ТНЕ HA P. I. Of Notation, or the Art Cof expreffing Numbers by their right Characters, and of Reading them a- right, when fo express'd. Page 1 CHAP. II. of Computation, and the CHAP. VII. Of the Addition, Sub- ftraction, Multiplication, and Divisi- CHAP. VIII. Of the Addition, Sub- ftraction, Multiplication, and Division, С Н А Р. I THE Young Gentleman's ARITHMETICK, BOTH Common and Algebraical. CHAP. I. Of Notation, or the Art of Expreffing Numbers by their right Characters, and of Reading them aright, when fo expreffed. A 1. RITHMETICK, like the Chap. I. Names of the other liberal Arts or Sciences, is of Greek Origi- Arithmenal, and imports, in that Lan- tick,what. guage, as much as the Art of right Numbring. 2. Right Numbring confifts, either in Denoting (or Expreffing) Numbers by their Diftinright Characters, which is called Notati-guishable into two 1 Chap. I. on, and comprehends under it the Art of general Reading Numbers aright, (forasmuch as Parts,No- he that can denote Numbers aright, can tation and read them aright, when fo denoted ;) or Computation. in Computing aright, by Adding Numbers together, or Subftracting them one from the other, and the like; which may therefore be called Computation. 3. Notation Notation is either Literal or Figural. Literal Notation is fo called, because two-fold. it expresses Numbers by Letters. 4. Literal what. It was formerly, if not ftill, made use Notation, of by most of the Eastern Nations, as the Hebrews or Jews, Chaldeans, Syrians, 5. Arabians, Perfians, &c. who all expreffed Notation their Numbers, by the Letters of their ufed by the respective Alphabets. Literal Nations. 6. tation of Eaftern The Greeks did likewise express Numbers by the feveral Letters of their AlOf the No- phabet. They had alfo another way of the Greeks. expreffing Numbers by the Initial Capital Letters of fome of their Numeral Words; as Π. Πέντε Five, Δ Δέκα, Ten, (*) Η κα H Hexaτὸν, an Hundred, X Xixo, a Thousand, M Mugio, Ten Thousand. 7. From this last Method of expreffing Of the No- Numbers used by the Greeks, the Latins tation of in all Probability deduced their Notation or Romans. by the initial Capital Letters of fome of the Latins, their (*) The Greek [H] or Eta was alfo by the Greeks used as a Note of Afpiration only; and thence the Latins took their H, as we from them. their Numeral Words, and other Cha- Chap. I. racters made from the faid Capitals, viz. V Five, X Ten, L Fifty, Can Hundred, D Five Hundred, M a Thousand. tural Cha both by the and La 9. Among the Latins as well as Greeks, the 8. Character I, denotes One; it being (*) na- I, the na tural, and therefore ufual even for the most racter of illiterate Perfons, to denote one fingle One; and Thing, by one fingle Stroke or Line. So used M, as being the initial (or first Letter) Greeks of Mille, is the Latin Character for a tins. Thousand. And whereas the old Way of writing this Letter was thus m, (for M, why which our Printers now a-days ufe Cl, Character or clǝ,) hence Half the faid Letter, D, of a Thoucame to be used by the Latins for Half a fand, and Thoufand, or five Hundred. And because Hundred. D of five this fame half Letter resembles a D, or the Letter I, with a C turned the wrong Way; hence Scribes and Printers have used the said D or I (inftead of the faid half D) to denote five Hundred. (*) One fingle Stroke or Line being the natural and most fimple Character of one fingle Thing, there was no Occafion for the Greeks or Latins to make use of the initial Capital Letter of their Numeral Word for One. And 'tis evident, the Latins did not. As for the Greeks it is commonly thought, that they took I for to denote One, as being the Initial of Ios, which fignifies One in their Language; but it feems much more natural to fuppofe, that the Word Los was ufed by them to fignify One, because I is the natural Mark for One; and that los was made from I, not I taken from tos. the Latin |