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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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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 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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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,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 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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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 336 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,...the other sides produced, proportionally: And if the fides, or the sides produced, be cut proportionally, the straight line which joms the points of section...
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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...
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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 sides of a triangle, it shall cut the other sides, or those produced, proportionally. 3. Equiangular parallelograms are to...
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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...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...and triangles, having equal bases, are to one another as their altitudes. PROPOSITION II. THEOBEM. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or the other sides produced ^proportionally ; and if the sides, or the sides...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1860 - 332 pages
...anil parallelograms that have equal altitudes, are to one another as their bases. PROP. II. THEOR. lj 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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