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The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and the mean proportional between the two bases of the frustum.

Triangular Pyramid Frustum

The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude…

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Equivalent Triangular Pyramids

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Illustration of a how to construct a square equivalent to the sum of two given squares.

Square Constructed to be Equal to the Sum of Two Given Squares

Illustration of a how to construct a square equivalent to the sum of two given squares.

Illustration of a how to construct a square equivalent to the difference of two given squares.

Square Constructed to be Equal to the Difference of Two Given Squares

Illustration of a how to construct a square equivalent to the difference of two given squares.

Diagram used to prove the theorem: "Two triangular pyramids having equivalent bases and equal altitudes are equivalent."

Equivalent Triangular Pyramids

Diagram used to prove the theorem: "Two triangular pyramids having equivalent bases and equal altitudes…