4 SO 
B O L 
POL 
? O L 
is a line containing the homologons sides 
ot the first nine regular polygons inscribed 
in the same circle ; that is, from an equilate- 
ral triangle to a dodecagon. 
POLYGONAL NUMBERS, are so call- 
ed because the units whereof they consist 
may be disposed in such a manner as to re- 
present several regular polygons. 
1 he side of a polygonal number is the 
number of terms of the arithmetical progres- 
sion that compose it ; and the number of an- 
gles is that which shews how many angles 
that figure has,. whence the polygonal num- 
ber takes its name. 
To find a polygonal number, the side and 
number of its angles being given, the canon 
is this : the polygonal number is the semi- 
difference of the fac turns of the square of the 
side into the number of angles diminished by 
two units, and of the side itself into the num- 
ber of angles diminished by four units. 
The several sorts of polygonal numbers, 
viz. the triangles, squares, pentagons, hexa- 
gons, &c. are formed from the addition of 
the terms of the arithmetical series, having 
respectively their common difference 1, 2, 3, 
4, &c. ; viz. if the common difference of the 
arithmetical is 1, the sums of their terms will 
form the triangles ; if 2, the squares ; if 3, 
the pentagons; if 4, the hexagons, &c. 
Thus : 
Arith. Prog. 1,2, 3 , 4, 5 , 6', 7. 
Trian. Nos. 1,3, 6 , 10 , 15 , 21 , 28 . 
Arith Prog. 1,3, 5 , 7, 9 , 11 , 13 . 
Square Nos. 1,4, 9 , 16 , 25 , 36 , 49 . 
{ Arith. Prog. 1,4, 7,10,13,16,19. 
( Pentag. N os. 1 , 5 , 1 2 , 22 , 35 , 5 1 , 70 . 
s Arith. Prog. 1,5, 9 , 13 , 17 , 21 , 25 . 
| Hexag. Nos. 1 , 6 , 15 , 28 , 45 , 66 , 91 
The sums of polygonal numbers collected 
in the same manner as the polygonal num- 
bers themselves^ are, out of arithmetical pro- 
gressions, are called pyramidal numbers. 
POLYGONUM, knot-grass, a g- mis of 
the trigynia order, in the octandria class of 
plants, and in the natural method ranking 
under the 1 2th order, holoraceae. There is 
no calyx ; the corolla is quinquepartite and 
calycine, or serving instead of a calyx ; there 
is one angulated seed. There are 36 spe- 
cies ; but the most remarkable, are : 
1. The bistorta, bistort, or greater snake- 
weed. 2. The viviparum, or smaller bistort. 
Both these perennials flower in May and 
June, succeeded by ripe seeds in August. 
They grow wild in England, &c. ; the first 
in moist, the other in mountainous situations. 
3. Oriental polygonum, commonly called 
persicaria. 4. i'agopyrum, buck-wheat or 
brank, rises with an upright, smooth, branchy 
stem, from about a foot and a half to a yard 
high, heart-shaped sagittated leaves, and the 
branches terminated by clusters of whitish 
flowers, succeeded by large angular seeds, 
excellent for feeding pigeons and most sorts 
of poultry. 
The root of a kind of bistort, according. to 
Gmelin; is used in Siberia for ordinary food. 
This species is by Haller called bistorta foliis 
ad oram nervosis, and by some other bota- 
nists bistorta montana minor. The natives 
call it mouka ; and so indolent are they, that, 
to save themselves the trouble of digging it 
out of the earth, they go in spring and pillage 
the holes of the mountain-rats, which they 
find filled with these roots. In our country, 
bistort is used as a medicine. All the parts 
of bistort have a rough austere taste, parti- 
cularly the root, which is one of the strongest 
of the vegetable astringents. It is employed 
in all kinds of immoderate haemorrhages and 
other fluxes, both internally and externally, 
where astringency is the only indication. It 
is certainly a very powerful styptic, and is to 
be looked on simply as such ; the sudorific, 
anti-pestilential, and other like virtues ascri- 
bed to it, it has no other claim to, than in 
consequence of its astringency, and of the 
antiseptic power which it has in common 
with other vegetable styptics. The largest 
dose of the root in powder is a single drachm. 
POLYGYNTA, among botanists, denotes 
an order or subdivision of a class of plants; 
comprehending such plants of that d ass as 
have a great number of pistils, or female or- 
gans of generation. See Botany. 
POLYHEDRON, in geometry, denotes a 
body or solid comprehended under many 
sides or planes. A gnomic polyhedron is a 
stone with several laces, whereon are ' de- 
scribed various kinds of dials. 
Polyhedron, polyscope, in optics, is a 
multiplying-glass or lens, consisting of several 
plane surfaces disposed into a convex form. 
See Optics. 
POLYMNTA, a genus of the poly garni a 
necessaria order, in the syngenesia class of 
plants, and in the natural method ranking 
under the 49th order, composite. The re- 
ceptacle is paleaceous ; there is no pappus; 
the exterior calyx is tetraphyllous, or penta- 
plyllous ; the interior decaphyllous, and com- 
posed of concave leaflets. There are five 
species. 
POLYNEMUS, polyneme, a genus of 
fishes of'the order abdominales. The gene- 
ric character is, head compressed, covered 
with scales; snout very obtuse and promi- 
nent ; gill-membrane five or seven-rayed ; 
separate filaments or setaceous processes near 
the base of the pectoral fins. 
1. Polynemus paradiseus. The genus po- 
lynemus may be considered as holding the 
same station among the abdominal fishes 
which the genus trigla does among the tho- 
racic; being distinguished by a similar cir- 
cumstance, viz. that of being furnished on 
each side, near the base of the pectoral fins, 
with several separate processes or articulated 
rays: these are, in general, much longer and 
more setaceous than in the trigla?, and, in some 
species, even exceed the length of the whole 
body. The species of polyneme are not 
very numerous, and are chiefly confined to 
the warmer latitudes. 
The polynemus paradiseus,' or mango-fish, 
as it is generally called, which seems to have 
been one of the first of the genus known to 
the Europeans, is an inhabitant of the Indian 
and American seas, and grows to the length 
of about 12 or 15 inches. It is a fish of an 
elegant shape, moderately broad in the mid- 
dle, and gradually tapering towards the tail, 
which is very deeply forked ; the scales are 
of moderate size, those towards the head and 
tail smaller than the rest ; the thoracic fila- 
ments are of excessive length, the superior or 
outward ones often extending far beyond the 
tail; the others gradually shorten, the first or 
lowermost extending about half the length of 
the body. The colour of this fish is gene- 
rally described as yellow, and its popular 
name of mango-fish is supposed to have been 
given it from that circumstance, as resets*-,' 
biing the colour of a ripe mango. Dr. Rus- 
sel, in his work on the Indian fishes, informs 
us, that the mango-fish is reckoned by much 
the. most delicate of any found at Calcutta. 
2. Polynemus plebeius. General appear- 
ance that of a mullet, but with the head very 
obtuse in front, the mouth appearing as if 
placed beneath ; colour silvery grey, with a 
dusky tinge on the upper parts, and several 
dusky lines running from head to tail above 
the lateral line ; scales rather large ; all the 
fins scaly to some distance from the base ; 
tail forked; thoracic filaments five in num- 
ber on each side; the first of these is said by 
Gmelin to exceed the length of the body, 
the rest decreasing gradually. 
This species is a native of the Indian 
and American seas, and is found about the 
coasts of several of the southern islands. It 
arrives at a very large size, measuiing up- 
wards of four feet in length. It is considered 
as an excellent fish for the table, and is in 
much esteem among the inhabitants of the 
Malabar coast. It is dressed in various ways, 
and is sometimes dried and salted for sale. 
Dr. Bloch informs us, on the authority of a 
correspondent on whom he could rely, that 
this fish is commonly known in India by the 
title of royal fish, on account of its excel- 
lence, and laments that Broussonet (who 
seems to have named it from its want of par- 
ticular splendour) should have given it the 
title of P. plebeius. 
3. Polynemus niloticus. This, according 
to Mr. Bruce, who describes and figures it in 
the Appendix to his Travels, is a large spe- 
cies, and may vie, for the elegance both of 
its form and taste, with any fish inhabiting 
the rivers running either into the Mediterra- 
nean or the ocean. The specimen from 
which Mr. Bruce’s figure was taken weighed 
32 pounds, but is said often to arrive at the 
weight of 70 or more. It is an inhabitant of 
the river Nile, where it is by no means un- 
common as far up the river as Syene and 
the first cataract. The whole body is cover- 
ed with scales of a brilliant silver-colour, so 
as to resemble spangles lying close together ; 
and there is no variety of tinge on the fish, 
except a shade of red on the end of the nose, 
which is fat and fleshy. 
We are informed by Mr. Bruce, that in 
order to take this fish, the Egyptian peasants 
prepare a pretty large mass or cake, consist- 
ing of oil, clay, flour, honey, and straw, 
kneading it with their feet till it is well incor- 
porated. They then take two handfuls of 
dates and break them into pieces about the 
size of the point of a finger, and stick them 
in different parts of the mass; into the heart 
of which they put seven or eight hooks with 
dates upon them, and a string of strong whip- 
cord to each. This' mass of paste is then 
conveyed by the fisherman or shepherd into 
the stream, the man sitting for this purpose 
on a blown up goat-skin. A\ hen arrived at 
the middle, he drops the mass in the deepest 
part of the stream ; and cautiously holding 
the ends of each of the strings slack, so as 
not to pull the dates and hocks out of the 
middle of the composition, he makes to shore 
again, a little below the speit where he has 
sunkjthe mass; and separating the ends of the 
strings, ties each of them, without straining, 
to a palm-branch fastened on the shore, to 
the end of which is fastened a small bell. 
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