Among other species are P. antisianus, P. fulgidus, P. auriceps and P. pavoninus, from various parts of South America, but though all are beautiful birds, none possess the wonderful singularity of the quezal.
An observer of very different mettle, the great lawyer d'Aguesseau, dwells on the "noble singularity, that gave him an almost prophetic air.
The singularity of its structure, its curious habits, and its peculiar economical value have naturally attracted no little attention from zoologists.
Amongst the legitimate reasons for suspecting the correctness of a text are patent contradictions in a passage or its immediate neighbourhood, proved and inexplicable deviations from the standards for forms, constructions and usages (mere rarity or singularity is not enough), weak and purposeless repetitions of a word (if there is no reason for attributing these to the writer), violations of the laws of metre and rhythm as observed by the author, obvious breaks in the thought (incoherence) or disorderly sequence in the same (double or multiple incoherence).
Singularity excites our wonder in Thaumastocheles zaleucus, v.
The singularities (I) and (3) have been termed proper singularities, and (2) and (4) improper; in each of the first-mentioned cases there is a real singularity, or peculiarity in the motion; in the other two cases there is not; in (2) there is not when the point is first at the node, or when it is secondly at the node, any peculiarity in the motion; the singularity consists in the point coming twice into the same position; and so in (4) the singularity is in the line coming twice into the same position.
Moreover (I) and (2) are, the former a proper singularity, and the latter an improper singularity, as regards the motion of the point; and similarly (3) and (4) are, the former a proper singularity, and the latter an improper singularity, as regards the motion of the line.
The curve (1 x, y, z) m = o, or general curve of the order m, has double tangents and inflections; (2) presents itself as a singularity, for the equations dx(* x, y, z) m =o, d y (*r x, y, z)m=o, d z(* x, y, z) m =o, implying y, z) m = o, are not in general satisfied by any values (a, b, c) whatever of (x, y, z), but if such values exist, then the point (a, b, c) is a node or double point; and (I) presents itself as a further singularity or sub-case of (2), a cusp being a double point for which the two tangents becomes coincident.
To complete Pliicker's theory it is necessary to take account of compound singularities; it might be possible, but it is at any rate difficult, to effect this by considering the curve as in course of description by the point moving along the rotating line; and it seems easier to consider the compound singularity as arising from the variation of an actually described curve with ordinary singularities.
520) is that every singularity whatever may be considered as compounded of ordinary singularities, say we have a singularity =6' nodes, cusps, double tangents and c' inflections.
The cases may be divided into sub-cases, by the consideration of compound singularities; thus when m= 4, n= 6, S = 3, the three nodes may be all distinct, which is the general case, or two of them may unite together into the singularity called a tacnode, or all three may unite together into a triple point or else into an oscnode.
Each singular kind presents itself as a limit separating two kinds of inferior singularity; the cuspidal separates the crunodal and the acnodal, and these last separate from each other the complex and the simplex.
Swift says that "with a singularity scarce to be justified he carried away more Greek, Latin and philosophy than properly became a person of his rank."