# Category:Euclid Book XII

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These proofs can all be found in Book $\text {XII}$ of Euclid's *The Elements*.

The specific form of these has been adapted from Sir Thomas L. Heath's *Euclid: The Thirteen Books of The Elements: Volume 3, 2nd ed.*

## Pages in category "Euclid Book XII"

The following 25 pages are in this category, out of 25 total.

### A

### C

### P

- Prism on Triangular Base divided into Three Equal Tetrahedra
- Prism on Triangular Base divided into Three Equal Tetrahedra/Historical Note
- Prism on Triangular Base divided into Three Equal Tetrahedra/Porism
- Proportion of Sizes of Tetrahedra divided into Two Similar Tetrahedra and Two Equal Prisms
- Proportion of Sizes of Tetrahedra divided into Two Similar Tetrahedra and Two Equal Prisms/Lemma

### S

### T

### V

- Volume of Cone is Third of Cylinder on Same Base and of Same Height/Historical Note
- Volume of Cone is Third of Cylinder on Same Base and of Same Height/Proof 1
- Volume of Cones or Cylinders of Same Height are in Same Ratio as Bases
- Volumes of Cones or Cylinders on Equal Bases are in Same Ratio as Heights
- Volumes of Parts of Cylinder cut by Plane Parallel to Opposite Planes are as Parts of Axis
- Volumes of Similar Cones and Cylinders are in Triplicate Ratio of Diameters of Bases
- Volumes of Similar Tetrahedra are in Triplicate Ratio of Corresponding Sides
- Volumes of Similar Tetrahedra are in Triplicate Ratio of Corresponding Sides/Porism
- Volumes of Spheres are in Triplicate Ratio of Diameters