Page:Cyclopaedia, Chambers - Volume 1.djvu/351

Rh thousand, is sometimes us'd an I between two C's, the one erect, the other inverted, thus, CIↃ: Agreeable to this, six hundred may be express'd IↃC; and seven hundred, IↃCC, &c.

The Roman Character is now seldom us'd, but in Inscriptions of publick Monuments, on Medals, Coins, &c. in the Dates, Chapters, &c. of Books, &c.

The French Character, so call'd, because invented and chiefly us'd by the French, is more usually denoted, Character of Accompt, or Finance.

It consists of six Figures; part taken from the Letters of the usual current Hand, and partly imagin'd by the Inventor: The six Characters are j,b, x, L, C, y The j consonant standing for one, the b for five, the x for ten, the L for fifty, the C for an hundred, and the last Character y for a thousand.

This Character is only an Imitation of the Roman Character; and its use is in most respects the same, particularly in what relates to the Combination of certain Letters, which plac'd before or after others, dininish or increase their Value. Indeed it has these Things peculiar in it, that when several Units occur successively, only the last is express'd: 2dly, That ninety, and the following Numbers to one hundred, are express'd thus, jjjj$xxx$ ninety; jjjj$xxxj$ ninety one; jjjj$xxxjj$, &c.

It is principally us'd in the Chambers of Accompts; in the Accompts given in by Treasurers, Receivers, Farmers, and other Persons concern'd in the Management of the Revenue.

A Specimen of each of these Characters follows.

CHARACTERS, in Printing, are the Letters or Types, by the various Arrangement whereof, are compos'd Forms; whence Impressions are taken, by means of a Press, on Paper. See Letter, Type; see also Form, Printing, &c.

For the Method of casting these Characters, see Letter-Foundery.

Character is also us'd in several of the Arts, for Abbreviatures, and Symbols, contriv'd for the more concise, immediate, and artful conveyance of the Knowledge of Things. See Abbreviature, and Symobol.

In this Sense of the Word, Paulus Diaconus refers the Invention of Characters to Ennius; who, he says, contriv'd the first eleven hundred. To these were many more added, by Tullius Tyro, Cicero's freed Man; and Philargyrus, Fannius, and Aquila, Freedmen of Mecænas.

Lastly, L. Annæus Seneca made a Collection of them, reduc'd them into order, and increas'd their Number to five thousand. Tyro's Notes may be seen at the End of Gruter's Inscriptions.

Valerius Probus, a Grammarian, in the Time of Nero, labour'd to good purpose in explaining the Notes of the Antients. Diaconus wrote an ample Treatise of the Explication of the Characters in Law, under the Reign of the Emperor Conrad I. and Goltzius another for those of Medals.

Characters, or Symbols, are now chiefly affected in the several Parts of Mathematicks; particularly Algebra, Geometry, Trigonometry, and Astronomy: as also in Medicine, Chymistry, Musick, &c. The principal of each Kind we shall here subjoin.

Characters us'd in Arithmetic and Algebra.

a, b, c, and d, the first Letters of the Alphabet, are the Signs or Characters that denote the given Quantities; and z, y, x, &c. the last Letters, are the Characters of the Quantities sought. See Quantity.

Note, Equal Quantities are denoted by the same Character.

m,n,r,s,t &c. are Characters of indeterminate Exponents, both of Ratios and Powers; thus x$xxx$, y$xxxj$, z$xxxjj$, &c. demote indeterminate Powers of different Kinds; m x, n y, r z, different Multiples, or Submutliples of the Quantities x,y, z according as m,n,r are either whole Numbers or Fractions.

+ Is the sign of real Existence, and is call'd the affirmative or positive sign; importing the Quantities to which it is prefix'd, to be of a real and positive Nature. See Positive.

It is also the Sign of Addition, and is read Plus, or more; thus 9+3, is read 9 plus 3; or 9 more 3; that is, nine added to 3, or the Sum of 9 and 3, equal to 12. See Addition.

- Before a single Quantity, is the Sign of Negation, or negative Existence; shewing the Quantity to which it is prefix'd to be less than Nothing. See Negative.

Between Quantities, it is also the Sign of Subtraction, and is read Minus, or less; thus, 14-2, is read, 14 minus, or abating 2: that is, the Remainder of 14, 2 after has been subtracted, viz. 12. See Subtraction.

= Is the Sign of Equality: thus, 9+3=14 -2; signifies, 9 plus 3, to be equal to 14, minus 2. See Equality.

This Character was first introduc'd by Harriot: Des Cartes in lieu of it uses ∝. Before Harriot there was no Sign of Equality at all.

Wolfius, and some other Authors, use the Character = for the Identity of Ratios; or to shew the Terms to be in a Geometrical Proportion; which most Authors express thus :: See that Character.

× Is the Sign of Multiplication, denoting the Quantities on either side to be multiply'd into one another: thus, 4 × 6, is read 4 multiply'd by 6; or the Factum, or Product of 4 and 6=24; or the Rectangle between 4 and 6.

Ordinarily, however, in Algebra, the Sign is omitted, and the two Quantities put together: Thus, b d expresses the Product of the two Numbers denoted by b and d, which suppose 2 and 4, the Product whereof is 8, signify'd by b d.

Wolfius and others, make the Sign of Multiplication a Dot (.) between the two Factors: Thus 6.2 signifies, the Product of 6 and 2 = 12. See Multiplication.

Where one or both the Factors are compounded of several Letters, they are distinguifh'd by a Line drawn over 'em: thus, the Factum of a+ b-c into d, is wrote d × $xxxjjj$.

Guido Grandio, and after him Leibnitz, Wolfius, and others, to avoid the Perplexity of Lines, in lieu thereof distinguish the Compound Factors, by including 'em in a Parenthesis, thus (a+b-c) d.

÷ Is the Character of Division : thus a ÷ denotes the Quantity a to be divided by b

Indeed, ordinarily in Algebra, the Quotient is express'd Fraction-wise; thus $$\frac{a}{b}$$ denotes the Quotient of a divided by b.

Wolfius, &c. make the Sign of Divifion thus, 8:4 denotes the Quotient of 8 divided by 4=2.

If either the Divisor or Dividend, or both, be compos'd of several Letters ; v. g. a+b, divided by c; instead of writing the Quotient Fraction-wife thus $$\frac{a+b}{c}$$ Wolfius, &c. include the compound Quantities in a Parenthesis ; thus, (a +b): c. See Division.

Is the Character of Involution, or of producing the Square of any Quantity by multiplying it by it self. See Involution.

The Character of Evolution; or of extracting the Roots out of the several Powers; the Reverse of. See Evolution.

Is the Sign of Majority, or of the Excess of one Quantity beyond another: Some use this, or this.

Is the Sign of Minority: these two Characters were first introduc'd by Harriot, and us'd since by Wallis and Lamy.

Other Authors use others; some this, ; but the generality none at all. See Minority.

The Sign of Similitude, commended in the Miscellanea Berolinensia, and us'd by Leibnitz, Wolfius, and others; tho the generality of Authors use none. See Simlitude.

The same Character is us'd in other Authors for the Difference between two Quantities, while 'tis yet unknown which is the greater. See Difference.

√ Is the Character of Radicality, and shews the Root of the Quantity, to which it is prefix'd, is extracted, or to be extracted: Thus, √ 25, or √$xxxjjjj$ 25, denotes the Square Root of 25, viz. 5. and √$xxxb$ 25, the Cube Root of 25. See Root. Rh