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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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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - Geometry - 1908 - 228 pages
...line are proportional to the corresponding two segments on the other . 406 On Triangles.:;: T. 11. — If a straight line be drawn parallel' to one of the sides of a triangle, it shall divide the other sides (internally or externally) in the same ratio (Euc VI. 2) 407 T. lie. —...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1911
...describe a segment of a circle containing an angle equal to a given rectilineal angle. 8. Prove 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. State the converse. 9. Prove that if two...
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The Teaching of Mathematics in the United Kingdom

Great Britain. Board of Education - Mathematics - 1912
...touch two given straight lines and pass through a given point. 8. Prove that, if a straight line is drawn parallel to one of the sides of a triangle, it will cut the other sides or those sides produced proportionally. Two parallel lines ABC, DEF are divided so that AB:BC::DE:EF;...
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Special Reports on Educational Subjects, Volumes 26-27

Great Britain. Board of Education - Education - 1912 - 1032 pages
...touch two given straight lines and pass through a given point. 8. Prove that, if a straight line is drawn parallel to one of the sides of a triangle, it will cut the other sides or those sides produced proportionally. Two parallel lines ABC, DEF are divided so that AB • BC : :...
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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - Mathematics - 1993 - 320 pages
...parallelograms which are under the same height are to one another as their bases. Proposition 2. // a straight line be drawn parallel to one of the sides of the triangle, it will cut the sides of the triangle proportionally; and, if the sides of the triangle...
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Mathematics: A Concise History and Philosophy: A Concise History and Philosophy

W.S. Anglin - Mathematics - 1994 - 283 pages
...in the proof. Book VI concerns similar (equiangular) triangles. The key result is Proposition VI 2: if a straight line be drawn parallel to one of the sides of a triangle, it cuts the sides of the triangle proportionately — and vice versa. In other words, if D is in side...
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The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Mathematical Association, Mathematical Association of America - Mathematics - 2003 - 572 pages
...Triangles and parallelograms which are under the same height are to one another as their bases. Prop 2: If a straight line be drawn parallel to one of the sides of a triangle, it will cut the sides of the triangle proportionally; and, if the sides of the triangle be cut proportionally, the...
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Calendar

University of St. Andrews - 1904
...Find the area of a regular pentagon whose side is 12 inches correct to two places of decimals. 10. If a straight line be drawn parallel to one of the sides of a triangle it will cut the other sides proportionally. If the sides AB and AC of a triangle ABC are bisected in E and F respectively, and...
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The Thirteen Books of Euclid's Elements

Euclid - 452 pages
...German text-books adopt the less rigorous method of appealing to the theory of limits. PROPOSITION 2. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the sides of the triangle proportionally ; and, if the sides of the triangle be cut proportionally, the...
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - Mathematics - 1998 - 516 pages
...abbreviation of "triangle". 2. = ft j& ff « - !• if ¥ ff » BU ft » ft mma Ju & & m &$ = Heath If a straight line be drawn parallel to one of the sides of a triangle, it will cut the sides of the triangle proportionally; and, if the sides of the triangle be cut proportionally, the...
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