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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

## 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. —...

## The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1911 - 616 pages
...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...

## The Teaching of Mathematics in the United Kingdom

Great Britain. Board of Education - Mathematics - 1912 - 632 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::DE:EF;...

## Special Reports on Educational Subjects, Volumes 26-27

Great Britain. Board of Education - Education - 1912 - 1048 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 : :...

## The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - Geometry, Non-Euclidean - 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...

## 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...

## The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

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...

## Calendar

University of St. Andrews - 1904 - 790 pages
...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...