 | James Robert Christie - Mathematics - 1866 - 428 pages
...angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is &c. 4. 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 &c. 5. If two straight lines meeting... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION 2. THEOREM. If a straight line be drawn parallel to one of the...a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION 2. THEOREM. If a straight line be drawn parallel to one of the...a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the... | |
 | Robert Potts - 1868 - 434 pages
...cut the other tides, or thect produced, proportionally : and conversely, if the sides, or the tides produced, be cut proportionally, the straight line...points of section shall be parallel to the remaining siae of the triangle. Let DE be drawn parallel to EC, one of the sides of the triangle .4 .BC. Then... | |
 | Euclid - 1868 - 138 pages
...ij firi тàç TOfiàç ¿iriÇiwy/iévq ivoiia trapa TijV Xotirijv IOTUI TOV Tpiyiâvov irXivpáv. If a straight line be drawn parallel to one of the sides of a triangle, it cuts t he other two sides proportionally ; and if the two sides he cut proportionally, the straight... | |
 | Edinburgh univ - 1868 - 336 pages
...lines drawn from the angles of a triangle to the bisections of the opposite sides meet in a point. 9. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sideSi or the other sides produced, proportionally ; and if the sides, or the sides... | |
 | Cambridge univ, exam. papers - 1870 - 272 pages
...in AB, QP is equal to the length of the tangent from Q. proportionally; and if the sides or the side produced, be cut proportionally, the straight line...be parallel to the remaining side of the triangle. Show that the straight lines joining the middle points of the opposite sides of any quadrilateral bisect... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...between the same parallels, therefore D is equal to E, AC therefore - is equal to =-. BL) PROPOSITION 5. If a straight line be drawn parallel to one of the sides of a triangle it shall cut the other two sides or those sides produced proportionally; and if two of the sides, or the sides produced, of... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...into which the parallelogram is then divided, must be equal, two and two. PROPOSITION II. THEOREM. If a straight line be drawn parallel to one of the sides of a triangle, it must cut the other sides, or those sides produced, proportionally. Let DE be drawn II to BC, a side... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...rect. (/, k); (v. 12) .-. A : H as c : k. (v.3> BOOK VI. COMPARISON OF STRAIGHT LINES. PROPOSITION I. 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. D Let DE be drawn || to BC, one of the sides of the A ABC. Then AD... | |
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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... 
