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A

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THE

THE

Young Gentleman's

ARITHMETICK,

BOTH

Common and Algebraical.

CHA P. I.

Of Notation, or the Art of Expreffing Numbers by their right Characters, and of Reading them aright, when fo expressed.

A

RITHMETICK, like the I. Names of the other liberal Arts Arithmeor Sciences, is of Greek Origi-tick, what, nal, and imports, in that Language, as much as the Art of right Numbring.

2.

Right Numbring confifts, either in Denoting (or Expreffing) Numbers by their Diftin right Characters, which is called Notati-into twe

B

on

guishable

Parts,No

tion.

general on, and comprehends under it the Art of tation and Reading Numbers aright, (forasmuch as Computa- he that can denote Numbers aright, can read them aright, when fo denoted ;) or in Computing aright by Adding Numbers together, or Substracting them one from the other, and the like; which may therefore be called Computation.

3.

Notation two-fold.

4.

ral.

Notation is either Literal or Figu

Literal Notation is fo called, beLiteral No- caufe it expreffes Numbers by Lettation, ters.

what.

ufed by the

5. It was formerly, if not still, made use Literal of by moft of the eastern Nations, as the Notation Hebrews or Jews, Chaldeans, Syrians, Aeaftern rabians, Perfians, &c. who all expreffed Nations, their Numbers by the Letters of their refpective Alphabets.

6. The Greeks did likewife exprefs NumOf the No-bers by the feveral Letters of their Altation of the Greeks. Phabet. They had alfo another Way of expreffing Numbers by the initial capital Letters of fome of their Numeral Words; as Π Πέντε Five, Δ Δέκα Ten, Η Ηεκατόν an Hundred, xxixos a Thonfand, M Mueror ten Thousand.

7.

From this last Method of expreffing Of the No- Numbers ufed by the Greeks, the Latins tation of the Latins, in all Probability deduced their Notation or Romans by the initial capital Letters of fome of their numeral Words, and other Cha

racters

racters made from the faid Capitals, viz. V Five, X Ten, L Fifty, C an Hundred, Dfive Hundred, Ma Thousand.

8.0

Among the Latins as well as Greeks, the Character I, denotes One; it being (*),the natu natural, and therefore usual even for moft illiterate Perfons, to denote fingle Thing, by one fingle Stroke Line.

ral Chara

the

one

or

der of One; and so used both by the Greeks and Latins.

9.

M, As being the initial (or firft Letter) of Mille, is the Latin Character for a M, why Thonfand. And whereas the old Way of the Latin ofthe Chara&er writing this Letter was thus CD, (for of a Thouwhich our Printers now a days ufe CIO, fand, and D of five or clɔ,) hence Half the faid Letter, D, Hundred. came to be used by the Latins for Half a Thousand, or five Hundred. And because 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 ID (inftead of the faid half D) to denote five Hundred.

(*) One fingle Stroke or Line being the natural and moft fimple Character of one fingle Thing, there was no Occafion for the Greeks or Latins to make ufe 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 seems much more natural to fuppofe, that the Word los was used by them to fignify One, because I is the natural Mark for One; and that los was made from I, not I taken from Ios.

10.

Character

In like manner C, being the Initial of C, why Centum, denotes in Latin an Hundred. the Latin And whereas the faid Letter was anciently of an Hun-writ thus, E, hence Half of it, viz. L, was dred, and used to denote among the Latins Half an Hundred or Fifty: Which half Letter refembling a Capital L, Printers fcruple not to use the Letter L, inftead thereof to denote Fifty.

Lof Fifty.

II.

X, why the Latin of Ten, and V of

Character

Five.

According to the fame Method it feems very probable, that D, as being the Initial of Decem, did at firft denote among the Latins Ten; and Half of the faid Letter D, viz. D, did thence denote half Ten or Five. Which faid half Letter refembling somewhat a V, therefore Printers (and Scribes) have not fcrupled to put the Letter V (inftead of the Letter D halved) for Five. And forafmuch as the whole Letter D came (as has been observed, Sect. 9.) to be used for five Hundred; therefore, there has been another Character found out for Ten, viz. two half D's joined with their Bottoms together, or two V's joined at the Points or narrow Ends together, and fo resembling an X, hence used to denote twice Five or Ten. 12. Thus much for the Original of the of the Roman or Latin Notation to a Thousand. Millenary, As for the Millenary Characters, whereof the La- by they expreffed Numbers above a

Characters

tins.

Thousand,