II. Another class of technical terms, which we find occurring as soon as speculative science assumes a distinct shape, consists of those which are intentionally constructed by speculators, and which contain some description or indication distinctive of the conception to which they are applied. Such are a _parallelogram_ (παραλληλόγραμμον), which denotes a plane figure bounded by two pairs of parallel lines; a _parallelopiped_ {262} (παραλληλοπίπεδον), which signifies a solid figure bounded by three pairs of parallel planes. A _triangle_ (τρίγωνος, _trigon_) and a _quadrangle_ (τετράγωνος, _tetragon_) were perhaps words invented independently of the mathematicians: but such words extended to other cases, _pentagon_, _decagon_, _heccædecagon_, _polygon_, are inventions of scientific men. Such also are _tetrahedron_, _hexahedron_, _dodecahedron_, _tesseracontaoctohedron_, _polyhedron_, and the like. These words being constructed by speculative writers, explain themselves, or at least require only some conventional limitation, easily adopted. Thus _parallelogram_, might mean a figure bounded by any number of sets of parallel lines, but it is conventionally restricted to a figure of _four_ sides. So a _great circle_ in a sphere means one which passes through the center of the sphere; and a _small circle_ is any other. So in trigonometry, we have the hypotenuse (ὑποτενοῦσα), or _subtending_ line, to designate the line subtending an angle, and especially a right angle. In this branch of mathematics we have many invented technical terms; as _complement_, _supplement_, _cosine_, _cotangent_, a _spherical angle_, the _pole of a circle_, or of a sphere. The word _sine_ itself appears to belong to the class of terms already described as scientific appropriations of common terms, although its origin is somewhat obscure.