| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 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 - 400 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 - 410 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 - 141 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
...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
...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 - 285 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 - 349 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 - 349 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... | |
| Braithwaite Arnett - 1874
...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, it shall cut the other sides, or** these produced, proportionally. 7. Equal parallelograms, which have one angle of the one equal to one... | |
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