On the Foundation And Technic of Arithmetic

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Every summit is said to be opposite to the face made by the other three; every edge opposite to that made by the two remaining summits.
A polyhedron is the figure formed by n plane polygons such that each side is common to two. The polygons are called its faces; their sects its edges; their vertices its summits.
One-third the product of the area of a face by the length of the perpendicular to it from the opposite vertex is the volume of the tetrahedron.
The volume of a polyhedron is the sum of
...the vol- umes of any set of tetrahedra into which it is cut.
A prismatoid is a polyhedron with no summits other than the vertices of two parallel faces.
The altitude of a prismatoid is the perpendicular from top to base.
MENSURATION. 79 A number of different prismatoids thus have the same base, top, and altitude.
If both base and top of a prismatoid are sects, it is a tetrahedron.
A section or cross-cut of a prismatoid is the polygon determined by a plane perpendicular to the altitude.
To find the volume of any prismatoid.


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