F I G

F I G

amounted to a fifteenth part of what each city or town had beenvalued at; or it was a fiiteenth of every man’s personal estate ac-cording to a reasonable valuation. In Doomsday book, thereare certain mentioned for levying this tribute yearly ; but since,any such tax cannot be levied out by parliament.

1'lF'i H, in music, one of the harmonical intervals or concords.See Interval. The tilth is the second in order of the concords,the ratio of the chord that affords it is 3 : 2. See Chord andConcord. ft is called fifth, as containing five terms or soundsbetween its extremes, and four degrees, so that in tne naturalscale of music, it comes in the fifth place or order from the funda-mental. The ancients called this tilth dlapenle. T tie imperfectand defective fifth called by the.ancients semi-diapente is less thanthe fifth by a less semitone.

Fig, or Fig-Tree. See Ficus . Figs are a considerable arti-cle in the materia medica, chieily employed in emollient cata-plasms and pectoral decoctions. The best are those which comefrom Turkey.

FIGARl’OLO, an island of Maritime Austria, on the coast ofIstria.

FIGEAC, a town of France , in the department of Lot, 27miles E. of (Jailors.

Fig-Gnat, in entomology. See Cui.ex.

FfGHIG, a town of Africa , in Biledulgerkl, S. of Atlas, 240miles E. S. E. of Mequinez. Lon. 1. 5. \V. i/at. 32. 20. N.

Fig-Tree Bay, a bay on the N. E. coast of Jamaica .

Fig-Tree Bay, a bay on the S. W. coast of St. Kitts .

FIGUEIRO Dos \ i.nhos, a town of Portugal , in Eslremu-dtira, 20 miles N. of Thomar.

FIGUEKA, FiGUERAS , or St. FERNANDO DE FI-GUERAS, a strong town of Spain in Catalonia , which was es-teemed impregnable, till the 27th Nov. 1794, when if v.as takenby the French , though garrisoned with 9107 men, and defendedby 171 pieces of cannon. The military chest, 200,000ib. of pow-der, ami a vast quantity of provisions, fell into the hands ot therepublicans. During the siege, the generals on both sides werekilled ; viz. citizen Dugomtnier on the 17th and Count de LaCnion on the 20th. It lies 10 miles \V. of Rosas. Lon. 2. 46.E. Lat. 42. 18. N.

FIGURABILITY, [from ftgurable,~\ the quality of being ca-pable of a certain and stable form.

FIGURAL, FIG UR ATE, or FIGURATIVE, a term ap-plied to whatever is expressed by obscure resemblances. The"’ord is chiefly applied to the types and mysteries of the MosaicLw ; as a.so to any expression which is not taken in its primaryand literal sense.

Figural, or Figurate Numbers, are such as do or may re-prestnt some geometrical figure in relation to which thev are al-ways considered, as triangular numbers, pentagonal numbers, py-ramidal numbers, See.

F igurate Numbers, are distinguished into orders accordingto their place m the scale of their generation, being all producedone from another, viz. by adding continually the terms of any one,the successive sums are the terms of the next order, beginningfrom the first order, which is that of equal units 1, l,l,l,&c.;then the 2d order consists of the successive sums of those of thefirst order, forming the arithmetical progression 1,2, 3,4, &c.;those of the 3d order the successive sums of those of the 2d, andare the triangular numbers 1, 3, 6, 10, 15, Ac. ; those of the 4thorder are the successive sums of those of the 3d, and are the py-raunda) numbers 1, 4, 10,20, 35, &c.: and so on, as below.

Order.

Name.

Numbers.

L Equals.l, i, i, i, i, See,

2. Arithmetical.1.2, 3, 4, 5, &c.

3- Triaugulars...1,3, 6,10, 15, &c.

A 1 yramidals .1, 4, 10, 20, 35, Ike.

N 2d Pyramitlals.1, 5, 15, 35, 70, &c.

6. 3d Pviamidals.1, 6, 21, 56, 126, Ac.

7. 4th Pyramidals.1, 7, 28, 84, 210, &c.

be^-s ‘‘{ Jo . ve ;,re considered as different sorts of triangular num-,s > being formed from an arithmetical progression, whose com-°n nuferenee is 1. If n be put for the number of terms in avol. n.— mo. 83 ,

series of any order, and from the expression — x

w.-f- 1

n + 2 n 3 n -j- 4

X

■ &c. a number of factors be taken

3 4 5

equal to the number which denotes the order, there will be hadthe sum of n terms ol that order, or, which is the same thing, the

n

nth term of the succeeding order; thus if» be equal to 5, — =

1

n n -j- 1 n n 1 « -f- 2

5, — x - =15, — x -X --= 35, &c. which

12 12 3

are the sums of 5 terms of the 1, 2, 3, &c. orders, or the 5thterm of the 2, 3, 4, &c. orders as in the above table. If thecommon difference of the generating arithmetical series be 2, thesuccessive sums will be the series ot square numbers; if it be 3,the series will be pentagonal numbers, or pentagons; if it be 4,the series w ill be hexagonal numbers, or hexagons, and so on.Thus :

Arithmetical.

‘

1st, Sums or Polygons,

2d. Sums, or 2d Poly-gons.

1, 2, 3, 4,

1, 3, 5, 7,

L 4, 7, 10,

1, 5, 9, 13,

Tri. 1, 3, 6, 10,

S.qrs. 1, 4, 9, 16,

Pent. 1, 5, 12, 22,

Hex. 1, 6, 15, 28,

1, 4, 10, 20,

1, 5, 14, 30,

1, 6, IS, 40,

1, 7, 22, 50, &c.

And the reason of the names triangles, squares, pentagons, hexa-gons, &c. is, that those numbers may be placed in the form ofthese regular figures or polygons.

FIGURE, in physics, expresses the surface or terminating ex-tremities of any body ; and considered as a property of body af-fecting our senses, is defined a quality which may be perceived bvtwo of the outward senses. Thus a table is known to be squareby the sight and by the touch.

Figures, in arithmetic, are certain characters whereby we de-note any number which may be expressed by any combination ofthe nine digits, &c. See Arithmetic.

Figure, in architecture and sculpture, signifies the represen-tation of tilings made in solid matter, as statues, &c.

Figure, in astrology, a description of the disposition of theheavens at a certain hour, in which the places of the planets andstars are marked in a figure of twelve triangles, called houses.

Figure, in conic sections, according to Apollonius , is therectangle made under the iatus rectum and transversum in thehyperbola and ellipsis.

Figure ofthe Diameter; the rectangle under any diameter,and its proper parameter is, in the ellipsis and hyperbola, called] the figure of that diameter.

Figure, in fortification, the pi in of any fortified place, or theinterior polygon, which, when the sides and angles are equal, iscalled a regular, and when unequal, an irregular figure.

Figure, in geometry ; the superficies included between one ormore lines, is denominated either rectilinear, curvilinear, ermixed, according as the extremities are bounded by right lines,curve lines, or both.

Figure, in grammar, a deviation from the natural rules of ety-mology, syntax, and prosody, either for brevity, elegance, orharmony.

Figure, in dancing, denotes the several steps which the dancermakes in order and cadence, considered as thev mark certain fi-gures on the floor.

Figure, in designing and painting, denotes the lines and co-lours which form the representation of any animal, but more par-ticularly of a human personage. See Painting , and Drawing.

Figure, in logic, denotes a certain order and disposition of themiddle term in any syllogism. Figures are fourfold. 1. Whenthe middle term is the subject of the major proposition, and the5 P predicate