^{page 97 note *} This name, signifying a figure bounded by three pairs of parallel planes, is admitted in crystallography; but the longer and less expressive ‘parallelepiped’ is too frequently used instead of it by mathematical writers and teachers. A hexahedron, with its angles acute and obtuse, is what is commonly called, both in pure mathematics and crystallography, a rhombohedron. A right angled hexahedron is a brick, for which no Greek or other learned name is hitherto to the front in usage. A rectangular equilateral hexahedron is a cube.

^{page 97 note †} For brevity I shall henceforth call the centre of gravity of a triangle, or of a tetrahedron, simply its centre.

^{page 99 note *} Thomson and Tait's Natural Philosophy, § 155; Elements, § 136.

^{page 99 note †} Thus we have an interesting theorem in the geometry of the tetrahedron:—If an ellipsoid touching the edges of a tetrahedron has its centre at the centre of the tetrahedron, the points of contact are at the middles of the edges.

^{page 99 note ‡} Thomson and Tait's Natural Philosophy, § 160; Elements, § 141.