| 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... | |
| James Maurice Wilson - Geometry - 1868 - 150 pages
...that PQ : LM :: QR : MN, (by TH. 3. CORS. 1, 2, 3). COR. 2. If a line be drawn parallel to one side **of a triangle, it will cut the other sides or the other sides produced proportionally.** COR. 3. The converse of this corollary is true. That is if a line cuts two sides of a triangle, both... | |
| 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... | |
| 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... | |
| Euclides - 1874 - 342 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 sides of a triangle, it** shall cut the other sides, or these produced, proportionally ; and conversely, if the sides, or the... | |
| 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... | |
| University of Madras - 1876 - 580 pages
...straight lines. III. Explain the terms " homologous sides," " duplicate ratio," and "ex equali." IV. (a) **If a straight line be drawn parallel to one of the sides of a triangle, it** shall Rut the other sides proportionally, (b) ABCD is a parallelogram, a point E is taken in BD the... | |
| Euclides, James Hamblin SMITH - 1876 - 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,** il must cut the other side*, or those sides produced, proportionally. Let DE be drawn || to BC, a side... | |
| J. G - 1878 - 408 pages
...648=2-81157501, log. 864=2'93651374, find log. 108. GEOMETRY, TRIGONOMETRY, CONICS. Afternoon Paper, 1. **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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