A X I 



Lord Bacon, tTierefore, ftrenuoiifl)'- contends, tliat they 

 fliould never be admitted upon coHJtCliire, or even upon the 

 authority of the learned ; but, as they are the general prin- 

 ciples and grounds of all learning, they (hould be canvaflcd 

 and examined with the moll fcrupulous attention, " ut 

 axiomatum corrigatur iniquitas, qua; plerumque in excmplis 

 vulgatis fundamcntum liabent." DeAu'jm. Sc. 1. ii. c. 2. 

 " Atque ilia ipfa putativa princlpia ad rationes reddendas 

 compellare decrevimus, quoufque plane conilant. Dillrib. 

 Operis. 



A late writer (fee Tatham's Chart, and Scale of Truth) 

 diftinguifhes between axioms intuitk^e, Viadjl-If-eviiLnl. The 

 former, he fays, pafs through the tirll inlets of knowledcre, 

 and flafh dirett conviction on the minds, as external objects 

 do on the fenfes, of all men; in the formation of the latter, 

 reafon judges by fingle comparifons, without the aid of a 

 third idea or middle term; fo that they have their evidence 

 in themfelves, and though induftivcly framed, they cannot 

 be fyllogiftically proved. If we admit this diftindion, and 

 its reafonablenefs muft be allowed, the charafter of intuitive 

 axioms will be reftridted to particular truths. See Induc- 

 tion, Reasoning, and Syllogism. 



Axiom, in Rhetoric, is ufed by Hermogenes to' denote 

 grandeur, dignity, and fublimity of llyle. 



AXIOPOLIS, in Ancient Gcogriiphy, a town of Lower 

 Moefia, according to Ptolemy, fituated near the fpot where 

 the Danube afTumedthe name of Iller; north-eaftof Durof- 

 torus. It is now a town of European Turkey, in Bulgaria, 

 called AKwpoli, on the right bank of the Danube. N. lat. 

 45=40'. E.long. 34°. 



AXIOS, a form of acclamation, anciently ufed by the 

 people in the eltiflion of bifhops. When they were all una- 

 nimous, they cried out a^i!^, he is •worthy, or aix^i®', un- 

 nvorthy. 



AXIOSIS, in Rhetoric, denotes a third part of an 

 exordium; fometimes alfo called atro'Soa-i;, and containing 

 fome new propofition more nearly relating to the matter in 

 hand, than the Tfclxo-if. 



Thus, in Cicero's oration pro Milone, the protafis is, 

 *' Non pofTum non timere, judices, vifa hac nova judicii 

 forma;" the xalatrMvn, " Nee enim ea corona confefTus 

 vefter cinftus eft qua folebat;" the afiiOTj, " Sed me recreat 

 Pompei coniilium, cujus fapientrE non futrit, qucm fententiis 

 judicum tradidit, telis militum dedere;" the bafis, /2x(7ic, 

 " Qiiamobrem adcfte animis, judices, & timorL'm,fi quem ha- 

 betis, deponite." 



AXIOTHEA, in Bi graphy, a female philofopher of 

 Greece, who lived in the time of Plato. Such was her 

 thirft for knowledge, that (he difguifed herfelf in man's 

 clothes, in order to attend the leftures of that philofopher, 

 Menag. in Diog. Laert. l.iii. c. i.'i. 



AXIS properly fignifies a line, or long piece of iron or 

 wood pairing through the centre of a fphcre, vvhich is move- 

 able upon the fame. In this fenie we fay, the axis of 

 a fphcre or globe; the axis, or axle-tree of a wheel, 

 &c. 



Axis, in Anatomy, is the fecond vertebra of the neck, 

 reckoning from the flvull. 



It is thus called, becaufe the firft vertebra, with the head, 

 move thereon, as an axis. See Skeleton. 



Axis, Spiral, in Architedure, is the axis of a twilled co- 

 column drawn fpirally, in order to tiace the circumvolutions 

 without. See Column, Tivijled. 



Axis of the Ionic capital is a lincpalfing perpendicularly 

 through the middle of the eye of the volute. 



Axis of the luorld, m AJlronomy, is an imaginary right 

 line, which is conceived to pafs through the centre of the 



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A X I 



earth, and to terminate at each end in the furface of the 

 m.undane fphcre. 



About this line as an axis, the fphere in the Ptolemaic 

 fyflem, is fnppofed daily to revolve. 



This axis is reprcfented by the hne PQ,P//ile II. AJroit. 

 Jig. 1 8. — The two extreme points in the furlace of the fphere, 

 viz. P and Q, are called its poles. 



Axis of tTie earth, is a right line upon which the earth 

 performs its diurnal rotation from weft to caft. 



Such is the line PQ^^^. 19. — The two extreme points 

 are alfo called poles. 



The axis of the earth is a part of the axis of the world 



It always remains parallel to itfelf, and at right angles with 

 the equator. See Angle, Inclination, and Paral- 

 lelism. 



Axis of a planet, is a line drawn through its centre, about 

 which the planet revolves. 



The Sun, Earth, Moon, Jupiter, Mars, and Venus, are 

 known, by obfervation, to move about their fevcral axes; and 

 the like motion is eafily inferred of Mercury, Saturn, and 

 the Georgian planet. 



Axis of tlie horixon, equator, ecliptic, zodiac, &c. arc right 

 lines drawn through the centres of thofe circles, perpeutS;cu- 

 lar to their planes. 



Axis, in Botany, a taper column placed in the centre of 

 fome flowers or katkins, about which the other parts arc dif- 

 pofed. It is fynonymous with columella. 



Axis, in Geometry. — Axis of rotation or circumvolution, 

 is an imaginary right line, about which any plane figure is 

 conceived to revolve, in order to generate a folid. 



Thus a fphere is conceived to be formed by the rotation 

 of a femicircle about its diameter or axis, and a right cone by 

 that of a right angled triangle about its perpendicular leg, 

 which is hete its axis. 



Axis is yet more generally ufed for a right line proceed- 

 ing from the vertex of a figure to the middle of its bafe. 



Axis of a circle or fphere, is a line palTing through the 

 centre of the circle or fphere, and terminating at each end 

 in its circumference. 



The axis of a circle, &c. is otherwife called its diameter. 



Axis of a right or rectangular cylinder, is properly 

 that quielcent riglit line, about which the reAangular 

 parallelogram turns, by wliofe revolution the cylinder is 

 formed. 



In general, the right line which joins the centres of the 

 oppofite bafesofcyhnders, whether they be right or oblique, 

 is denominated their axis. 



Axis of a right cone, is the right line or fide upon which 

 the right-angled triangle forming the cone makes its motion. 

 Hence it follows, that only a right cone can properly have 

 an axis; becaufe an obhque one cannot be generated by any 

 motion of a plane figure about a right Lne at rclL But 

 becaufe the axis of a right cone is a right line drawn from 

 the centre of its bafe to the vertex; the writers of conies, 

 by way of analogy, likewife call the like line, drawn from 

 the centre of the bale of an obhque cone to the vertex, its 

 axis. 



Axis of a conic fedion, is a right line pafTing through the 

 middle of the figure, andbifeiEliiig all the ordiuates at light 

 angles. 



Thus if Ar iPlaie, Conies, fg. ^i.) be drawn perpfudi- 

 cularly to FE, fo as to divide the fcCtion into two equal 

 parts, it is called the axis ef the fcSior., 



Or, the axis of a conic feftion is a line drawa from the 

 principal vertex, or vertices, perpendicular to the tangent at 

 that point. 



As IS, Iranfverfe, called alfo thejr^ or principal axis of an 

 3 E elhpfe. 



