Page:Cyclopaedia, Chambers - Volume 2.djvu/811

 SUR

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SURCHARGE of the Forcft, is when a Commoner puts more Beafts in the Forcft than he has a Right to. See Forest.

SURCINGLE, a Girdle, wherewith 'the Clergy of the Church of England ufually tye their Caflbcks.

SURCOAT, a Coat ot Arms, to be wore over other Armour. See Coat of Arms.

SURD, in Arithmetick, an irrational Number, or Quan- tity ; or a Number, ISc that is incommenfurate to Unity. See Irrational Number.

When any Number or Quantity hath its Root propos'd to

SUR

To Reduce •/ 2) V : a a 2)

■ X

4

V :bb

f. a and y 1 :.h b

V-

To reduce Surds

to the loveft Terns pojfble : Divide tin

be extracted, and yet is not a true figurate Number of that ^"' VJ ty tllc greater! Square, Cube, Kcpiadraie, i^c, or any ^ Kind ^ that is, if its fquare Root being demanded, it is not ?_ v'BljJ* Power, which you can difcover is contain'd in

a true Square: If its Cube Root being requird, itfeif be not a true Cube, 0-e. then it is impoflible to affign, either in whole Numbers or Fractions, any exact Root ot luch Num- ber propos'd.

And whenever this happens, it is ufual in Mathematicks, to mark the requir'd Root of fuch Numbers or Quantities, by prefixing before it the proper Mark of Radicality, which is y 1 : 'Ihus -/ : 2 fignifies the Square Root of 2, and ?

V : 16, or ■/ : (3) 16, fignifies the Cubic Root of 16 : Which Roots, becaule they are impoflible to be exprefs'd in Numbers exactly, (for no effable Number, either Integer or Fraction, multiply'd into itfeif, can ever produce 2 ; or be- ing multiply'd Cubically, can ever produce 16) are very properly call'd Surd- Roots.

There is alio another Way of Notation now much in Ufe, whereby Roots are exprefs'd without the Radical Sign, by their Indexes : Thus, as x l, it', *', e?C, fignify the Square

x\ fignify the

Cube, and 5th Power of x ; fo Square Root, Cube, &c. of x.

The Reaion of which is plain enough ; for Since y* : x is A Geometrical mean Proportional between 1 and x, fo a is an Arithmetical mean Proportional between o and 1 ; and therefore as 2 is the Index uf the Square of x, 7 will be the proper Index of its Squate Root, i$c.

Oblerve alio, that for Convenience, or Brevity's Sake, Quantities or Numbers, which are not Surds, are often ex- prefs'd in the Form of Surd Roots, Thus, y' : 4 y 1 :2-

4 3 3

•/ : 27, &c. fignify, 2—3, gfc.

But tho' thefe Surd Roots (when truly fuch) are inex- prefiible in Numbers, they ate yet capable of Atithmetical Operations, (fuch as Addition, Subftrailion, Multiplication,

11, and will meaiure it without any Remainder ; and then prefix the Root ol that Power before the Quotient, or Suri, to divided, and this will produce a new Suri of the lame Value with the former, but in more fimple Terms. Thus, V ■ i6aab, by dividing by 16 a a, and prefixing the Root 4 a, will be reduc'd to this, 4 a ■/ : b, and ■/ : 12, will be

deprefs'd to 2 / : 3. Alfo y/ :c £> r will be brought down to b y' : cr.

This Reduftion is of great Ufe whenever it can be per- form 'd : But it no fuch Square, Cube, Biquadrate, &c. can be found for a Divifor, then you mull fin.i out all the Di- vifors of the Power of the Surd propos'd; and then lee whether any of them be a Square, Cube, t$c. or fiich a Power as the Radical Sign denotes ; and if any fuch can be found, let that be ufed in the fame Manner as is abovcfaid, to free the Surd Quantity in Part from the Radical Sign. Thus, if / : 288 be propos'd; among its Divifors will be found the Squares, 4, 9 , ,g, 3 6> an d , 44 ; by which, if 288 be divided, there will arile the Quotients 72, 32, 18, 8, and 2; wherefore inftead of y 1 .-288, you mav put 2 •/=72, or 3v /: 3 2, or 4/: 18, or 6 y' • 8, or laflly, 12 y" : 2, and the fame may be done in Species. But for the whole Arithmetic of Surds, fee Kerfefs Algebra, and others on the lame Subject.

SURETY of the Peace, (fo call'd, becaufe the Party that was in fear, is thereby fecur'd) is the acknowledging a Bond to the Prince, taken by a competent Judge of Record, for the keeping the Peace. See Peace.

This Peace, a Juftice of the Peace may command, either as a Mimffer, when commanded thereto by higher Autho- rity ; ot as a Judge, when he dorh it of his own Power, de- riv'd from his Commiflion.

Surety of the good abearing, differs from this ; that where-

the Peace is not broken without an Affrav, or luch like ;

Divifion, &c) which how readily to perform, the Algebraift the Surety de bono geftu may be broken by'ihe Number of

ought not to be ignorant

Surds are either Simple, which are exprefs'd by one fingle Term ; ot Compound, which are form'd by the Addition or Subftraclion of fimple Surds : As 1/ : 5 -j- y : 1 : -y/ : 5 —

V : 2, or •/ : 7 -f- ■>/ : % : Which laft is call'd an univerfal Root, and fignifies the Cubic Root of that Number, which is the Refult of adding 7 to the Square Root of 2.

To reduce rational Quantities to the Form of any Surd Roots affign'd j involve the rational Quantity according to the Index of ihe Power of the Surd, and then prefix before it the Radical Sign of the Surd propos'd. Thus to reduce tf=I0, to the Form of 1/ : i$=;&, you mult fquare a = 10 ; and prefixing the Sign, it will Itand thus, ■/ ; a a = 1/ : 100, which is the Form of the Surd defir'd.

4

So alfo, if 3 were to be brought to the Form of y' : 12, you mult raife 3 up to its fourth Power, and then prefixing

4 &

the Note of Radicality to it, it will be -/ .- 81, or 8 1 '

4

which is in the fame Form with ^/ : 12.

And this Way may a fimple Surd Fraction, whofe Radi- cal Sign refers only to one of its Terms, be changed into another, which /hall refpe£l both Numerator and Denomi-

-y/ ~ 2 2 <

nator. Thus is reduc'd to y/ : and, to

-/ : 4

y' : j where the Radical Sign affefts both Numera- tor and Denominator.

To reduce fimple Surds, having different Radical Signs, (which are call'd Heterogeneal Surds) to others that may have one common Radical Sign, or which are Homogeneal ; divide the Indexes of the Powers by their greatelt common Divifor, and let the Quotients under the Dividends; then multiply thofe Indexes crols-ways by each other's Quotients, and before the Product fet the common Radical Sign -y/ : with its proper Index : Then involve the Powers of the given Roots alternately, according to the Index of each other's Quotient 5 and before thofe Produ&s, prefix the com- mon Radical Sign before found.

a Man's Company, or by his or their Weapon, or Harnefs.

SURFACE, in Geometry. See Superficies.

SURFEIT, an Indi/pofition caus'd by Exceis in Eating or Drinking, that h, by over-charging the Stomach. It is ufually attended with Eruptions, and iometimes with a Fever. See Plenitude.

SuRFEiT-#^/(?ri is a Water diftill'd from Poppies, and other Herbs, proper to cure Indigeftions.

SURGE : The Sailors call a Wave or Billow of the Sea a Surge: Alfo, when they are heaving at the Capflan, if the Cable happen to (lip back, a little, they lay. The Cable fums.

SURGERY. SeeCHiRuRGERY.

SURMOUNTED, is the Herald's Term for the Bearing of one Ordinary upon another : thus in the adjoining Figure, a Pile is /w- mounted of a Chevron, Harris.

SURNAME, a Name added to the Pro- per or BaptifmalName, to denominate the Perfon of fuch a Family. See Name.

'Twas the Romans hrft introduced the Ufe of Hereditary Names 5 and that on Occafions of their League with the Sahines j for the Confirmation whereof, it was agreed, That the Romans fhould prefix Sabine Names, and 'the Sabines t Roman Names, to their own.

Thefe new Names became Family Names, or Surnames, and the old Ones continued perfonal Names. The former they call'd Ccgnomina % and the latter ^r^nomina. SeePaJENO- men and Cognomen.

When they came to be ufed among the French and EngHp, they were call'd Slir-names or Sir-names, not becaufe they are the Names of the Sire or Father ; but, according to Cambden y becaufe they are fuper-added to the perfonal Name 5 or, rather, with Du Cange, becaufe at firft, this Family-name

was wrote over (Sur) the other Name thus : ^ C £™jf° U

In lieu of Surnames, the Hebre~vs, to keep up the Memory of their Tribes, ufed the Name of their Father, with the Addition of Sen, Son ; as Melchi 'Men-Addi, AddlSen Cofam, ££?c. fo the Greek, "UafO- tS AeaJW** ; Icarus, the Son of Dedalus, Dedalus the Sou of Eupalmus, (£c.

So, alfo, the ancient Britons, Ceonred, Ceohvaldwg, Ceol- ivald Cuthing, that is, Ceonred Son of Ceokvald, Son of Cuth 5 and in the fame Scnfe, the later Jfelp ufe Jlp for Map, Son,