M ATHEMATICKS (μαθηματική ) originally fignified any Difcipline, or Learning (nois); but now is the cience, or rather thofe Sciences, which enable us to onfider the various Relations and Properties of 'uantity. 2. Mathematicks may be confidered as confifting two Parts, viz. 1. Pure, fimple, or abftracted, which treats of uantity confidered in the Abftract, i. e. without by Relation to Bodies, or fenfible Objects. 2. Mixt Mathematicks confider Quantity as bfifting in material Beings. This is a very extene Part of the Mathematicks." 3. Mathematicks are also divided (by fome Authors) into Speculative and Practical. Speculative treats only of the fimple Knowledge of the Thing propofed, contenting itself with the bare Discovery of Falfhood, or the Investigation of Truth. Practical fhews fomething ufeful, or advantageous to Mankind. 4. Quantity, (Quantité, Fr. Quantitas, Lat.) may be defined to be whatever admits of any Kind of Computation, or Menfuration; or which, by Comparifon, may be faid to be greater, or lefs, than another Thing of the fame Nature. 5. Unity, (Unitas, Lat.) is the Idea we have of any Thing confidered as alone and undivided; or as feveral Things collected into one Whole; (not taking Notice of any Differences that may happen to be amongst them in other Refpects;) as one Pen, one Ship, one Flock, &c. in Contradiftinction to a Multitude, or many, as Pens, Ships, Flocks, &c. 6. A Number (Nombre, Fr.) is either an Unit, or two or more Units collected together. * It is by Numbers that we explain how many the Objects of our Knowledge are, as how many Men, Houfes, Ships, &c. Numbers are divided into three Kinds, Integers, Fractions, and Surds. An Integer is that which am Unit measures; a Fraction is measured by a Submultiple of the Integer; a Surd is incommenfurable by Unity. (In writing Numbers we make Ufe of thefe Arabian Characters, o, nothing; 1, one; 2, two; 3, three; 4, four; 5, five; 6, fix; 7, feven; 8, eight; 9, nine.) Thus 3, when confidered as fo many diftinct Things, as 3 Farthings, (3) is an Integer, or whole Number, and is meafurable by an Unit; for I is contained exactly 3 Times in 3: But when Farthings are confidered as Part of a Penny, as 3, (three 3 * It has been difputed, whether an Unit be a Number, by fome ingenious Writers; however, it is evident, that, the Definitions of Terms being arbitrary, it may be defined, so that an Unit may, or may not be a Number.. (three Fourths, or 3 Parts of four) then it (viz. 4) is a fractional Number; and is measurable by a Submultiple or Part of the Integer, viz. by, one Fourth of the Integer; for one Fourth is contained in three Fourths, exactly three Times. As to a furd Number, it cannot be well explained in this Place; and therefore we fhall refer the Reader to EVOLUTION in this Effay; and for the Definitions of Multiple and Sub-multiple, to MULTIPLICATION and DIVISION refpectively. 7. Arithmetick, ( àpidμis and μerpéw) is that Part of the Mathematicks which teaches fome of the chief Properties of Numbers, with the Methods of applying them to Computation in the common Purposes of Life; fuch, for In:cance, is computing the Value or Price of any Parcel of Goods, either bought or fold. There are feveral Kinds of Arithmetick, as Vulgar, Decimal, &c. but in this Effay we fhall only illuftrate and demonstrate the Elements of Vulgar Arithmetick; fo called from its being that which is most commonly used and beft understood by the Vulgar, or common People. CHA P. II. Of NOTATION. 8. Y Notation, (Notatio, Lat.) or Numeration, reading and writing Numbers. That this may be regularly treated of, the first Thing to be done is to explain the Characters we intend to make Ufe of; which are as follows: ., Therefore. +, is the Sign, or Mark for (More, or) Plus, or And. the Sign for (Lefs, or) Minus. *, the x, the Sign of Multiplication, as 2x3, is, 2 multiplied by 3. , the Sign of Divifion, as 42, is, 4 divided by 2. , equal to, or the Sign of Equality. We have already taken Notice, that 1, is the Mark for I or an Unit; 2, two; 3, three; 4, four; 5, five; 6, fix; 7, feven; 8, eight; 9, nine; and o, for nothing: Now, the better to explain what we mean by thefe Names, it may be proper to obferve, that 1+1=2, is called, in our Language, Two. 1+1+1+1+1=5, Five. Or thus, 1+1=2, 2+1=3, 3+1=4, 4+1=59 5+1=6, 6+1=7, 7+1=8, 8+1=9, and 9+1 is called Ten; and ten Tens a Hundred, ten Hun-dreds a Thousand, a thousand Thousands a Million, a Million of Millions a Billion, a Million of Billions a Trillion, a Million of Trillions a Quadrillion, &c. The intermediate Numbers are thus named: Ten and one are called Eleven; ten and two, Twelve; ten and three, Thirteen; ten and four, Fourteen; ten and five, Fifteen; ten and fix, Sixteen; ten and feven, Seventeen; ten and eight, Eighteen; ten and nine, Nineteen; ten and ten, Twenty: Then twenty and one we call Twenty-one; twenty and two, Twenty-two, &c. till we come to twenty and ten, which we call Thirty; the next. ten, Forty; the next, Fifty; the next, Sixty; feven tens, Seventy; eight tens, Eighty; nine tens, Ninety; ten tens, a Hundred: Then we fay on a hundred and one, a hundred and two, &c. |