Page:Cyclopaedia, Chambers - Volume 2.djvu/558

 QUA

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all which, notwithstanding the Proportions onfe to another, and to the to 7r£,v r or vait Abyfs of infinite Space (wherein is the Locus of all things that are, or can be j or to the Solid of infinite Length, Breadth, and Thicknefs taken all

manner of ways) are eaflly affignable- For the Space-

between two Planes is to the Whole, as the Angle of thofe Planes to the 360 Degrees of the Circle. As for Cones and Pyramids, they are as the fpherjeal Surface intercepted by them, is to the Surface of the Sphere ; and therefore Cones are as the verfed Sines of half their Angles, to the Diame- ter of the Circle : Thefe three forts of infinite Quantity are analogous to a Line, Surface, and Solid ; and, like them, cannot be compofed, or have any Proportion one to another.

Quantities, in Algebra, are indeterminate Numbers, or things referr'd to Unity in the general.

Quantities are properly the Subject of Algebra; which is wholly converfantin the Computation of fuch Quantities. See Algebra.

The given Quantities are ufed to be noted by the firft Letters of the Alphabet a t b, c, d, Sec. the Quantities [ought by the laft z, y, x, &c. See Characters.

Algebraical Quantities are of two kinds 5 Tofitive, and Negative.

Pofitive, or Affirmative Quantities are thofe which are greater than nothing ; and which are affected with the Sign — f- prefix'd ; or fuppofed to be fo. See Positive.

Negative, or 'Privative Quantities are thofe lefs than nothings which are affected with the Sign — > prefix'd. See Negative.

Hence, 1. Since -f- is the Sign of Addition, and — the Sign of Subftraction 5 a pofitive Quantity is produced by adding any real Quantity to nothing 5 e.gr. o -J- 3 = 3 ; and o + a — + a. And a privative Quantity is produced by fubftracting any real Quantity out of nothing; e.gr. q — 3 = — 3 5 and o — a = — -a.

For an Illuftration— Suppofe when you are quite

dcftiiute of Money, fomebody gives you an hundred Pieces j you have then an hundred Pieces more than nothing ; which Pieces constitute % pofitive Quantity.

On the contrary, fuppofe you have no Money, yet owe an hundred Pieces ; yi,u have then an hundred Pieces lefs than nothing 5 for you mufl pay an hundred Pieces to have juit nothing. This Debt is a negative Q^iantity.

'\ hus in local Motion, Progrefs may be call'd a p$tiu& Quantity, and Regrcfs a negative one j becaufe the firft increafes, and the fecond dimmifhes the Space pafs'd tover.

And in Geometry, if a Line drawn towards any Part be accounted an affirmative Quantity ; another the contrary way wiil he a negative one.

3. P 'rival 'ive Quantities, therefore, are the Defects of foe pofitive Quantities ^hereby they are underflood ; and, contequentlj are no real Quantities : For we meafure the D c et} by the Quantity detective ; and thus it becomes in- telligible.

Since one Defect may exceed another, (e.gr. if feven be wanting, the Defect is areaterthan if only three be wanting) and fince privative Quantities are the Defect oi real Quan- tities'-, on privative Quantity 'being taken a certain Num- ber of times, may exceed another. Wherefore privative Quantities are homogeneous to one another.

4. But (ii ce the Defects of a pofitive Quantity taken any number of times can never exceed the pofitive Quantity, but grows ftill the more deficient 5 privative Quantities are heterogeneous to pofitive ones.

5. Since, then, privative Quantities are heterogeneous to pofitive ones, homogeneous to privative ones ; there can be no Ratio between^ privative and a pofitive Qiiantity, but there is a Ratio between privative ones. £. gr.

■ — 5 » . — j*» : : 3: 5. The Ratio, here, is the fame as if the Quantities were, pofitive. But it may be noted, that between 1 and — 1, and between — 1 and j, the Ratio is very different.

Addition a/Quantities, i. If the Quantities denoted by the fame Letter be affected with the fame Sign, the Numbers prefix'd to 'em are added as in common Arithme- tic. 2. If they be affected with different Signs, the Ad- dition is changed into Subftraction ; and to the Remainder is prefix'd the Sign of the greater. ;. Quantities denoted by different Letters, are added by means of the Sign -f- j as in the following Example.

QUA

4# + ib — zc — '5 d — g 5 a — z fr^y c -\-id — 35

9#-f-4C — 3d-

•4g

a — b

a—b-j-c

Subjir a ft ion of Qv ant it ies 5 fee Substruction. Mu tipiication andSDivifion ^/Quantities 5 fee Mul- tiplication and Division.

Combination of "Quantities ; fee Combination.

If a poutive Quantity be multiply'd, or divided by another pofitive Quantity, the Refult is a pofitive Quan- tity. * PS -

2. If a negative Quantity be multiply'd, or divided by a pofitive, the RefuLt is a negative.

3. If a negative Qttantity be multiply'd, or divided by another negative, the Rel'ult is a pofitive.

4. If a pofitive Quantity be multiply'd, or divided by a negative, the Refult is a negative Quantity.

Quantity, in Grammar, is the Meafure, or Magni- tude of the Syllables ; or that which determines them to be call'd long, or fhort. See Grammar, Prosody.

This Quantity is the Object of Profody $ and it is the regard to this that diitinguifhes Verfe from Prole. See Veb.se.

The Oeconomy and Arrangement of the Quantities, i. e. the diftribution of long and fhort Syllables, make what we call the Numbers. See Numbers.

The Quantities are ufed to be dittinguifh'd among the Grammarians by the Characters ^ port, and ~ long. See Character.

The Proportion betwixt the long and fhort Syllables may be generally nVd the fame as between the Crochet and Quaver in Mufic 5 viz,, as 2 to 1. See Time.

In molt Languages there are fome Syllables whofe Quan- tities vary, as the Meafure requires ; as in the Englift Record and Record.

Some Authors confound the Qjtant it ies with the Accent : But the difference is glaring ; tiie former being the length or fhortnefs of a Syllable, the latter rhe raifing or falling of the Voice. See Accent.

From two Quantities, viz. long and fhort Syllables, arife all the Varieties of Poetic Feet, which ate very great. Horace alone ufes no lefs than twenty-eight. Yet rhe

Greeks went vaftiy beyond the Romans in this refpi'd i

In effect, as many ways as two Quantities may be varied by compoficion, and tranfpofition from two to fix Syllables, fo many different Feet have the Greek Poets contrived, and that under diftinct Names, to the Number of 124. Tho* it is the Opinion of fome of the Learned, that Poetical Numbers may be fufficiently explain'd from the Feet of two or three Syllables, into which the reft are to be refolved.

The Feet form'd by the Antients of the long and fhort Syllables immediately 5 are the Spondee, confiiiing of two long Syllables j the Pyrrhic, of two fhort ones ; the tro- chee, of a long and fhort Syllable ; and the Iambic, of a long and fhort Syllable. See Spondee, Trochee, Iam- bic, &c-

Thofe of three Syllables are the Molojl, confiding of three long Syllables j the 'Tribrach of three fhort ones; the ^Datlyl of one long and two fhort Syllables; and the A'tapefi of two fhortand one long Syllable. See Dactyl, Anap&st, Tribrach, X3c.

The Englifb Tongue admits of no Feet above two Syl- lables, tho' both the Latin and Greek allow of fix.

Our Heroic Verfes confift of five long and five fliort Syllables intermix'd alternately ; tho' not fo ftrictly but that the Order may be difpenfed withall. Dryden varies them with admirable Beauty > fometimes his Heroic Verfe begins with along Syllable follow'd by two fhort ones.

The truth is, the Quantity of the Syllables is but little fix'd in tho modern Tongues, and there is (till lefs regard had to it in the Composition of modern Verfes 1 ■■ -The want of Feet, or rather the fhortnefs and uniformity of our Feet, makes a world of difference between the Numbers of the antient and modern Verfe. Our Poets are fetter'd, and their Fetters are fo fhort, but two poor Links, that it's no wonder they can make no extraordinary Motions.

The Antients fubfifted by their Quantities alone ; fo well were they diltinguifh'd, and fuch a Variety and Harmony did they afford. Our Quantities make fuch poor Mufic, that we are forced to call in the Gothic Aids uf Rhime to diftinguifhour Verfe from Profe. See Ode.

Yet have Attempts been made to fettle our Verfe on the antient and natural footing of Quantities, in exclufion of Rhime, and with fuch fuccefs too, (witnefs the Immor- tal Paradife Loft) as fee ms to leave the practice of Rhi-

ming iLexcufable The French have likewife attempted

the fame in their Tongue, particularly jfodelet, and after him Pafquier, Pajferat, and Rapin ; but they have all fail'd. See Rhime.

QUANTUM meruit, an Action upon the Cafe, grounded upon a Promife to pay a Man for doing fo much as he fhould deferve or merit.

QUARANTA1N, in old Law-Books wrote Quaren- tene, or Quarantena, denotes the Space of forty Days.

The Term is borrow 'd from the French ; and is fome- times ufed for the time of Lent. See Len t.

Qua.