POL 



POL 



plants, may be given in the palmetto, 

 ginseng, Indian date plum. 3, Herma- 

 phrodite and female on the same plant, 

 as in the peliitory and oracle. 4. Her- 

 maphrodite and female on different plants, 

 as in most species of the ash-tree. 



POLYGAMY, a plurality of wives or 

 husb.tnds, in the possession of one man 

 or woman, at the same time. 



POLYGLOTT, among divines and cri- 

 tics, chiefly denotes a Bible printed in 

 several languages. In these editions of 

 the Holy Scriptures, the text in each lan- 

 guage is ranged in opposite columns. The 

 first polyglott Bible was that of Cardinal 

 Ximenes, printed in 1517, which con- 

 tains the Hebrew text, the Chaldee Pa- 

 raphrase on the Pentateuch, the Greek 

 version of the LXX., and the ancient 

 Latin version. After this, there were 

 many others, as the Bible of Justiniani, 

 Bishop of Nebio, in Hebrew, Chaldee, 

 Greek, Latin, and Arabic; the Psalter, 

 by John Potken, in Hebrew, Greek, 

 Ethiopic, and Latin ; Plantin's Polyglott 

 Bible in Hebrew, Chaldee, Greek,' and 

 Latin, with the Syriac version of the New 

 Testament; M. le Jay's Bible, in Hebrew, 

 Samaritan, Chaldee, Greek, Syriac, La- 

 tin, and Arabic; Walton's Polyglott, 

 which is a new edition of Le Jay's Poly- 

 glott, more correct, extensive, and per- 

 fect, with several new oriental versions, 

 and a large collection of various readings, 

 &c. 



POLYGON, in geometry, a figure with 

 many sides, or whose perimeter consists 

 of more than four sides at least : such are 

 the pentagon, hexagon, heptagon, &c. 



Every polygon may be divided into as 

 many triangles as it has sides ; for if you 

 assume a point, as a, (see Plate XII. 

 Miscel. fig. 14), any where within the 

 polygon, and from thence draw lines to 

 every angle, a b, a c, a d, &c. they shall 

 make as many triangles as the figure has 

 sides. Thus, if the polygon hath six 

 sides (as in the figure above) the double 

 of that is twelve, from whence take four, 

 and there remains eight : 1 say, that all 

 the angles, b, c, d, e, f, g. of that poly- 

 gon, taken together, are equal to eight 

 right angles. For the polygon having 

 six sides, is divided into six triangles; 

 and the three angles of each by 1.32 

 Eucl. are equal 10 two right ones ; so 

 that, all the angles together make twelve 

 right ones ; but each of these triangles 

 hath one xag-Je in the point, , and by it 

 they complete the space round the same 

 point ; and all the angles about a point 

 are known to be equal to four right 



ones, wherefore those four taken from 

 twelve, leave eight, the sum of the right 

 angles of the hexagon. So it is plain the 

 figure hath twice as many right angles as 

 it hath sides, except four. 



Every polygon circumscribed about a 

 circle, is equal to a rectangle d-triangle, 

 one of whose legs shall be the radius of 

 the circle, and the other the perimeter 

 (or sum of all the sides) of the polygon. 

 Hence, every regular polygon is equal to 

 a rectangled-triangle, one of whose legs 

 is the perimeter of the polygon, and the 

 other a perpendicular drawn from the 

 centre to one of the sides of the polygon. 

 And every polygon circumscribed about 

 a circle is bigger than it; and every 

 polygon inscribed is less than the circle, 

 as is manifest, because the thing con- 

 taining is always greater than the thing 

 contained. The perimeter of every poly- 

 gon circumscribed about a circle, is 

 greater than the circumference of that 

 circle, and the perimeter of every poly- 

 gon inscribed is less. Hence, a circle is 

 equal to a right-angled triangle, whose 

 base is the circumference of the circle, 

 and its height the radius of it. 



For this triangle will be less than any 

 polygon circumscribed, and greater than 

 any inscribed ; because the circumfer- 

 ence of the circle, which is the base of 

 the triangle, is greater than the compass 

 of any inscribed, therefore it will be 

 equal to the circle. For, if this triangle 

 be greater than any thing that is less than 

 the circle, and less than any thing that is 

 greater than the circle, it follows, that it 

 must be equal to the circle. This is 

 called the quadrature, or squaring of the 

 circle ; that is, to find a right-lined figure 

 equal to a circle, upon a supposition that 

 the basis given is equal to the circum- 

 ference of the circle ; but actually to find 

 a right line equal to the circumference 

 of a circle, is not yet discovered geome- 

 trically. 



POLYGON, in fortification, denotes the 

 figure of a town, or other fortress. The 

 exterior or external polygon is bounded 

 by lines drawn from the point of each 

 bastion to the points of die adjacent bas- 

 tions ; and the interior polygon is formed 

 by lines joining the centres of the bas- 

 tions. 



POLYGONS, prob' .'ins concerning. 1. On 

 a regular polygon to circumscribe a cir- 

 cle, or to circumscribe a regular polygon 

 upon a circle ; bisect two of the angles 

 of the given polygon, A anclB, (fig. 15), 

 by the right lines, A F, B F ; and on the 

 point, P, where they meet, with the 



