P A P P A P 231 and Eratosthenes, thirty-three books in all, the substance of which lie intends to give, with the lemmas necessary for their elucidation. With the mention of the Porisms of Euclid we have an account of the relation of porism to theorem and problem. In the same preface we have enunciated (a) the famous problem known by Pappus s name Having given a number of straight lines, to find the geometric locus of a point such that the lengths of the perpendiculars upon, or (more generally] the lines drawn from it obliquely at given inclina tions to, the given lines satisfy the condition that the product of certain of them may bear a constant ratio to the product of the remaining ones ; (b) the theorems which since the 17th century have been called by the name of Guldin, but appear to have been dis covered by Pappus himself. Book vii. contains also (1) under the head of the de detcrminata sectione of Apollonius, lemmas which, closely examined, are seen to be cases of the involution of six points ; (2) important lemmas on the Porisms of Euclid (see PORISM); (3) a lemma upon the Conies of Apollonius, which is the first statement of the constant relation between the distances of any point on a conic from the focus and directrix. Lastly, book viii. treats principally of mechanics, the properties of the centre of gravity, and some mechanical powers. Inter spersed are some questions of pure geometry. Proposition 14 gives a simple construction for the axes of an ellipse, when a pair of con jugate diameters are given. Of the whole work of Pappus the best edition is that of Hultsch, bearing the title Pappi Alexandrini Collectionis qux supersunt e libris manuscriptis edidit Latino interpretatione et commentariis instruxit Fridericus Hultsch, Berlin, 187<>-78. Previously the entire collection had been published only in a Latin translation, Pappi Alexandrini mathematics: collectiones a Federico Commandino Urbinate in latinum converses et commentariis illvstratx, Pesaro, 1588 (reprinted at Venice, 1589, and Pesaro, 1602). A secoml edition of this work was published by Carol us Manolessius, entitled Pappi Alexandiini mathematics coUecliones a Federico Commandino Urbinate in latinum conversx et cointnentai iis illustrattc, in hoc nostra edit tone innumeris quibus scatebant mendis et prxcipue in Grxco contextu. diligenter vindicate, Bologna, 1660. The merits of these two works are discussed by Hultsch, who remarks that the editor of the second edition, so far from making good the title and his boastful preface, has actually much marred the original book. Of books which contain parts of Pappus s work, or treat incidentally of it, we may mention the following titles: (1) Pappi Alexandrini col/ectiones mathe- matlcie nunc primum Greece edidit Herm. Jos. Eisenmann, Libri quinti pars altera, Parisiis, 1S24. (2) Pappi Alexandrini Secundi Libri Mathematical Col lectionis Fragmentum e codice MS. edidit Latinum fecit Notitque illvstravit Johannes Wallis, Oxonias, 1688. (3) Apollonii Pergxi de sectione rationis libri duo ex Arabico MSto latine versi, Accedunt eiusdem de sectione spatii libri duo restittiti, Priemittitur Pappi Alexandrini priefatio ad VJJmum collectionismathe- maticx, nunc primum grxce editn : cum lemmatibus eiusdem Pappi ad has Apol lonii librof, Opera et studio Edmundi Halle.y, Oxonii, 1706. (4> Apollonii Pergaii fonicorum libri IV, priores cum Pappi Alexandrini lemmatis tx codd. MSS. Orxcis edidit Edmundus Halleius, Oxonias, 1710. (-5) Der Sammlung des Pappus von Alexandrien siebentes und achtes Buck griechisch und deutsch herausgegeben von C. I. Gerhardt, Halle, 1871. (T. L. H.) PAPUAN LANGUAGES. The languages spoken in NEW GUINEA (q.v.) and other islands peopled by Papuas differ more widely from the Malayo-Polynesian languages than those of the Negritos in the Philippine Islands do from the dialects of the contiguous Malayan tribes. In fact, they form as separate a class by themselves as the Melanesian languages do as contradistinguished from the Polynesian group. From the meagre grammatical sketch of the Mafor (or Nufor) language the only one to which the Dutch missionaries have paid some attention, but which may be taken as a type of the class we gather that the verb has the subject pronoun prefixed in the singular, dual, and plural ; past time is expressed by the word kivdr, "already," prefixed, and futurity by nerri, "still," added to the verb ; certain modifications of the sense are effected by i being prefixed, and others by i being affixed, to the radical vowels a, o, or u, and others again by the substantive affix ia (plur. sici). Much uncertainty, however, still prevails as to the precise import of those grammatical forms. See J. L. van Hasselt s Woordenboek and Beknopte Spraakkunst der Noefoorsche taal, both of which appeared at Utrecht in 1876 ; Fr. Miiller s Grundriss der Sprach- wissenschaft, i., ii. p. 30 sq. ; and more especially G. von der Gabelentz and A. B. Meyer, Beitrdge zur Kenntniss der Melanesischen, Mikronesischen, und Papuanischen Sprachen, Leipsic, 1882, and their essay, " Einiges iiber das Verhaltniss des Mafoor zum Malayischen, " in Bijdragen tot de taal-, land-, en volkenkunde van Neder- landsch- Indie, for 1883. The former of these publications contains also a survey of the literature on the subject. Vocabularies of the languages spoken by the various coast tribes with whom Europeans have come in contact have been collected by S. Miiller, Von Rosenberg, Miklucho Maclay, and others. An intercomparison of those voca bularies not only shows great phonetical divergencies, especially in the liquids r and I, but also in many cases the same absence of word affinity in consequence of which neighbouring Melanesian tribes are known to be unable to understand one another. PAPYRUS, the paper reed, the Cyperus Papyrus of Linnseus, was in ancient times widely cultivated in the Delta of Egypt, where it was used for various purposes, and especially as a writing material. As, however, the plant is now extinct in Lower Egypt, it is believed that it was not indigenous there, but was probably introduced from Nubia, where it is found at the present time, as well as in Abyssinia. Theophrastus (Hist. Plant., iv. 10) adds that it likewise grew in Syria ; and, according to Pliny, it was also a native plant of the Niger and Euphrates. From one of its ancient Egyptian names, P-apu, was derived its Greek title ird-n-vpos, Lat. papyrus. By Herodotus it is always called fivfiXos, a word which was apparently also of Egyptian origin. The first accurate description of the plant is given by Theophrastus, from whom we learn that it grew in shallows of 2 cubits (about 3 feet) or less, its main root being of the thickness of a man s wrist, and 10 cubits in length. From this root, which lay horizontally, smaller roots pushed down into the mud, and the stem of the plant sprang up to the height of 4 cubits, being triangular and tapering in form. The tufted head or umbel is likened by Pliny to a thyrsus. The various uses to which the papyrus plant was applied are also enumerated by Theo phrastus. Of the head nothing could be made but garlands for the shrines of the gods ; but the wood of the root was employed in the manufacture of different utensils as well as for fuel. Of the stem of the plant were made boats, sails, mats, cloth, cords, and, above all, writing material (TO. /3i/3icL). The pith was also a common article of food, and was eaten both cooked and in its natural state. Herodotus too notices its consumption as food (ii. 92), and incidentally mentions that it provided the material of which the priests sandals were made (ii. 37). He likewise refers to the use of byblus as tow for caulking the seams of ships ; and the statement of Theophrastus that King Antigonus made the rigging of his fleet of the same material is illus trated by the ship s cable, otrXov /3vj3ivov, wherewith the doors were fastened when Ulysses slew the suitors in his hall (Odyss., xxi. 390). That the plant was itself used also as the principal material in the construction of light skiffs suitable for the navigation of the pools and shallows of the Nile, and even of the river itself, is shown by sculptures of the period of the fourth dynasty, in which men are represented in the act of building a boat with stems cut from a neighbouring plantation of papyrus (Lepsius, Denkm., ii. 12). It is to boats of this description that Isaiah probably refers in the " vessels of bulrushes i upon the waters " (xviii. 2). If the Hebrew gome (**3) also is to be identified with the Egyptian papyrus, something may be said in favour of the tradition that the bulrushes Papyrus.
