# Category:Euclid Book XI

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These proofs can all be found in Book $\text {XI}$ 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 XI"

The following 42 pages are in this category, out of 42 total.

### C

- Common Section of Bisecting Planes of Cube Bisect and are Bisected by Diagonal of Cube
- Common Section of Planes Perpendicular to other Plane is Perpendicular to that Plane
- Common Section of Two Planes is Straight Line
- Common Sections of Parallel Planes with other Plane are Parallel
- Condition for Equal Angles contained by Elevated Straight Lines from Plane Angles
- Condition for Equal Angles contained by Elevated Straight Lines from Plane Angles/Porism
- Construction of Parallelepiped Similar to Given Parallelepiped
- Construction of Solid Angle equal to Given Solid Angle
- Construction of Solid Angle from Three Plane Angles any Two of which are Greater than Other Angle
- Construction of Solid Angle from Three Plane Angles any Two of which are Greater than Other Angle/Lemma
- Construction of Straight Line Perpendicular to Plane from point not on Plane
- Construction of Straight Line Perpendicular to Plane from point on Plane

### L

### P

- Parallelepiped cut by Plane Parallel to Opposite Planes
- Parallelepiped cut by Plane through Diagonals of Opposite Planes is Bisected
- Parallelepiped formed from Three Proportional Lines equal to Equilateral Parallelepiped with Equal Angles to it formed on Mean
- Parallelepipeds are of Equal Volume iff Bases are in Reciprocal Proportion to Heights
- Parallelepipeds of Same Height have Volume Proportional to Bases
- Parallelepipeds on Equal Bases and Same Height are Equal in Volume
- Parallelepipeds on Same Base and Same Height whose Extremities are not on Same Lines are Equal in Volume
- Parallelepipeds on Same Base and Same Height whose Extremities are on Same Lines are Equal in Volume
- Plane through Straight Line Perpendicular to other Plane is Perpendicular to that Plane
- Planes Perpendicular to same Straight Line are Parallel
- Planes through Parallel Pairs of Meeting Lines are Parallel
- Prisms of equal Height with Parallelogram and Triangle as Base