A line through the centroid of a plane figure (drawn in the plane of the figure) is a central line, and a plane through the centroid of a solid figure is a central plane, of the figure.
Hence the volume of each element of the solid figure is to be found by multiplying the area of the corresponding element of the trapezette by 1, and therefore the total volume is 1 X area of trapezette.
Similarly the first moment of a solid figure may be regarded as obtained by dividing the figure into elementary prisms by two sets of parallel planes, and concentrating the volume of each prism at its centre.
A briquette may therefore be defined as a solid figure bounded by a pair of parallel planes, another pair of parallel planes at right angles to these, a base at right angles to these four planes (and therefore rectangular), and a top which is a surface of any form, but such that every ordinate from the base cuts it in one point and one point only.
These formulae also hold for converting moments of a solid figure with regard to a plane into moments with regard to a parallel plane through the centroid; x being the distance between the two planes.
The Pythagorean school of philosophers adopted the theory of a spherical earth, but from metaphysical rather than scientific reasons; their convincing argument was that a sphere being the most perfect solid figure was the only one worthy to circumscribe the dwellingplace of man.
Of a plane or solid figure are found in the same way by multiplying each element by the square, cube, ...
This implies the treatment of a plane or solid figure as being wholly comprised between two parallel lines or planes, regarded by convention as being vertical; the figure being generated by an ordinate or section moving at right angles to itself through a distance which is called the breadth of the figure.