Page:Cyclopaedia, Chambers - Volume 2.djvu/557

 Q,UA

( P34)

Q.UA

tofmical Qualities, feeCosMiCAL Quality.

Quality is alfo ufed for a kind of Title given to cer- tain Ferfons in regard of their Territories, Signories, or other Pretentions. See Title.

Thus the King of Great Britain takes the Quality of King of France: The King of 'Poland that of King of Sweden : The King of Sardinia that of King of Cyprus imAjerufalem : The Czars of Ruffia and Kings of Spam,

holePages of Qualities The Emperor of China Velocity into the Mafs ;

&e Quality ut, Son of the Sun. . . Confidently of the Qu

Quantity of entire Motion The Cartefians define the

entire Motion as the momentary one, by the tasStum of the Mafs, or Quantity of Matter, into the Velocity ; but fince Motion is a fucceffive Being, and has no parts co-exilling together, its Quantity ought to be estimated by the Aggie- gate of the feveral i J aits exifting fucceffively ; and is there- fore equal to the Factum of the Momenta into the Time.

Quantity of momentary Motion, is the Faclum of the or a Mcalute arifing from the joint'

affumes the Quality ofSon of the Sun. . r Confident,™ of the Quantity of Matter, and *e Velocity

QUAM duife benegefferit, a Claufe frequent in Letters of the Motion of the Body 5 the Motion of any VVhole bc-

Fater,ts, or Grants of Uffices, to fecure them fo long as ing the Sum or Aggregate of the Motion in all the feveral

the Perron they are granted to, null not be guilty of abu- Parts. See Motion.

f th ■ f m Hence, in a Body twice as great as another, moved with

"Thus e tr we find it in thofe given to the Barons of an equal Velocity, the Qiiautity of Motion is double ; if

' ates that they (hall hold the the Velocity be double alio, the Quantity of ^ the Motion

the Exchequer ; where it inti

fame as long as they fhall behave themfelves well : which is to berefirain'd to the Matters of their Offices; and Signifies no more than the Law would have imply 'd, had the Office been granted exprefsly for Life.

A Grant, therefore, with this Claufe, is equivalent to a Grant for Life. See Baron, Judge, Justice, SSc.

QUANTITY, Quantitas, any thing capable of Efti- mation, or Menfuration ; or, which being compared with another thingof the fame kind, may be faid to be greater, or lefs, than ; equal, or unequal to, it.

Mathematics is the Science or Doctrine of Quantity. See Mathematics. .

Quantity is a general Attribute, apply d in a very diffe- rent M anner to things of vety different Nature ; whence it is impoflibla to give any univerfal Definition thereof.

Qu tltity is apply'd both to Things, and to Modes ; and this, either lingularly, and to one; or plurally, and to fe- deral —In the fitd Cafe it is call'd Magnitude, in the

latn.r Multitude. See Magnitude, ci'c.

Quantity may be reduced 10 four Claffes, via.

1-tiylical, or Natural Quantity, which is ot two kinds ; viz. 1. That which N-. meiu i.ifties us with, inMatter, and

its Extensions. See Body and Extension And, 2.

In the Powers, and Forces of Natural Bodies 5 as Gravity, Motion, Light, Hear, Cold, Rarity, Dtnfity, &. See Force, Gravity, &c.

Moral Quantity, which de, ends on the Winners of Men,

and the fro Determination of their Wills As th Prices

and Valu- s of Thin, si Degrees of Dignity and Power, Good and Evil, Merit and Demerit, Rewards and Puniih- ments, iSc.

Notiona' Quantity, arifing from the Operation of the

Underilandieg

inuatmn See Duration,

-Such"as the iargenefs or narrowneis of the Opacity of the Mind, and Jre Conceptions In

Lo ic, TJniverfals, Predicaments, &C, In Grammar,

the Quantity and Meamre of Syllables, Accents, Tones,

'j'ranfcendental Quantity, as Duration, the Cont: of any Being, Exigence, Time, i$c. See Dur Time, £*jf;.

Quantity is alfo popularly diflinguifh'd into Hifcrete and Continued.

Difirete Quantity, is when the Parts whereof it con- fifts, cxift distinctly and unconnected together ; which makes what we call Number. See Discrete.

The Antients diltinguifh'd this into two kinds, vie. Per- manent, asNumerusNumeranSi and Succeffive, asSpeech.

Continued Quantity, is wnen the Pans ate connected

together i his, again, is of two kinds ; either fucceffive

and improper, as Time. See Time.

Or permanent and proper, as Space. See Sp ace.

•Permanent Quantity is further diftinguifhable into length, breadth, and depth. See Line, Surface, and Solid.

Wolfus gives us a more precife Notion of Mathematical Quantity, and its two Species of Difcrete and Continued — "Whatever isreferr'd to Unity in the fame manner as one right Line to another, is what we call Quantity, or Number in general. See Number.

If, now, the thing be refetr'd to a given Unit, as 3, it is call' d a determinate Number : if to Unity in the general, or at large, it is call'd ^Quantity; which, on this Principle, is the fame with indeterminate Number.

Thus, e.gr. the breadth of a River is accounted a Qiian- tity : If, then, itbeenquir'd how greatitis? To conceive its Quantity we take fome Unit at pleafure, and feek the Relation of the breadth hereto ; and according to the diffe- rent Unit affumed, exprefs the breadth of the River in a different determinate Number.

The breadth of the River, therefore, is a Quantity con- fider'd as referr'd to a vague Unit, or to Unity at large ; but the Unit being determined, the thing is understood by a determinate Number.

In this fenfe, Algebra is the Arithmetic of Quantities.

SeeALGEBRA.

Quantity of Motion, in Mechanics, is of two kinds, viz. of momentary Motion, and of entire Motion.

will be quadruple. Hence the Quantity of momentary Motion coincides with what we call Momentum, or Impe- tus of a moving Body. See Momentum.

In the Collifion of Bodies, the Quantity of momentary Motion, which is found by taking the Sum of Motions tending the fame way, or their difference if they tend to- wards contrary Parts ; is not at all changed by any Actions of the Bodies on one another. See Percussion.

Quantity of Matter in any Body, is the Product of the Denfity into the Bulk ; or a Quantity arifing from the joint Consideration of its Magnitude and Density. See Buliu

As, if a Body be twice as denfe, and take up twice as much Space as another, it will be four times as great.

This Quantity of Matter is the belt difcoverahle by the abfolute weight of Bodies. See Mass, Weight, tj/G.

Quantity Infinite Tho' the Idea of Magnitude in- finitely great, or fuch as exceeds any assignable Quantity, does include a negation ot Limits; yet ate not all fucii Magnitudes equal amongSt themfelves ; but befides infinite Length, and infinite Area, there are no lefs than three feve- ral forts of infinite Solidity ; all of which are Qiiantitates fui generis ; and thofe of each Species are in given Pro- portions.

Infinite Length, or a Line infinitely long, is to be confi- der'd, either as beginning at a Point, and fo infinitely ex- tended one way; or elfe both ways from the fame Point : in which Cafe the one, which is a beginning Infinity, is one half of the Whole, which is the Sum of the beginning and ceafing Infinity, or Infinity a parte ante, and a parte poft, which is analogous to Eternity in Time or Duration, in which there is always as much to follow as is pair, any Point ot Moment of Time. See Eternity.

Nor does the Addition or Subtraction of Time, Length or Space of Time, alter the Cafe, either as to infinity or Eterniiy ; fince neither the one or the other can be any Part of the 'vVliole.

As to infinite Surface or Area, any right Line infinitely extended both ways on an infinite Plane, divides that Plane into equ il Parts, trie one to the Right, and the other to the Left of the faid Line ; bur if from any Point in fuch a Piane, two right Lines be infinitely extended, lo as to make an Angle ; the infinite Area, intercepted between thefc infi- nite ngt. 1 Lines, is to the whole infinite Plane, as the Arch of a Circle drawn on the Point of Concourfe of thofe Lines as a Centre, intercepted between the faid Lines, is to the Circum- fetence of the Circle ; or as the Degrees of the Angle to the 360 Degrees of a Circle.

For an Example — 'Two infinite right Lines meeting at a right Angle on an infinite Plane, do include a quarter Part of the whole infinite Area of fuch a Plane : If two paral- lel infinite Lines be fuppofed drawn on fuch an infinite Plane, the rirea intercepted between them will belikewife infinite; but at the fame time will be infinitely lefs than the Space intercepted between two infinite Lines, that are inclined, tho' with never fo fmall an Angle, for that in the one Cafe the given finite Diftance of the parallel Lines di- minifhes the Infinity in one Degree of Dimenfion ; whereas in a Sector, thete is Infinity in both Dimensions; and con fe- quently the Quantities are one infinitely greater than the other, and there is no Proportion between them.

From the fame Confideration arife three feveral Species of infinite Space or Solidity ; for a Parallelepiped, or a Cylinder infinitely long, is greater than any finite Magni- tude, how great foever ; and all fuch Solids fuppofed to be form'd on a given Bafis, are in proportion to one another, as thofe Bafes. But if two of thofe three Dimenfions are wanting, as in the Space intercepted between two parallel Planes infinitely extended, and at a finite diftance ; or with infinite length and breadth, with a finite thicknefs ; all fuch Solids fhall be as the given finite Diflances one to another.

But thefe Quantities, tho' infinitely greater than the other, are yer infinitely lefs than any of thofe wherein all

the three Dimenfions are infinite -Such are the Spaces

intercepted between two inclined Planes infinitely extended ; the Space intercepted by the Surface of a Cone, or the Sides of a Pyramid, likewife infinitely continued, i$c. of

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