Form and Mapping

Based on Dr. Felix Behrend's book "Form and Mapping", Ferdinand Hirt in Breslau 1932.

Contents

 Point and line Symmetry in space Sphere, line and plane Cube and parallelepiped, square and rectangle Position of a line in space Concept of congruence Tangential cone and cylinder Application of the similarity theorems to right-angled triangle The Plane Congruence theorems Sphere and cone Link between similarity and area Location of planes in space Group of motions Practical geometry Application of similarity rules to circle Measurement of length Group of motions and flippings Area Steady subdivision Plane figures Method of proof Area of square and rectangle Area of similar figures and volume of similar bodies Cube and parallelepiped, square and rectangle Geometric construction task Area of parallelogram Perspective similarity Cylinder and sphere, circle and ellipse Practical geometry Shear Perspectively similar figures in a plane Angle and its measurement General quadrangle Area of triangle Solution of construction tasks with the aid of perspective similarity Square pyramid, tetrahedron & cone, isosceles, right-angled & equilateral triangles Parallelogram Area of trapezoid Group of similarity transformations Truncated pyramid and cone. Isosceles trapezoid Rectangle Complementary parallelograms Polygons with centre and centre lines Parallel displacement Rhombus Area of polygons Straight prisms with centre, body axes and planes of symmetry Strip Square Conversion tasks Regular bodies Translation in space Trapezoid Pythagoras' Theorem Circle, Preliminaries Layers Parallelepiped and block Volume of cube and block Computation of p Prism and cylinder Rhombohedron Volume of parallelepiped Area of figures with curved boundaries Rotation Cube Concept of similarity Volume of pyramid Rotation in space Circle, point and line Proportion of segments Volumes of inclined prism, cone, cylinder, truncated pyramid and cone Surfaces of rotation Circle and angle Partitioning ratio of directed distances Vertical parallel projection Reversed and central symmetry Circle and triangle Construction of partitioning scale Practical geometry Reflection (flipping) and axial symmetry Chord quadrangle Harmonic ratio Oblique parallel projection Construction of axi-symmetric figures Tangent quadrangle Application of Ray Theorem to triangle Applications to triangle Relative location of two circles Similarity of figures Perpendicular parallel projection of the circle Sides and angles of a triangle Common tangents of two circles Similarity construction Affinity

Index