0 I] a straight lme 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 fides, or the sides...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...a given circle into segments, one of which shall contain an angle double of that in the other. 12. 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. MECHANICS AND HYDROSTATICS. FRIDAY, January 16, 1857. 9 to 12. FIRST...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 12 pages
...the circle whose centre is the vertex of the isosceles triangle and radius one of its equal sides, 2. If a straight line be drawn parallel to one of the...the other sides, or those produced, proportionally. 3. Equiangular parallelograms are to each other in the ratio compounded of the ratio of their sides....
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859
...iTI r ro/i Iiriuyfvi/ uoa irap rrjv \onri}v tarai rov Tfiyivov ir\tvpv. If a straight line be drawn parallel to one of the sides of a triangle, it cuts t fie other two sides proportionally ; and if the two sides be cut proportionally, the straight...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 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 sides produced, be cut proportionally,...
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