PAPPUS 



PAPYRUS 



745 



return. Pappenheim arrived at Liitzen at the 

 moment when Wallenstein's army was on the 

 point of being completely routed, and at the head 

 of his cuirassiers he charged the left wing of the 

 Swedes with such iury as to throw it into con- 

 fusion, and for a moment change the fortune of 

 the battle. He was mortally wounded in the last 

 charge, and died a few hours afterwards at Leipzig, 

 November 7, 1632, with a smile on his countenance, 

 after learning that Gustavus Adolphus was dead. 

 ' God be praised ! ' he said : ' I can go in peace, 

 now that that mortal enemy of the Catholic faith 

 has had to die before me.' 



Pappus. See COMPOSITE. 



Pappus OF ALEXANDRIA flourished about the 

 end of either the 3d or the 4th century A.D. Which 

 of these dates Ls the more probable it is difficult to 

 determine, owing to conflicting evidence, but recent 

 opinion inclines to the former. Suidas states that 

 Pappus was a contemporary of Theon, thus placing 

 him towards the end of the 4th century, and 

 ascribes several treatises to him. These treatises 

 have not survived, and the only work by which 

 Pappus is now known, his Mathematical 

 Collection, receives no mention from 

 Snidas. This work consisted of eight 

 books, the first and the earlier part of the 

 second of which are lost, and its interest 

 is mainly, though not exclusively, histori- 

 cal. From what remains of the second 

 book, it is conjectured that the first two 

 books were arithmetical. The third book 

 explains some of the methods for the 

 duplication of the cube, treats of the pro- 

 gressions and the five regular polyhedra. 

 The fourth book discusses the figure 

 called the arbelos ( ' a shoemaker's knife ' ), 

 the spiral of Archimedes, the conchoid of 

 Nicomedes, and the quadratrix of Dino- 

 stratus. The fifth book contains some 

 theorems regarding isoperimetrical figures 

 plane and solid, and a short account of 

 the semi-regular solids of Archimedes. 

 The sixth book comments on some of 

 the works of Theodosius, Aristarchus of 

 Samoa, anil Euclid. From the seventh 

 book, which is the longest and most valu- 

 able of the Collection, is derived a large 

 part of our knowledge of Greek geometry. 

 Many of the writings here analysed are 

 no longer extant, and it is on the indi- 

 cations (in the notable instance of 

 Euclid's Porixms, the very obscure indications) 

 which Pappus gives of the object or the contents 

 of them that the geometers of the 17th and 18th 

 centuries relied for their restorations of these 

 writings. The eighth book is devoted mainly to 

 mechanics. The mathematical interest of the Col- 

 lection does not equal the historical, but several of 

 the books contain important theorems, the dis- 

 covery of which is probably due to Pappus himself. 

 One of these has oeen long associated with the 

 name of Guldinus ( 1577-1643). Some others have 

 received a brilliant development from the mathe- 

 maticians of modern times. The last six books of 

 the Mathematical Collection were translated into 

 Latin by Commandinus, an Italian geometer, and 

 were published in 1588 ; another edition appeared 

 in 1660. Fragments of the Greek text have been 

 printed at various times in England, France, and 

 Germany, but the only complete edition is that 

 of Fridericus Hultsch, Pappt Alexandrini Collec- 

 tionis qua supersunt (3 vols. Berlin, 1876-78). 



Papua. See NEW GUINEA. 



Papnles, or PIMPLES, are 'solid small eleva- 

 tions of the skin,' and may be either pale in colour 



or inflammatory and more or less red. Papules 

 occur as an early stage in the development of the 

 eruption in many skin diseases e.g. in eczema, 

 where they speedily become vesicles; or in acne, 

 where they become pustules. The papular diseases 

 proper, where the eruption in its fully developed 

 form consists of papules, are lichen amf prurigo. 



Papy'rus, a genus of plants of the natural 

 order Cyperaceoe, of which there are several species, 

 the most important being the Egyptian Papyrus or 

 Papyrus of the ancients (P. antiq-uorum, Cyperus 

 papyrus of Linna?us) a kind of sedge, 8 to 10 feet 

 high, with a very strong, woody, aromatic, creep- 

 ing root, long, sharp-keeled leaves, and naked, 

 leafless, triangular, soft, and cellular stems, as 

 thick as a man's arm at the lower part, and at their 

 upper extremity bearing a compound umbel of 

 extremely numerous drooping spikelets, with a 

 general involucre of eight long filiform leaves, 

 each spikelet containing six to thirteen florets. 

 By the ancient Egyptians it was called papu, from 

 which the Greek papyrus is derived, although it 

 was also called by them byblos and deltas. The 

 Hebrews called it gome, a word resembling the 



Papyrus. 



Coptic c/om, or ' volume ; ' its modern Arabic name 

 is berdi. The plant is nearly extinct in Lower 

 Egypt, but is found in Nubia (whence it was 

 probably introduced into Egypt) and Abyssinia. 

 It still crows in the Jordan Valley, in the neigh- 

 bourhood of Jaffa, and also of Sidon, in parts of 

 the Sinai Desert, and in Sicily. It is often a con- 

 spicuous feature in African vegetation. It is repre- 

 sented on the oldest Egyptian monuments, and as 

 reaching the height of about ten feet. It was 

 grown in pools of still water, growing ten feet 

 above the water, and two beneath it, and restricted 

 to the districts of Sais and Sebennytus. The 

 papyrus (not merely P. papyrus, but P. dives, 

 which is still found in Egypt) was used for many 

 purposes, both ornamental and useful, such as 

 wreaths for the head, sandals, boxes, boats, and 

 cordage, but the P. papyrus was valued principally 

 for a kind of paper called by its name. Its pith 

 was boiled and eaten, and its root dried for fuel. 

 The papyrus or Paper (q.v. ) of the Egyptians, 

 made of strips of its pith in layers, was of the 

 greatest reputation in antiquity, and it appears 

 on the earliest monuments in the shape of long 

 rectangular sheets, which were rolled up at one 



