F I G 
S6S 
F I G 
FIGHT,/. Battle's 
Gabriel, lead forth to battle thefe my fons 
Invincible, lead forth my armed faints. 
By thoufands and by millions rang’d for fight. Milton. 
Combat; duel : 
Herilus in fingle fight I flew. 
Whom with three lives Feronia did endue; 
And thrice I fent him to the Stygian fhore, 
’Till the laft ebbing foul return’d no more. Drydcn. 
Something to fcreen the combatants in (hips: 
Whoever faw a noble fight, 
That never view’d a brave fea-fight! 
Hang up your bloody colours in the air, 
Up with your fights and your nettings prepare. Dryden. 
FIGHT'ER,/. Warrior; duellift: 
O, ’tis the coldefl youth upon a charge, 
The moft deliberate fighter! Dryden. 
FIGFIT'ING, part. adj. Qualified for war ; fit for 
battle.—An hoft of fighting men went out to war by bands. 
2 Chron .—Occupied by war; being the fcene of war: 
In fighting fields as far the fpear I throw, 
As flies the arrow from the well-drawn bow. Pope. 
Fighting and quarrelling is prohibited by fiatute, in a 
church, or church-yard, &c. on pain of excommunication, 
and other corporal punifhment, by fiat. 5 and 6 Edw. VI. 
c. 4. 
FUG I, a town of Japan, in the ifiand of Ximo. 
FIG'MENT,./. [ figmentum , Lat.] An invention; a 
fiGion ; the idea feigned.—Upon the like grounds was 
raifed the figment of Briareus, who dwelling in a city 
called Hecatonchiria, the fancies of thofe times afiigned 
him an hundred hands. Brown. 
FI'GNAN; a town of France, in the department of the 
Upper Garonne : three leagues fouth-fouth-eaft of Caftel- 
Sarafin, and feven north-north-weft of Touloufe. 
Fl'GO, or Fisju, a province of Japan. 
FIGUEI'RO-DOS-VENHOS, a town of Portugal, in 
the province of Eftremadura, fituated near fome lofty 
mountains, on a fmall river which runs into the Zezere ; 
celebrated for its wine : twenty miles north of Thomar. 
FTGUE'RAS, or St. Fernando de Figueras, a 
ftrong fortrefs of Spain, called the Key of Catalonia , and 
fuppofed to be impregnable. It was taken by the repub¬ 
lican French on the 20th of November, 1794. The gar- 
rifon, which confided of 9107 men, were made prifoners ; 
150 pieces of cannon, and an immenfe quantity of ftores 
and provifions, were found in this place. 
FI'GULATE, adj. [figulus, Lat.] Made of potters’ 
clay. . 
FIGURABI'LITY,/. The quality of being capable 
of a certain and liable form. 
FI'GURABLE, adj. [figure, Lat.] Capable of being 
brought to certain form, and retained in it. Thus lead 
is figurahle , but not water.—The differences of impveflible 
and not itnprellible, figurahle and not figurable, fciflible and 
not fcifTible, are plebeian notions. Bacon. 
FI'GURAL, adj. Reprefented by delineation.—Incon¬ 
gruities have been committed by geographers in the figu- 
ral refemblances of feveral regions. Brozvn. 
FI'GURATE, adj. [figuratus, Lat.] Of a certain and 
determinate form.—Plants are all figurate and determi¬ 
nate, which inanimate bodies are not; for look how far 
the fpirit is able to fpread and continue itfelf, fo far goeth 
the fhape or figure, and then is determined. Bacon .—Re- 
fembling any tiling of a determinate form; as, figurate 
ftcnes retaining the forms of ftietls, in which they were 
formed by the deluge. 
Fi'gurate Counterpoint, in mufic, that wherein 
there is a mixture of difcords along with the concords. 
Harris. 
Fi'gurate Descant, in mufic, that wherein difcords 
are concerned, as well, though not fo much, as concords; 
and may well be termed the ornament or rhetorical part 
of mufic, in regard that in this are introduced all the va¬ 
rieties of points, figures, fyncopes, diverfities of meafures, 
and whatever elfe is capable of adorning the compofitiom. 
Harris. 
Fi'gurate Numbers, thofe which reprefent fome 
geometrical figure, fuch as a triangle, pentagon, or py¬ 
ramid, &c. They are treated of at great length by Mac. 
laurin, in his Fluxions; Simpfon, in his Algebra; and 
Malcolm, in his Arithmetic ; but the following account 
of them by Dr. Hutton is the moft perfpicuous. Figurate 
numbers are diftinguifhed into orders, according to their 
place in the fcale of their generation, being all produced 
one from another, viz. by adding continually the terms 
of any one, the fuccefiive fums are the terms of the next 
order, beginning from the firft order, which is that of 
equal units 1, 1, 1, 1, Sec. then the fecond order confifts 
of the fuccefiive fums of thofe of the firft order , forming 
the arithmetical progreflion 1, 2, 3, 4, &c. thofe of the 
third order are the fuccefiive fums of thofe of the fecond, 
and are the triangular numbers 1, 3, 6, 10, 15, Sec. thofe 
of the fourth order are the fuccefiive films of thofe of the 
third, and are the pyramidal numbers 1, 4, 10, 20, 35, 
&c. and fo on, as below : 
Order. Name. Numbers. 
1. Equals, 1, 1, 1, 
2. Arithmeticals, 1, 2, 3, 
3. Triangulars, 1, 3, 6, 
4. Pyramidals, 1, 4, 10, 
3. Second pyramidals, 1, 5, c< 15, 
6. Third pyramidals, 1, 6, 21, 
7. Fourth pyramidals, 1, 7, 28, 
5 > 
35 > 
1. 
4 , 
10, 
20, 
35 , 70, &c. 
56, 126, &c. 
84, 210, See. 
Sec. 
See. 
Sec. 
Sec. 
The above are all confidered as different forts of trian¬ 
gular numbers, being formed from an arithmetical pro- 
grefiion whole common difference is 1. But if that com¬ 
mon difference be 2, the fuccefiive fums will be the feries 
of fquare numbers; if it be 3, the feries will be pentago-^ 
nal numbers, or pentagons; if it be four, the feries will 
be hexagonal numbers, or hexagons ; and fo on. Thus : 
Arillime- 
ticals. 
Sums, or 
Polygons. 
2d Sums, or 
2d Polygons. 
J» 2 > 3 > 4 , 
1, 3 . 5 , 7 > 
4 > 7 > 10 > 
A 3 . 9 > 
Sec. 
Tri. 1, 3, 6, 10 
Sqrs. 1, 4, 9, j6 
Pent. 1, 5, i2, 22 
Hex. 1, 6, 15, 28 
1, 4, IO, 20 
1 9 5 > ' 4 . 3 ° 
1, 6, 18, 40 
1, 7 > 22 > 50 
And the reufon of the names triangles, fquares, penta¬ 
gons, hexagons, Sec. is, that thofe numbers may be placed 
in the form of thefe regular figures or polygons, thus : 
Triangles 
Squares 
© o 
o o 
16 
0000 
0000 
0000 
0000 
Pentagons • 
o o 
o o 
* I 2 
GOO 
o e 
o o 
o o 
IIexago'ns 
6 
o o 
*5 
o 
o o 
o o 
But. 
