POL
319
POM
H
Hat t*v e ^ lightened by such ornamentation. We regretH p rg . 1,1 the present day any prejudices should be found^’hlinog a o a 'nst its introduction into our ecclesiastical^'Urchgg ’• ' Ve * lave > however, more than one of our recent? n< l We f V 1 w hich such assistance has not been despised ;^<11*0 ^ SUre that tliP f*rmfrn«t hptwppn siii’h ami flip. p.nlfl^all a
an d the grand effect of their buildings was con-
e ^r v
sure that the contrast between such and the cold-ry p . uf the majority, will at length prevail againstflis tor ri (i^ u< ^ ce - aie S* a d to be able to allude, also, to theR ^ a hli(. < u 1 *his art to its proper position, in the instance ofHat it s U| lding such as the British Museum , and we trustI“OLypS? ss there will lead to its general adoption.
Hte, for m an ornament prevalent in Gothic arcliitee-
'^’fcles 6< * a m °ulding, disposed in a number of segments,ei 'ta e ^ ‘ ’ Producing projecting points at their intersections,^ u,/ll 'ef 0 jp >S e ' thus we have trefoil, consisting of three cusps;
POLyrw! hour ; and polyfoil, of any number above four.atl( l ytovtct (f rom rroXvyuivoQ, formed from iroXvg, many,B ' eter cons' 0 ”®^ a multilateral figure, or one whose peri-ls ts of more than four sides and angles.
'■*»«}. jj ait * es and angles be equal, the figure is called at) d' 01 ' similar polygons, see Similar.
- e t r sit] es S a, ( e distinguished according to the number of- • 1 hose of five sides are called pentagons ; those
-i!“
of
-. V) flpsy, V4 Ittc OIUL-O UlO vanvu f
®9°ns ; those of seven, heptagons; those of eight,I> 0 , > «c. ‘
b 6 nSZ*- General Properties of.
8 ’tiany t'- 1 ® ’—h- That every polygon may be divided intojargon, t ri L n8les as il hat' 1 sides. 2. The angles of anyj| a, ing ’f _ en together, make twice as many right angles,f H fiv e g 1 -",'’ as the figure hath sides. Thus, if the polygon,, UUr > tlie r g es ’ the double of that is ten ; whence, subtractingOK^Hbed ^ e , mains six right angles. 3. Every polygon, cir-tfi 6 °i wl 10 , ut; a circle, is equal to a right-angled triangle,e e peri^ , Se e S s is the radius of the circle, and the otheref er f f e» u i er ’ or surn of all the sides of the polygon. Hence,8 ' v hose e ] e ai P°b'gon is equal to a right-angled-triangle, onetli^'P-’Uli * S the perimeter of the polygon ; and the otherft tl >0 *>'' , 'on U Ar ’ c * rawn from the centre to one of the sides of
’ enee °.uiso,
c - r n il s
^•^tno j 6 SatlQe likewise appears hence, that the thingc h‘c| n ’ . l ^per^ Vei S leater than the thing contained.
“ygon.
n • i •
r gi;r tlvm *°’ ever y potygon circumscribed about a circle is
and
f°'iQv! rirn eter
'°'v s ,
every polygon inscribed is less than the
i thingHence,
s grra! rneter °f ever y polygon circumscribed about airn eter er „th an the circumference of that circle; andthat a • ev p r y polygon inscribed, less: whence itHfib * 8 the . Clr< de is equal to a right-angled triangle, whoseeerijj 8 ; since \ r i C ^ ni ^ erence °f the c ’ rc le, an d its height theH a,1 d i> 118 ,r ' an gle is less than any polygon circum-hij c { n g ther^p tei " .^ mn an y inscribed.
Tl° ® a d a r - e , 0Ie18 want > n g to the quadrature of the circle,Pfitp' 6 s ubjoi n 11 i'ne equal to the circumference of a circle.^in» n< ^ Cu lars r table gives the areas of polygons and their8 Sa PPosoa roni the centre to one of the sides, the side'i^!i^q«al to unity,dumber
des.
Area.
Perpendiculars.
.433013
.2886751
1.000000
.5000000
1.720477
.6881910
2.598076
.8660254
3.033912
1.0382617
4.828427
1.2071068
6.181824
1.3737387
7.694209
1.5388418
9.365640
1.7028437
11.196152
1.8660254
To apply this rule generally, multiply the square of theside of the given polygon by the number found in the tableof areas for a polygon, having the same number of sides asthat whose area is required.
POLYGRAM, (Greek, koXvs and ypayya,) in geometry,a figure consisting of many lines.
POLYHEDRON , or Polyedron, (from mXvtdpor, formedfrom jroXve, many, and lepa, side,) a body comprehended undermany rectilinear sides, or planes.
If the sides of the polyhedron be regular polygons, allsimilar and equal, the polyhedron becomes a regular body,and may be inscribed in a sphere ; that is, a sphere may bedrawn round it, so that its surface shall touch all the solidangles of the body.
POLYHEDROUS FIGURE, a solid contained under, orconsisting of, many sides. See Polyhedron .
POLYSTYLE, (Greek, ttoXvq, many, and otvXov, acolumn,) a term applied to buildings which are surroundedby a multitude of columns.
POMEL, a boss or knob terminating a conical or dome-shaped roof.
POMPEII, an ancient city of Naples, overwhelmed inthe first century by the same disastrous catastrophe whichdestroyed Herculaneum . It is said to owe its name to thetriumphant pomp in which Hercules led his captives along thecoast after his conquest of Spain : it was probably situate onan arm of the sea, and served as a port for the inland towns;which inlet of the sea has been filled up by successive erup-tions, besides that which destroyed the town. It is aboutfourteen miles from Naples, on the road to Nocera. FromNaples to Torre del Greco , the highway is almost a street, soclose are the villas, villages, and towns to each other. Asthe road runs along the coast, and at the foot of Vesuvius ,every break gives on one side a view of the bay, on theother of the mountain. Torre del Greco still presents, in itsshattered houses, half-buried churches, and streets almostchoked up with lava, a melancholy instance of the ravagesof the eruption. The depth of the destructive torrent is, insome places, twenty-five feet, so that the entrance into severalhouses is in the second story, and into one church, throughthe great window over the western door. Some edifices wereentirely destroyed : others were surrounded, incrusted, andfilled with lava, and may perhaps give a very accurate ideaof the state of Herculaneum at the time of its destruction.The town of Torre del Greco was supposed, by Cluverius, tooccupy the site of Herculaneum , because the distances nearlycorresponded; and inscriptions have been found that seem tocorroborate this conjecture. In fact, making allowances forthe extent of the ancient town, there is little more than three-fourths of a mile difference, so that its name and jurisdictionextended probably much farther. In the vicinity of thisplace are the ruins of ancient barracks, which were the quar-ters of a legion of Roman soldiers, and behind the barracksare two theatres, one small, and supposed to have beencovered, the other large ; both these edifices were lined withmarble, beautifully paved, and in every respect highly-finished.These theatres are exactly of the same form as the TeatroOlimpico of Palladio at Verona ; having, like it, a narrowproscenium, and three entrances, one large and the other twoless, to the stage, from the scenery behind. These theatres,when discovered, were nearly entire, but though they havebeen stripped of all their decorations, they still retain all theirgreat characteristic features. Behind the little theatre is atemple of Isis, occupying an angle formed by two streets.Some have supposed that oracles were issued from this tem-ple, and have declaimed against the priestcraft that was prac-tised here; but it does not appear that oracles were ever
i
u