L I N 



L I N 



tVie Dumnii ; whicVi, in both the fi)und and fignification of 

 the name, bears fo grerat a refemblance to Liiihthgow, that 

 it is moft probably the fame place, though its fituation 

 does not exaftly agree with that affigned by Ptolemy, who 

 is far from being correft in this particular, 



LINDY, in Geography, a town of Africa, in Querimba, 

 S. lat. ()- 58'. E. long. 41' 4'. 



LINE, in Geomtlry, a quantity extended in length only, 

 without either breadth or thicknefs. 



A line is fuppufed to be formed by the flux or motion 

 of a point ; and is to be conceived as the termination or 

 limit of a furface, and not as a part of that furface, how- 

 ever fmall. 



There arc two kinds of lines ; tiiz. nght lines, and curve 

 lines. 



If the point A moves towards B ( P/. X. Geometry, Jig. I ) 

 by its motion it defcribes a line: and this, if the point 

 go th.' neareft way towards B, will be a right or ftraight 

 line, whofe definition therefore is the neareft or fhortell 

 diilance between any two points, or a line, all whofe points 

 tend tlic fame way. It the point go any way about, as in 

 the lines A C B, or A c B, it will trace out either a crooked 

 line, as the upper A r B ; or elfe two or more ftraight ones, 

 as in the lower AC, C B. 



Right lines are all of the fame fpecies : but curves are of 

 an infinite number of different fpecies ; we may conceive 

 as many as there are different compound motions, or as many 

 as there may be different ratios between their ordinatcs and 

 abfcifTas. 



Curve lines are ufually divided \nXo gmmetrlcal 3^\A mecha- 

 nical. The former are thofe which may be found exaftly 

 and fecurely in all their points. (See Gkometrical /;nf.) 

 The latter are thofe, fome or all of whole points are not 

 to be found precifely, but only tentatively, or nearly. 



Accordingly, Defcartes and his followers define geome- 

 trical lines, thofe which may be expretfed by an algebraic 

 equation of a determinate degree ; which equation is alfo 

 called locus. 



The fame perfons define mechanical lines thofe which can- 

 not be exprefTed by an equation of a determinate degree. 

 Others,' confidcring that thofe called by Defcartes mecha- 

 riicalXvaa, notwithllanding their not being of a determinate 

 degree, are not Icls precife and cxaft, and confequently not 

 lefs geometrical than the others ; it being this precifion 

 which conflitutes the geometricity of the line : for this 

 reai'on, choofe rather to call thofe lines which are reducible 

 to a determinate degree, algebraical lines ; and thofe which 

 are not, tranfceiulcntal lines. 



Lines are alfo divided into thofe of iha Jirjl order, feccnd 

 vrder, third order, &c. See Curve. 



Sir Ilaac Newton enumerated feventy-two lines of the 

 tliird order, and Mr. Stirling found four more ; fince that 

 Mr. Stone has found two others, which had efcaped fir 

 Ifaac and Mr. Stirling. The two fpecies added are to be 

 reckoned among the hyperbolico-parabolical curves. Enu- 

 nier. Lin. Tert. Ordin. Linea. Tert. Ordin. Neutoniansc, 

 O.xon. 1717. Svo. Phil. Tranf. N^4;6. 5 6. SeeCuRVE. 



Lines, confidered as to their pofitions, are e'llhur paral- 

 lel, perpendicular, or oblique ; the eonflruftios and proper, 

 ties of each whereof, lee under Parallel, Perpekuicu- 



iAR, fvC. 



Euclid's fecond book treat* moftly of lines, and of the 

 effefts of their being divided, aad again multiplied into one 

 another. 



Lines, Algebraic, are divided into different orders, accord- 

 ing to the degree of thtir ecpiations, Thefe degrees are 



S 



ertimated, as in determined equations, by the degree of the 

 higheft term of the equation. 



Thus a-\-by-\-cs=:o, is a general equation, es- 

 prelfnig the nature of lines of the firll order, or of ftraight 

 lines. 



The equation tt -\- b y -\- c x ■\- d y y -\- e x y +fxx = o, 

 reprefents the lines of the fecond order ; that is, the conic 

 fcftions, and the circle, which is one of them. 



And the equation a -\- by ■\- c x ■\- d y y -\- exy + 

 fxx -\- g y^ + /; X y y + i x'y + /.i-' = o, exprelTes in 

 general tlie lines of the third order. And the lines of the 

 fourth and higher orders may be exprefTed in the like man- 

 ner. Sec Cramer Introd. a 1' Analyfe des Lignes Courbes, 

 p. J2, feq. Mr. Cramer ufes tlie terms lines of tlie fecond, 

 third, fourth, &c. order, and curve of the fecond, third, 

 fourth, &c. order, iudiiferently. Sir Ifaac Newton has 

 made a diftinftion, according to him. See CuRVK. 



LiKE.s. circular, converging, diverging, generalln:;, helifphe- 

 rlcal, hyperbolic, logijlic, nuigneticat, normal, proportional, qua- 

 drature, reciprtcal, roiervalian, and "vertical. Sec tlie refpedtive 

 adjectives. 



J..1NE of the y]pfides, in Jljlronomy, is the line which joins 

 the apfides ; or it is the greater axis of the orbit of a 

 planet. 



Line, Fiducial, the line Or ruler which paffes through the 

 middle of -.n allroiabe, or tlie like inilrument ; and on which 

 the fights are fitted ; otherwife c?\\i:A alliidade , index, dioptra, 

 and niedlellnliim. 



Line, Horizontal, a line parallel to the horizon. 



LiNE.s, Ifochronal and Meridian. See the adjeftives. 



Link 0/ the Abodes, in yljironomy, is the line which join,? 

 the nodes of tlie orbit of a planet, or the common feftion of 

 the plane of the orbit with the plane of the ecliptic. 



Line, Hnrti,ontal, in Dialling, is the common feftion of 

 the horizon, and the dial-plate. 



Lines, Horary, or Hour-lines, are the common interfcftions 

 of the hour-circles of the Iphere, with the plane of the 

 dial. See Hou,\ry, and HouR-nVr/cj. 



Line, Suh/lylar. See Substylah. 



Line, Equinodial, is the common interfeAion of the equi- 

 noftial, and tlie plane of the dial. 



Line, Contingent. See Conti^'Gf.nt. 



Lines, Dialling and Meridian. See the refpeftive ad- 

 jeftives. 



Line, in Fencing, is that part of the body direftly oppo- 

 fite to the enemy, wherein the fhoulders, the right arm, and 

 the fword, ought always to be found ; and wherein are alfo 

 to be placed the two feet, at the diftance of eighteen inches 

 from each other. 



In this fenfe, a man is faid to be in his line, to go out of 

 his line, &c. 



Line, in Fortification, is fometimes taken for a ditch, bor- 

 dered with its parapet ; and fometimes for a row of gabions, 

 or facks of earth, extended leiigthwifc on the ground, to 

 ferve as a fhelter againit the enemy's fire. 



When the trenches were carried on within thirty paces of 

 the glacis, they drew two lines, one on the right, and the 

 other on the left, for a place of arms. 



For the difference between trenches or approaches, and 

 lines, fee Intrenchment. 



Lines are generally made to fliut up an avenue or entrance 

 to fome place ; the fides of that entrance being covered by 

 rivers, woods, mountains, morafles, or other obftruAions, 

 not eafy to be paiTed over by an army. When they are 

 conflrufted in an open country, they are carried round the 

 place to be defended, and ref'-mble the lines furrounding a 

 camp, called lines of circumvallation. Lines are iikewife 



thrown 



