t a L, 
and in the natural method ranking under the 
12 tli order, holoraeeae. The calyx is triphyl- 
Jous ; and there are live calciform petals, 
with one seed almost naked. There are five 
species, of no note. 
POL\ GALA, millcwort, a genus of the 
octandria order, in the diadelphia class of 
plants, and in the natural method ranking 
under the 33d order, lomentacese. The ca- 
lyx is pentaphyllous, with two of its leaflets 
wing-shaped and coloured ; the legumen is 
obcordate and bilocular. There are 45 spe- 
cies, of which the most remarkable are: 
1. The vulgaris, or common milkwort, is 
a native ot the British heaths and pastures. 
The root of this plant has a bitter taste, and 
has been found to possess the virtues of the 
American rattlesnake root. It purges with- 
out danger, and is also emetic and diuretic; 
sometimes operating all the three ways at 
once. A spoonful of the decoction made by 
boiling an ounce of the herb in a pint of wa- 
ter till one-halt has exhaled, has been found 
serviceable in pleurisies and fevers, by pro- 
moting a diaphoresis and expectoration ; and 
three spoonfuls of the same taken once an 
hour, has proved beneficial in the dropsy and 
anasarca. It has also been found serviceable 
in consumptive complaints. 
2. The senega, or seneka, rattlesnake- 
wort, grows naturally in most parts of North 
America. 1 he root ot this species operates 
more powerfully than the last ; but besides 
the virtues of a purgative, emetic, and diu- 
retic, it has been recommended as an anti- 
dote against the poison of a rattlesnake ; but 
this opinion is now exploded. It still, how- 
ever, maintains its character in several dis- 
orders. Its efficacy, particularly in pleuri- 
sies, is most fully established in Virginia: 
formerly near flity out of one hundred died 
of that distemper ; but by the happy use of 
this root hardly three out of the same number 
have been lost. 
As the seeds of the r. ttlesnake-wort sel- 
dom succeed even in the countries where the 
plant is a native, the best method of propa- 
gating it is to procure the roots from Ame- 
rica, and plant them in a bed of light earth in 
a sheltered situation, where they will thrive 
without any other culture than keeping them 
free from weeds. But though the plant will 
stand out ordinary winters, it will be proper 
to cover it during that season with old tan- 
ner’s bark, or other mulch, to keep out the 
frost. 
POLYGAMIA {moxat, man y, and 7«/aoj, 
marr.ag ). 1 his term, expressing an inter- 
communication of sexes, is applied, bv Lin- 
naeus, both to plants and llo > ers. A polyga- 
mous plant is that which bears both herma- 
maph'rodite flowers and male or female, or 
both. 
POLYGAMY, the plurality 7 of wives or 
husbands, m the possession ot one man or 
woman, at the same time. By the laws of 
England, polygamy is made felony, except 
in the case oi absence beyond the seas for 
seven years; and where tile absent person is 
living in England, Wales, or Scotland, and 
the otiier party has notice cA it, such marry- 
ing is felony bv the statute 1 Jac. 1. c. 11. 
POLYG LOTT, among divines and cri- 
tics, chiefly denotes a bible printed in several 
languages. In these editions of the holy 
scriptures, the text in each. language is ranged 
io opposite columns. 
PO L 
Tile first polyglott bible was that of 
cardinal Xiinenes, printed in 1517, which 
contains the Hebrew text, the Chaldee para- 
phrase on the pentateuch, the Greek version 
ot the LXX, and the antient Latin version. 
After this, there were many others : as the 
bible 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 poly- 
glott 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, Latin, 
and Arabic ; Walton’s polyglott, which is a 
new edition ot Le Jay’s polyglott, more cor- 
rect, 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 polygon may be divided into as 
many triangles as it has sides : for if you as- 
sume a point, as a (Plate Miscel. fig. 191), 
any where within the polygon, and from 
thence draw lines to every angle ab, ac, ad, 
&c. they shall make as many triangles as the 
figure has sides. Thus, if the polygon has 
six sides (as in the figure above), the double 
of that is twelve, from whence take four, and 
there remain eight : then all the angles b, c, 
d, e,f, g, of that polygon, taken together, 
are equal to eight right angles. For the 
polygon having six sides, is divided ipto six 
triangles ; and the three angles of each, by 
1. 32 End. are equal to two right ones; so 
that all the angles together make twelve right 
ones: but each of these triangles has 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 
angles ot the hexagon. 
So it is plain the figure has twice as many 
right angles as it has sides, except four. 
2. E. D. 
Every polygon circumscribed about a cir- 
cle is equal to a rectangled triangle, one ot 
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 re- 
gular polygon is equal to a rectangled tri- 
angle, one of whose legs is the perimeter of 
the polygon, and the other a perpendicular 
drawn trom the centre to one of the sides of 
the polygon. And every polygon circum- 
scribed about a circle is bigger than it, and 
every polygon inserted is less than the circle; 
as is manifest, because the thing containing is 
al.vuys less than the thing contained. 
The perimeter of even polygon circum- 
scribed about a circle is greater than the cir- 
cumference of that circle, and the perimeter 
ot every polygon inscribed b 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 anv 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 inscribed, 
therefore it will be equal to the circle. Tor, 
d this triangle is greater than any thing that 
POL 4 79 
is less than the circle, and less than any 
thing that is greater than the circle, it fol- 
lows that it must be equal to the cin le. Thi% 
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 actually to find a right line 
equal to t he circumference of a circle, is not 
yet discovered geometrically. See Circle. 
Probl vis concerning polngons. 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 (Plate Miscell. tig. 192), 
by the right lines AF, BF ; and on the point 
F, where they meet, with the radius AF, 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 construct 
the polygon as in the following problem. 
2. On a given line to describe any given re- 
gular polygon. Find the angle oi the poly- 
gon in the table, and in E s r et. off an angle 
equal thereto ; then drawing EA = ED, 
through the points E, A, D, describe a c ircle, 
and in this applying the given right line as 
often as you can, the polygon will be de- 
scribed. 3. To find the sum of all the an- 
gles in-any given regular polygon. Multiply 
the number of sides by 180°; from the pro- 
duct subtract 360°, and the remainder is the, 
sum required: thus, in a pentagon, 180 x o 
— 900, and 900 — 360 = 540 =. the sum of > 
all the angles in a pentagon. 4. To find the 
area of a regular polygon. Multiply one side 
ot the polygon by halt the number of sides ; 
and then multiply this product by a perpen- 
dicular let fall irom the centre of the circum- 
scribing circle, and the product will be the 
area required : thus, it AB (the side of a pen- 
tagon) = 54 x 2\ — 135, and 135 X 29 ‘ 
(the perpendicular) == 3915 = the area re- 
quired. 5. To find the area of an irregular 7 
polygon, let it be resolved into triangles, and 
the sum of the areas ol these will be the area- 
of the polygon. 
the following Table exhibits the most re- 
markable particulars in all the polygons, up to 
the dodecagon of 12 sides ; viz. the angle at the 
centre, the angle of the polygon, and the area 
of the polygon, when each side is 1. 
No. of 
sides. 
Name of 
polygon. 
Angle 
at cent 
Angleof 
polyg. 
Area. 
3 
Trigon 
120° 
60° 
0.4330127 
4 
Tetragon 7 
90 
90 
1.0000000 
5 
Pentagon 
72 
108 
1.7204774 
6 
Plexagon 
60 
120 
2.5980762 
7 
Heptagon 
51.3 
y 
3.6339124 
8 
Octagen 
45 7 
135 
4.8284271 
9 
Nonagon 
40 
140 
6.1818242 
10 
Decagon 
36 
144 
7.6942088 
11 
Undecagon 
32—— 
I47 t 3 t 
9.3656399 
12 
Dodecagon 
30 
150 
11.1961524 
: olygon", in. fortification, denotes tire 
figure of a town or other fortress. 
The exterior or external polygon is bound- 
ed by lines drawn from the pomt of each ba-- 
; lion. to the points of the adjacent bastions.-. 
And the interior polygon is formed bv hues , 
joining the centres of the bastions. . 
Line of Polygons, on the French, sec tors, , 
