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◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-12-proportional-stereometry / Subsection: Propositions from Book 12

Subsection: Propositions from Book 12

This subsection contains the propositions from Book 12 of Euclid's “Elements”.

Table of Contents

  1. Proposition: Prop. 12.01: Areas of Similar Polygons Inscribed in Circles are as Squares on Diameters
  2. Proposition: Prop. 12.02: Areas of Circles are as Squares on Diameters
  3. Proposition: Prop. 12.03: Tetrahedron divided into Two Similar Tetrahedra and Two Equal Prisms
  4. Proposition: Prop. 12.04: Proportion of Sizes of Tetrahedra divided into Two Similar Tetrahedra and Two Equal Prisms
  5. Proposition: Prop. 12.05: Sizes of Tetrahedra of Same Height are as Bases
  6. Proposition: Prop. 12.06: Sizes of Pyramids of Same Height with Polygonal Bases are as Bases
  7. Proposition: Prop. 12.07: Prism on Triangular Base divided into Three Equal Tetrahedra
  8. Proposition: Prop. 12.08: Volumes of Similar Tetrahedra are in Cubed Ratio of Corresponding Sides
  9. Proposition: Prop. 12.09: Tetrahedra are Equal iff Bases are Reciprocally Proportional to Heights
  10. Proposition: Prop. 12.10: Volume of Cone is Third of Cylinder on Same Base and of Same Height
  11. Proposition: Prop. 12.11: Volume of Cones or Cylinders of Same Height are in Same Ratio as Bases
  12. Proposition: Prop. 12.12: Volumes of Similar Cones and Cylinders are in Triplicate Ratio of Diameters of Bases
  13. Proposition: Prop. 12.13: Volumes of Parts of Cylinder cut by Plane Parallel to Opposite Planes are as Parts of Axis
  14. Proposition: Prop. 12.14: Volumes of Cones or Cylinders on Equal Bases are in Same Ratio as Heights
  15. Proposition: Prop. 12.15: Cones or Cylinders are Equal iff Bases are Reciprocally Proportional to Heights
  16. Proposition: Prop. 12.16: Construction of Equilateral Polygon with Even Number of Sides in Outer of Concentric Circles
  17. Proposition: Prop. 12.17: Construction of Polyhedron in Outer of Concentric Spheres
  18. Proposition: Prop. 12.18: Volumes of Spheres are in Triplicate Ratio of Diameters

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