Page:Cyclopaedia, Chambers - Volume 1.djvu/222

 AXI

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A XI

The Word is a diminutive of Axis; q. 'd. little Axis. See Axis.

Abfceffes in the Axilla are ufually dangerous, on account of the many Blood- Veffels, Lymphaticks, Nerves, &c. thereabout, which form large Plexus's. See Ulcer.

By the antient Laws, Criminals were to be hang'd by the Ax- illa, if they were under the Age of Puberty. See Hanging, Puberty, &c.

Axilla, in Botany, is the fpace comprehended between the Stems of Plants and their Leaves. See Plant, Stem, Leaf, &c.

Hence we fay, thofe Flowers grow in the Axilla of the Leaves, /. e. at the Bafe of the Leaves or their Pedicles. See Flower,

AXILLARY, Axillaris, in Anatomy, fomething that be- longs to the Axil/a) or lies near them. See Axilla.

Axillary Vein is one of the fubclavian Veins; which pafling under the Arm-pits, divides it felf into feveral other Veins. See Subclavian and Vein.

Axillary Artery is a Remainder of the Trunk of the fub- clavian Artery ; which palling under the Arm-pits, changes its Name, and is call'd Axillary. See Artery.

The fecond Vertebra of the Back is alfo call'd Axillary >; in re- gard it is the neareft to the Arm-pits. See Axis and Verte bra.

AXINOMANCY, Axinomantia, a Species of Divination, or Method of foretelling future Events by means of an Ax or Hatchet. See Divination.

The Word is form'dfrom the Greek »\m t fecuris, and f**mfte, divbiatio.

This Art was in good repute among the Antients; and was performed by laying an Agat-ftone on a red-hot Hatchet. See Agat.

AXIOM, Axioma, a felf-evident Truth ; or a Propofition whofe Truth every Perlbn perceives at firft light. See Truth and Proposition.

Thus, that the whole is greater than a Part ,■ that a thing can- not give what it felf has not; that a thing cannot be and not be at the fame time; that' from nothing, nothing can arife, &c. are Axioms.— The Word is Greek? *%wp>* 3 q. d. dignitas, Autloruas, or even Effatum: Whence Cicero in lieu thereof ufes the Word Pronuntiatum.

By Axioms, call'd alfo Maxims, are understood all common Notions of the Mind, whofe Evidence is fo clear and forcible, that a Man cannot deny them without renouncing common Senfe and natural Reafon. See Maxim, Evidence, &c.

The Rule of Axioms is this, that whatever Propofition exprelTes the immediate clear Comparifon of two Ideas without the help of a third, is an Axiom.— On the other hand, a Truth which does not arife from an immediate Comparifon of two Ideas, is no Axiom. See Idea, Relation, &c.

Wolf us aiTigns the ElTence of an Axiom thus : Whatever Pro- pofition arifes immediately from the Coniideration of a lingle

Definition, is an Axiom Thus it neceflarily following from the

Genefis of a Circle, that all right Lines drawn from the Centre to the Circumference thereof, are equal; inafmuch as they all re- prefent the fame Line in different Situations: This is an Axiom, See Definition.

Hence, the Truth of Axioms being perceived by the meer Intui- tion of aDefinkion,* they need no Demonftration-: Since they are neceflarily as true, as the Definition is juft. See Demonstra- tion.

Several Authors abufe this Property of Axioms? and obtrude for Axioms the Premises of Syllogifms, which they are not able to prove— Euclid himfelf lies liable to Exception on this Account, having atfutned the Equality of Figures which mutu- ally agree, or are congruous to each other, as an Axiom. See Congruency.

Axioms-, in effect, ftriiftly fpeaking, are no other than identick Propofitions.— Thus to fay that all Right Angles are equal to each other, is as much as to fay, all Right Angles are Right Angles : Such Equality being implied in the very Definition, the ve- ry Name. See Definition.

My Lord Bacon propofes a new Science, to confift of general Axioms, under the Denomination of Philofophia prima. See Phi- losophy, Knowledge, &c.

Axiom is alfo an eftablifhed Principle in fome Art or Science. See Principle, ojre.

Thus, it is an Axiom in Phyficks, that Nature difcovers her- felf moft in the fmalleft Subjects ; that Nature does nothing in vain ; that Effects are proportional to their Caufes, <£yc. Thus it is an Axiom in Geometry, that things equal to the fame third are alfo equal to one another ; that if to equal things you add Equals, the Sums will be Equal, &c. So it is an Axiom in Opticks, that the Angle of Incidence is equal to the Angle of Reflection, <&c. It is an Axiom in Medicine, &c. that there is no fincere Acid in the human Body, &e.

In this Senfe the general Laws of Motion are call'd Axioms ; as, that all Motion is Re&ilinear, that Action and Re-adion are equal, &c. See L#ws of Nature.

Thefe particular Axioms, it may be obferved, do not immedi- ately arife from any firft Notions or Ideas, but are deduced from certain Hypothefes : This is particularly obfervable in phyfical Matters, wherein, as feveral Experiments contribute to main one

Hypothefis, fo feveral tfypothefes contribute to one Axiom. See Hypothesis, &c.

AXIS properly fignifies a Line or long Piece of Iron or Wood paffing through the Centre of a Sphere, which is. moveable up- on the fame. See Sphere.

In this Senfe we fay the Axis of a Sphere, or Globe ; the Ax- is, ox Axle-Tree of a Wheel, &e. See Globe, Wheel, &c.

Axis of the World, in Aftronomy.— The Axis of the World is an imaginary Right Line, conceived to pafs through the Centre of the Earth, and terminating at each End in the Surface of the mundane Sphere. See Sphere.

About this Line as an Axis, the Sphere, in the Ptolemaic Sy- ftem, isfuppofed daily to revolve. See Earth and Rotati- on. See alio Ptolomaic.

This Axis is reprefented by the Line PQ, Tab. Aflronomy, Fig. 52. —The two extream Points hereof, in the Surface of the Sphere, in%. Pand Q, are called its Voles. See Pole.

Axis of the Earth, is a Right Line, upon which the Earth performs its diurnal Rotation. See Earth, Rotation, &c.

Such is the Line PQ^ Tab. Geography, Fig. j. — The two ex- tream Points hereof are alfo called Poles. See Pole.

The Axis of the Earth is a Part of the Axis of the World. — It always remains parallel to it i'elf, and at Right Angles with the Equator. See Parallelism.

Axis of a Planet, is a Line drawn through the Centre thereof, about which the Planet revolves. See Planet, &c.

The Sun, Moon, and all the Planets, except Mercury and Saturn, are known, by Observation, to move about their feve- ral Axes j- and the like Motion is eafily infcir'dof thofe two. See Sun, Moon, Mercury, Saturn, &c.

Axes of the Horizon, the Equator, Ecliptic, Zodiac, Sec. are Right Lines drawn through the Centres of thofe Circles per- pendicularly to the Planes thereof. See Circle. See alio Ho- rizon, Ecliptic, Eqjjator., &c. See alio Plane, &c.

Axis, in Mechanicks. — The Axis of a Ballavce is the Line up- on which it moves or turns. See Ballance.

Axis of Ofcillatmi, is a Right Line parallel to the Horizon, paffing through the Centre, about which a Pendulum vibrates. See Oscillation and Pendulum.

Axis, in Geometry. — Axis of Rotation, or Circumvolution, is an imaginary Right Line, about which any plane Figure is con- ceived to revolve, in order to generate a Solid. See Solid, Ge- nesis, &c.

Thus a Sphere is conceived to be formed by the Rotation of a Semicircle about its Diameter or Axis, and a Right Cone by that of a Right Angle Triangle about its perpendicular Leg, which is here its Axis.

Axis of a Circle or Sphere, is a Line paffing through the Centre of a Circle or Sphere, and terminating at each End, in the Cir- cumference thereof. Sec Circle and Sphere.

The Axis of a Circle, &c. is otherwife call'd the Diameter thereof — Such is the Line AB. Tab. Geometry. Fig. 27. See Diameter.

Axis is yet more generally ufed for a Right Line proceeding from the Vertex of a Figure to the Bafe thereof. See Figure, Vertex, and Base.

Axis of a Cylinder is properly that quiefcent Right Line about which the Parallelogram turns, by whofe Revoiunon the Cylin- der is formed. See Cylinder.

Though, both in Right and Oblique Cylinders, the Right Line joining the Centres of the oppohte Balis, is alio called the Axis of the Cylinder.

Axis of a Co?ic is the Right Line or Side upon which the right angled Triangle forming the Cone makes its Motion. See Cone.

Hence it follows that only a Right Cone can properly have an Axis; in regard an Oblique one cannot be generated by any Motion of a Plane Figure about a Right Line at reft.

But in Regard the Axis of a Right Cone is a Right Line drawn from the Centre of its Bafe to the Vertex,- in Analogy hereto the Writers of Conicks do likewife call the fame Line drawn from the Centre of the Bafe of an Oblique Cone to the Vertex, the Axis thereof.

Axis of a Veffel, is that Quiefcent Right Line paffing through the Middle thereof, perpendicularly to its Bafe, and equally di- ftant from its Sides.

Axis of a Conick Section, is a Right Line paffing through the Middle of the Figure, and cutting all the Ordinates at Right Angles. See Conick Section.

Thus if AP, Tab. Conicks, Fig. 31. be drawn perpendicularly tq MN, foas to divide the Section into two equal Parts j it is called the Axis of the Section. See Section.

Tranfverfe Axis, called alfo the firft or principal Axis of anEI- liphs or Hyperbola, is the Axis AP, laft defined : Being thus called in contradiftindtion to the conjugate or iecondary Axis. See Transverse.

The Tranfverfe Axis in the Ellipfis the longcft ; and in the Hyperbola cuts the Curve in the Points A and P. Fig. 32.

Conjugate Axis, or fecond Axis of the Ellipfs, is the Line FF, Fig. 31. drawn through the Centre of the Figure C, parallel to the Ordinate MN, and perpendicularly to the Tranfverfe Axis AP; being terminated at each extream. by the Curve. See Ellipsis.

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