POL 
husbands, in the possession of one man or 
woman, at the same time. 
POJjYGLOTT, among divines and cri- 
tics, chiefly denotes a Bible printed in se- 
veral languages. In these editions of tlie 
Holy Scriptures, the text in each language 
is ranged in opposite columns. The first 
polyglott Bible, was that of Cardinal Xi- 
Jnenes, printed in 1517, which contains the 
Hebrew text, the Chaldee Paraphrase on 
the Pentateuch, the Greek version of the 
LXX., and the ancient Latin version. Af- 
ter this, there were many others, as tiie Bi- 
ble of Justiniani, Bishop of Nebio, in He- 
brew, Chaldee, Greek, Latin, and Arabic ; 
the Psalter, by John Potken, in Hebrew, 
Greek, Ethiopic, and Latin ; Plantin’s Po- 
lyglott Bible, in Hebrew, Chaldee, Greek, 
and Latin, with the Syriac version of the 
New Testament ; M. le Jay’s Bible, in He- 
brew, Samaritan, Chaldee, Greek, Syriac, 
Latin, and Arabic; Walton’s Polyglott, 
which is a new edition of Le Jay’s Poly- 
glott, more correct, extensive, and perfect, 
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 polygori may be divided into as 
many triangles as it has sides; for if you as- 
sume a point, as a, (see Plate XII. Miscel. 
fig. 14), any where within the polygon, and 
from thence draw lines to evei y angle, a h, 
ac, ad, &c, they shall make as many trian- 
gles as the figure has sides. Thus, if the po- 
lygon hath six sides (as in the figure above) 
the double of that is twelve, from whence 
take four, and there remains eight : I say, 
that all the angles, b, c, d, e,f, g, of that po- 
lygon, 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 
to two right ones ; so that all the angles to- 
gether make twelve right ones; but each 
of these triangles hath one angle in the 
point, a, 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 an- 
gles of the hexagon. So it is plain the fi- 
gure hath twice as many right angles as it 
hath sides, except four. 
Every polygon circumscribed about a 
circle, is equal to a rectangled-triangle, one 
POL 
of whose legs shall be the radius of the cir- 
cle, and the other the perimeter (or sum of 
all the sides) of the polygon. Hence, evei-y 
regular polygon is equal to a rectangled-tri- 
angle, 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 circum- 
scribed about a circle is bigger than it ; and 
ever y polygon inscribed is less than the circle, 
as is manifest, because the thing containing 
is always greater than the thing contained. 
The perimeter of every polygon circumscrib- 
ed about a circle, is greater tlian tire circum- 
ference of that circle, and the perimeter of 
every polygon inscribed is less. Hence, a 
circle is equal to a right-angled triangle, 
whose base is the circumference of the cir- 
cle, and its height the i-adius of it. 
For this triangle will be less than any po- 
lygon circumscribed, and greater than any 
inscribed ; because the circumference of 
the circle, which is the base of the triangle, 
is greater than the compass of any inscrib- 
ed, 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 cir- 
cle, it follow's, 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 circumference of the circle; but ac- 
tually to find a right line equal to the cir- 
cumference of a circle, is not yet discover- 
ed geometrically. 
Polygon, in fortification, denotes the 
figure of a town, or other fortress. The 
exterior or external polygon is bounded by 
lines drawn from tlie point of each bastion 
to the points of the adjacent, basliops ; and 
the interior polygon is formed by lines join- 
ing tlie centres of the bastions. 
Polygons, problems concerning. 1. On 
a regular polygon to circumscribe a circle, 
or to circumscribe a regular polygon upon 
a circle : bisect two of the angles of the 
given polygon, A and B, (fig. 15), by the 
right lines, A F, B F ; and on the point, F, 
where they meet, with the radius, A F, de- 
scribe a circle, which will circumscribe the 
polygon. Next to circumscribe a polygon, 
divide 360 by the number of sides required, 
to find e F d; which set off from the centre, 
F, and draw the line, de, on which con- 
struct the polygon as in the following pro- 
blem. 2. On a given line to describe any 
given regular polygon ; find the angle of the 
