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