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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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Parliamentary Papers, Volume 30

Great Britain. Parliament. House of Commons - Bills, Legislative - 1853 - 520 pages
...quadrilateral figure which can be inscribed in a circle are together equal lo 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 Elements of Plane Geometry

Euclid - 1845 - 328 pages
...divided internally at C and externally at D in the ratio 7:3; find the length of CD. 189. PROP. 1. If a straight line be drawn parallel to one of the sides of a triangle, it cuts the other sides (or those sides produced) proportionally; and, conversely, if a straight line...
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Calendar

University of St. Andrews - 1900 - 670 pages
...and two of its opposite sides AB and CD are parallel ; show that AC is equal to BD. 11. Show that, if a straight line be drawn parallel to one of the sides of a triangle, it cuts the other sides, or those sides produced, proportionally. Through a point 0 in the base BC of...
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Parliamentary Papers, Volume 43

Great Britain. Parliament. House of Commons - Great Britain - 1863 - 616 pages
...Compare the sides of an equilateral triangle, and an equilateral hexagon inscribed in a circle. 9. 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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Calendar

University of Cambridge - 1850 - 648 pages
...circle, shew iha: their intersections will form a hexagon, equilateral but not generally equiangular. 5. 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 tbe sides, or the sides produced,...
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Pass school, group A (-D).

Oxford univ, exam. papers, 2nd publ. exam - 1884 - 594 pages
...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 sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides...
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Examination,Midsummer,1879

Education Department - 1879 - 1130 pages
...the area of the hexagon is double the area of an equilateral triangle inscribed in the circle. 10. 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. Three circles whose radii are as 1:2:4...
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Parliamentary Papers, Volume 16

Great Britain. Parliament. House of Commons - Great Britain - 1874 - 814 pages
...of the square inscribed in any circle is half that of the square described about the same circle. 6. If a straight line be drawn parallel to one of the sides of a triangle, CAVALBT AN it shall cut the other sides, or these produced, proportionally. IHTANTRY. 7. Equal parallelograms,...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volume 18

1874 - 750 pages
...it Ш the original triangle is equal to a right angle. 5. Describe a circle about a given square. 6. If a straight line be drawn parallel to one of the sides of a triangle, CAVALBT ARD it shall cut the other sides, or these produced, proportionally. INPAMTRT. 7. Equal parallelograms,...
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Calendar

University of St. Andrews - 1896
...the weight supported is 17 Ib. 12. To find the position of the centre of gravity of a plane triangle. If a straight line be drawn parallel to one of the sides of a triangle so as to cut off one-fourth of its area, find the centre of gravity of the quadrilateral remaining....
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