617 



POLYGLOTTS. 



POLYGON AND POLYHEDRON. 



618 



a manner as to involve him in very great distress. The whole, of the 

 Complutensian Polyglott is comprised in this of Antwerp, besides 

 another Chaldee paraphrase of a part of the Old Testament, a Syriac 

 version of the New Testament, and the Latin translation of Santes 

 Pagninus, altered by the editor, Arias Montanus. The Old Testament 

 is in four columns, two in each page, a Latin interpretation of the 

 Septuagint forming one of the columns, with a Chaldee paraphrase on 

 the lower part of the left-hand page, and a Latin interpretation on 

 that of the right. In the New Testament the versions are similarly 

 arranged, Syriac being in place of the Hebrew, and the Latin of 

 Pagninus answering to the Latin interpretation of the Septuagint. 

 The types are bold and finely formed, and the paper is of a yellowish 

 cast and of excellent quality. The sixth, seventh, and eighth 

 volumes consist of lexicons, grammars, and other aids for understand- 

 ing the contents of the preceding volumes. Of this Polyglott 500 

 copies only were printed, and the greater number of these were lost in 

 being conveyed by sea to Spain, so that it is more rare than even its 

 predecessor of Complutum. 



III. The Parisian Polyglott. This was printed at Paris, by 

 Antony Vitre, 1628-1645^ in 10 vols. large folio. The editor was 

 Guido Michael le Jay, who at this time was a layman, but afterwards 

 became an ecclesiastic. He had several learned associates, and he 

 might have had the patronage of Cardinal Richelieu, but, refusing this 

 favour and venturing to publish the work at his own expense, he 

 brought ruin upon himself. This splendid performance contains all 

 that is in the two preceding Polyglotts, with the addition of an Arabic 

 vrr-inn of the Old and New Testament, a Syriac version of the former, 

 and the Samaritan Pentateuch. These additions however are made 

 separately, so that, though the Parisian Polyglott contains portions of 

 the Bible in seven languages, its pages do not exhibit at one view more 

 than the Antwerp Polyglott. These ten volumes, in imperial folio, 

 present attractions of no ordinary kind. The paper, though perhaps 

 not so fine as that of the Antwerp Polyglott, is beautiful ; the types 

 are large, clear, and elegantly formed ; the engraver's art moreover is 

 appropriately displayed in furnishing occasional embellishments ; in a 

 word, the Parisian Polyglott is altogether as magmficent a work as can 

 we'll be conceived. 



IV. The London Polyglott. This was edited by the learned Brian 

 Walton, who became afterwards bishop of Chester. It is in six vols., 

 large folio. It was published by subscription, and the volumes came 

 out in the following order : the first volume in September, 1654 ; the 

 second in July, 1655 ; the third in July, 1656 ; and the last three in 



" And thus," says Dr. Twells (' Life of Pocock'), " in about 

 four years was finished the English Polyglott Bible, the glory of that 

 age, and of the English church and nation, a work vastly exceeding all 

 former attempts of that kind, and that came so near perfection as to 

 discourage all future ones." Some portions of this Polyglott are 

 printed in seven languages, all open at one view. No one book is 

 given in nine languages ; but nine languages are used in the course of 

 the work, namely, Hebrew, Chaldee, Samaritan, Syriac, Arabic, 

 Persian, Ethiopic. Greek, and Latin. A vast body of introductory 

 matter is in the first volume, and the sixth ia made up of various 

 reelings, critical remarks, &c. Brian Walton was assisted by a number 

 of men who formed a constellation of oriental and general scholars, 

 such as perhaps have appeared together at no other period during the 

 whole history of our country. One of these men was Dr. Edmund 

 Castell, who published his ' Lexicon Heptaglotton' in 1669, two vols., 

 folio. This is a lexicon of the seven oriental languages occurring in 

 Walton's Pulyglott, and it has grammars of all these languages pre- 

 fixed. It generally accompanies the Polyglott, which can hardly be 

 pronounced complete without it. Walton's work is by no means equal 

 in appearance to the three preceding Polyglotts, but in point of solid 

 usefulness to the biblical scholar it is far beyond any one of them. 

 The eight volumes form an extraordinary collection of aids for study- 

 ing the original scriptures. As the London Polyglott is frequently 

 found in private libraries, a more minute description of its contents 

 appears to be unnecessary. Its history is recorded at length in Arch- 

 deacon Todd's ' Memoirs of the Life and Writings of the Right Rev. 

 Brian Walton, D.D., lord bishop of Chester/ 2 vols. 8vo., London, 

 1821, a work which comprises also notices of all Walton's co- 

 adjutors. 



V. Bagster's Polyglott. This work was published by the enterpris- 

 ing bookseller by whose name it is known, in 1 voL folio, London, 

 1831. The Old Testament is in eight languages, and the New Testa- 

 ment in nine. Eight languages are exhibited at once upon opening 

 the book. The languages are Hebrew, Greek, English, Latin, German, 

 Italian, French, Spanish, and Syriac, the New Testament being given 

 in the last language as an appendix. To these are added the Samaritan 

 Pentateuch in Hebrew characters ; the notes and readings of the 

 Maxorites ; the chief variations of the Vatican text of the .Septuagint 

 (which is followed in this Polypi. ,tt), ;ind of the Alexandrian as 

 ^ivi-71 by Grabe, Oxford; and of the Greek Testament the whole ol 

 the selected vari" < given by Griesbach in his own edition of 



. 1805. Prefixed to the work are fifty pages of prolegomena in Latin 

 by Professor Lee, of Cambridge. The types are small, but <! 

 elegant, and the paper is of excellent quality. The whole volume pre- 

 sents a very handsome appearance. 



< >n the subject of Polyglott Bibles in general, the reader will be 



gratified by consulting Home's ' Introduction ;' Butler's ' Hora 

 Jiblicse ;' Clarke's ' Bibliographical Dictionary ;' Le Long's ' Biblio- 

 ,heca Sacra,' improved by Masch. There are many more Polyglotts 



than these we have mentioned. Among the latest is a ' Biblia Poly- 



glotta,' in four languages Hebrew, Greek, Latin, and German ; it was 

 mblished during 1850-55, under the editorship of Dr. R. Stier and 

 Dr. Theile. It contains, vol. i., the Pentateuch ; vol. ii., the historical 

 woks and the Prophets, Daniel excepted ; vol. iii., the poetical books, 

 Daniel, and miscellaneous ; vol. iv., the New Testament. 

 PO'LYGON and POLYHEDRON. The word polygon means figure 



of several angles, and polyhedron means solid of several faces : the first 

 s used for a plane bounded by straight lines, the second for a solid 

 sounded by planes. We shall in this article state the general 



properties of both kinds of figures, reserving the particular consideration 

 >f those which have equal sides or equal faces for the articles REGULAR 



FNJI-RES, SOLIDS, &c. 



The Elements of Euclid confine themselves to convex polygons, and 

 jo a limited number of polyhedrons. The most general propositions 



with respect to polygons as polygons, that is, which are true whatever 

 ;he number of sides may be, are as follows : they are either in the 

 Elements or immediately deducible from them. 



1. The internal angles of a polygon of n sides are together always 

 equal to n 2 pairs of right angles. See ROTATION for the full meaning 

 of this proposition. 



2. \Vhen a figure of an even number of sides is inscribed in a circle, 

 the sum of the first, third, fifth, &c., angles is equal to the sum of the 

 second, fourth, sixth, &c., angles. But when a figure of an even number 

 of sides is described about a circle, for angles read sides in the preceding 

 property. 



3. Any one side of a polygon is less than the sum of all the others. 

 The first-mentioned theorem remains true beyond the limits of 



Euclid's meaning, namely, so long as the figure 

 of n sides can in any way be divided into n 2 

 triangles : that is, in fact, as long as no side of 

 the figure crosses any other side. Thus the 

 adjoining polygon of 10 sides, being divisible 

 into 8 triangles, has the sum of all its angles 

 equal to 16 right angles, four of these angles 

 being each greater than two right angles. 



To make a rule which'shall connect the angles 



of any polygon whatsoever, that is, of any figure, however irregular, 

 hi which a point returns by a succession of straight lines to the point 

 from whence it set out, would be difficult in the ordinary way t>f 

 measuring angles. On this subject see Siutf. 



A polygon of n sides or edges has one face, and n angular points or 

 corners : that is, the number of faces and corners together exceed the 

 number of edges by 1. On one side of the polygon let another polygon 

 be described : it is then obvious that the two polygons have two 

 comers in common, but only one edge, or else three corners and two 

 edges, Ac, ; that is, whatever nca corners are added, one more new 

 edge is added : or, since one face is added, the number of faces and 

 corners is increased by the same as the number of edges. The same 

 may be proved of every new polygon which has one or more sides in 

 common with any of the old ones : and since at the outset the number 

 of corners and faces exceeds the number of edges by 1, and since every 

 alteration adds the same to both sides of this equation, it remains true 

 throughout. Whence the following theorem : let any number of 

 polygons, in the same plane or not, bu so connected that each has ono 

 side or more in common with one or more of the others : call each 

 polygon one face ; each side, to how many polygons soever it may 

 belong, one edge ; and each angular point, no matter how many angles 

 may be collected there, one corner : the number of faces and corners 

 will always exceed the number of edges by one. 



Lit there be a solid polyhedron, and beginning from one given face, 

 annex the others successively : the preceding theorem will remain true, 

 so long as each face which is added adds one or more new edges. But 

 it is obvious that when the polyhedron is completely finished, with the 

 exception of the last face, the completion of the solid, by counting the 

 last face, adds no new edge and no new corner, these having been com- 

 pletely laid down in former faces. Hence,* in every solid poly- 

 hedron, the number of faces and corners exceeds the number of edges 

 by two. 



Again, on a given face of a polyhedron as a base, let a second poly- 

 hedron be constructed, and on a given face of that a third, and so on, 

 it being permitted to include several faces from different polyhedrons 

 among the faces of the new one. In the part of each new polyhedron 

 which belongs to the preceding ones, as already shown, the corners and 

 faces exceed the number of edges by one ; and the same also in the 

 new portion. But since one new polyhedron is added at every step, it 

 follows that the new faces and corners are the same in number as the new 

 edges and polyhedron. But at the beginning, counting one polyhedron, 

 the faces and corners outnumber the edges and polyhedron by one (since 



* The present mode of demonstrating this well known theorem was given, 

 for the first time to his knowledge, by the author of this article, in the ' Phil. 

 Mag.' j but he has since found that it in substantially containe<t (under mathe- 

 matical symbol" which rather conceal its simplicity) in a memoir by M. Cauchy, 

 in the ' Journal de 1'Ecole Polytechniquc.' 



