Books Books 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 ## Manual of Euclid: Books IV, V, VI.

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... ## Elementary Geometry, Volume 2

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... ## The Elements of Plane and Solid Geometry

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... ## Elements of geometry, containing books i. to vi.and portions of books xi ...

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... ## Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874 - 130 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, it shall cut the other sides, or these produced, proportionally. 7. Equal parallelograms, which have one... ## The Elements of Euclid, containing the first six books, with a selection of ...

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... ## Euclidian Geometry

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... ## The Madras University Calendar, Volume 1

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... ## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 382 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... 