Chap. I.

IO.

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

II.

Character

According to the fame Method it seems X, why very probable, that D, as being the Inithe Latin tial of Decem, did at firft denote among of Ten, the Latins, Ten; and half of the faid and V of Letter D, viz. v, did thence denote half Ten or Five. Which faid half Letter resembling somewhat a V, therefore Printers (and Scribes) have not scrupled to put the Letter V (instead of the Letter D halved) for Five. And forafmuch as

Five.

I 2. Of the

the whole Letter D, came (as has been obferved, 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 togother, and fo refembling an X, hence ufed to denote twice Five or Ten.

Thus much for the Original 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.

Thoufand,

"Thousand, they were deduced from the Chap. I. Letter M, as is fhewn in the following Table.

ATABLE of the Numeral Characters used by the Romans or Latins.

13. A Table of the numeral

Characters used by the La

tins.

an hundred Thousand.

I five hundred Thousand.

CCCCI၁၁၁၁ a Million.

were Obferva

By these Characters variously joined to- 14. gether or repeated, the Latins wont to express their Numbers.

it is to be observed, that

Where

tions con

cerning the Latin Notation.

15.

1. Characters of greater Value, are regularly and generally placed before ChaObfervatiracters of lefs Value. Thus VI denotes on the ft. Six, XI Eleven, LX Sixty, CX an Hundred and Ten, MDCCXXIII (the present Year of Chrift) one Thoufand feven Hun dred and Twenty Three.

16.

Obfervati

2. I and X are fometimes placed before Characters of greater Value, namely, on the ad.

B 3

I before

Chap. I. I before V or X, and X before L or C ; in which Cafe, (†) the Value of I and X is to be fubftracted from the Value of the following Character. As IV Four, IX Nine, XL Forty, XC Ninety.

17.

3. V and L are never repeated, and Obfervati- none of the other Characters above four on the 3d. Times. Thus IIII (or IV) Four, but V Five; XXX Thirty, but XL Forty; LXXX Eighty, but XC Ninety; CCCC four Hundred, but D five Hundred. And thus much for the Roman or Latin Notation of Numbers.

!

18.

Notation

Con

In reference to literal Notation, it reOf the Al- mains now only to observe, that there is gebraical another numeral Ufe of Letters, namely, by Letters. Algebraical; according to which any Letter is put to denote any Number. cerning which, fee more Chap. 9. Proceed we here to figural Notation, or Of the nine the Way of expreffing Numbers by FiFigures. gures; whereby are understood the Characters commonly made ufe of to denote Numbers among us, and are these Nine, viz. 1 One, 2 Two, 3 Three, 4 Four, 5 Five, 6 Six, 7 Seven, 8 Eight, 9 Nine.

19.

Numeral

(+) Some ufe IIX instead of VIII to denote Eight, and XXC instead of LXXX to denote Eighty, &c.

20.

Every

two Parts,

minative

In order to perceive, wherein lies the Chap. I. great Difference between literal and figural Notation, it is to be known, that in all Numbers (confidered even in them- Number felves, and without any Refpect to the confifts of Things number'd) are diftinguishable two a DenoParts. Whereof one may be called the and Nudenominative Part, as being that which merative, tells us, what the numeral Quantity is which is number'd, whether Units, or Tens, or Hundreds, &c. The other may be called the numerative Part, as telling how many Units, or Tens, or Hundreds, (c.) are denoted. Thus in the Number ten Thoufand, Thousand is the Denominative, Ten is the numerative Part in twenty (i.e. two Tens) Tens is the Denominative, Two the Numerative; and fo in the leaft Number of all, viz. one (i. e. one Unit) Unit is the Denominative Part, One the Numerative.

21.

Difference

tation

This being premised, the great difference between literal and figural Notation The great confifts in this, that numeral Letters are between reftrained always to denote one and the literal and fame, both denominative and numerative figural NoPart of the Number, which they exprefs; wherein whereas numeral Figures are reftrained it confifts. always to denote only the fame numerative Part, and vary as to the denominative Part, according to the various Places wherein they ftand. For Inftance: The Letter

B 4

Chap. I. Letter V always denotes five Units,whereas the Figure 5 denotes five Units, or Tens, or Hundreds, (c.) according to the Place wherein it ftands; as 555 denotes five Handred fifty-five.

thod of figural Notation.

Hence arifes the more expedite Manner of expreffing Numbers by Figures, than by Letters. For Inftance: The present Year of our Lord requires nine Letters to exprefs it, viz. MDCCXXIII; whereas it may be expressed only by these four Figures 1723. And in expreffing fome other Numbers, there is a much greater Difference; as for Example, MDCCLXXVII 1777, MDCCCLXXXVIII 1888.

Now Figures thus (always retaining only their Numerative Value, but) changing their denominative Value, according to the Place or Rank wherein they ftand; hence the whole Art of figural Notation is comprehended in the following Table.

Trillions.

Billions.

Millions. Units.

Thds. Units. Thds. Units. Thds. Units. Thds. Units. &c. 222, 222. 222, 222. 222, 222, 222, 222. HTU, HTU. HTU, HTU. HTU,HTU. HTU,HTU,

24. In the fore going Table are thefe ParThe Places ticulars obfervable.

of Figures

how reck

1. That numeral Places are reckoned zed. from the Right-hand, and fo cohtrary to the Order wherein the Figures are read,

So