Book:Euclid/The Elements/Book VI

Contents

 * Book VI: Theory of Proportions as applied to Plane Geometry
 * Definitions
 * Proposition 1: Areas of Triangles and Parallelograms Proportional to Base
 * Proposition 2: Parallel Line in Triangle Cuts Sides Proportionally
 * Proposition 3: Angle Bisector Theorem
 * Proposition 4: Equiangular Triangles are Similar
 * Proposition 5: Triangles with Proportional Sides are Similar
 * Proposition 6: Triangles with One Equal Angle and Two Sides Proportional are Similar
 * Proposition 7: Triangles with One Equal Angle and Two Other Sides Proportional are Similar
 * Proposition 8: Perpendicular in Right-Angled Triangle makes two Similar Triangles
 * Proposition 9: Construction of Part of Line
 * Proposition 10: Construction of Similarly Cut Straight Line
 * Proposition 11: Construction of Third Proportional Straight Line‎
 * Proposition 12: Construction of Fourth Proportional Straight Line
 * Proposition 13: Construction of Mean Proportional‎
 * Proposition 14: Sides of Equiangular Parallelograms are Reciprocally Proportional‎
 * Proposition 15: Sides of Equiangular Triangles are Reciprocally Proportional‎
 * Proposition 16: Rectangles Contained by Proportional Straight Lines
 * Proposition 17: Rectangles Contained by Three Proportional Straight Lines
 * Proposition 18: Construction of Similar Polygon
 * Proposition 19: Ratio of Areas of Similar Triangles
 * Proposition 20: Similar Polygons Composed of Similar Triangles
 * Proposition 21: Similarity of Polygons is Equivalence‎
 * Proposition 22: Similar Figures on Proportional Straight Lines
 * Proposition 23: Ratio of Areas of Equiangular Parallelograms
 * Proposition 24: Parallelograms About Diameter are Similar
 * Proposition 25: Construction of Figure Similar to One and Equal to Another
 * Proposition 26: Parallelogram Similar and in Same Angle has Same Diameter
 * Proposition 27: Similar Parallelogram on Half a Straight Line
 * Proposition 28: Construction of Parallelogram Equal to Given Figure Less a Parallelogram
 * Proposition 29: Construction of Parallelogram Equal to Given Figure Exceeding a Parallelogram
 * Proposition 30: Construction of Golden Section
 * Proposition 31: Similar Figures on Sides of Right-Angled Triangle
 * Proposition 32: Triangles with Two Sides Parallel and Equal
 * Proposition 33: Angles in Circles have Same Ratio as Arcs