vation con cing or Reading of Num nits is given, to the fecond fix Figures the general Name of Millions, to the third fix Figures the general Name of Bilions, to the fourth fix Figures the general Name of Trillions, &c. Hence every fix Figures, reckoning from the Right-hand, is called a Period; and every Period is diftinguished into two half Periods. Now by a Billion is meant, in, fhort, what is otherwife called a Million of Millions; and by a Trillion, is meant a Million of Millions of Millions. And the like is to be understood of Quadrilli ens, Quintillions, Sextillions, &c. 27. 4. Though the Name Units is regularAn Obfer ly to be understood, as applied to every cerning the half Period alternately, and alfo to the Pronoun whole firft Period; yet 'tis not ufual to pronounce the fame in reading Numbers. Thus the first three Figures 222 are ufually read thus, two Hundred twenty two, without adding Units of Units. And in like Manner, the third three Figures, 222, are usually read thus, two Hundred twenty two (not Units of Millions, but fimply) Millions. bers: 28. The fore going Ob By the fore-going Obfervations duly apprehended, it will be easy to read the fervations Number confifting of twenty-four Fior Rules gures, and contained in the Table of ficoncerning gural Notation, (Sect. 23 ;) namely, by tation, il firft dividing the faid Number into its figural No Periods i 1 Periods by full Stops, and then into its luftrated half Periods by Comma's, as above in the by an Ex ample, refpective Table; and then pronouncing each three Figures diftinctly with their proper Denominations, thus ; Two Hundred Twenty-two Thousand, two Hundred Twenty-two, Trillions. Two Hundred Twenty two Thousand, two Hundred Twenty-two, Billions. Two Hundred Twenty-two Thousand, two Hundred Twenty two, Millions. Two Hundred Twenty two Thousand, two Hundred Twenty two, (Units.) In like manner, the following Number of twenty Figures, viz. 97.546,832.172,945.631,874, is to be read thus Ninety-feven, Trillions. Five Hundred Forty fix Thousand, eight Hundred Thirty-two, Billions. One Hundred Seventy-two Thousand, nine Hundred Forty five, Millions. Six Hundred Thirty-one Thousand, eight Hundred Seventy-four (Units.) Where it is to be obferved, that, as in this, fo in other Numbers, it frequently happens, that the laft Period (or half Period) is often not compleat. 29. And again by another Example From what has been faid concerning 30. figural Notation, it evidently appears, of the Ufe of Cythat as the numerative Values of the nine phers. Figures are known by their Shape, viz. 1 One,' ■ One, 2 Two, 3 Three, (&c.) fo their denominative Values depend upon their Places, and are therefore variable. Thus in the Number expreffed in the Table, (fet down in Sect. 23.) the Figure 2 in the firft Place denotes two Units, in the fecond Place two Tens, in the third Place two Hundreds, in the fourth Place two Thousands, &c. Hence it appears, that in order to denote juft two Tens or Twenty, without any Units; it is neceffary to fhew fome how or other, that the Figure 2 ftands not in the first Place, but in the fecond Place. And to this End ferves (what is called) a (*) Cypher 3 namely, to fill up fuch antecedaneous Places, as are vacant of fignificant Figures, and thereby to fhew the respective Places of the fignificant Figures. Thus 2 (put by it felf, and fo understood to be in the first Place) denotes two Units; but 20 (i. e. 2 with a Cypher afore it, whereby is fhewn, that the faid 2 ftands in the fecond Place) denotes two Tens or Twenty. In like manner, 200 denotes two Hundreds; and 2,000 two Thon (*) Hence it is most probably derived from an Arabick Word, denoting a Vacancy. It is by Way of Diftinction termed by fome the infignificant Figure, as fignifying no Number it felf; the other Nine being termed fignificant Figures. Sands; Sands; and 2.000,000 two Millions, &c. preffing by ber propo As what has been faid concerning figu- 31. ral Notation, if rightly apprehended, is of denoabundantly fufficient to teach any one of ting or ex a competent Capacity, how to read any Figures Number propofed, and already expreffed any Num by Figures; fo is it in like manner abun- fed. dantly fufficient to teach, how to exprefs by Figures any Number propofed. For Inftance: Suppose it be required to exprefs twenty two Millions. From what has been faid, it is known, that the Figures 22 denote Twenty-two. And, becaufe twenty-two Millions is a fhorter Way of fpeaking (as has been obferved, Sect. 27.) for twenty two Units of Millions; and by the Table of figural Notation, (Sect. 23.) it is known, that Millions is the general Name of the fecond Period, and Units of Millions the Name of the first half whole Period of the faid fecond Period; hence it is known also, that 22 must stand in the two first Places of the fecond Period, i. e. in the 7th and 8th Places from the Beginning, and confequently muft have fix Cyphers fet before it, (namely, to fill up all the fix Places of the firft Period, which in this Number is void of fignificant Figures,) to make it denote twentytwo Millions; which is therefore denoted thus, 22 000 000. 32. And thus much for Notation (Literal Integers or as well as Figural) of Integers or whole Numbers, Numbers. Where it is to be observed, and Fra- that Numbers are fo called, when the tions, what. Things number'd are confider'd as fo many whole Things; whereas fhould the fame Things be confider'd as Fragments or Parts of any Thing elfe, then the Number is call'd a Fraction. For Example: Ten Shillings confider'd by themfelves, or as fo many whole Shillings, is esteem'd a whole Number; but ten Shillings confider'd as ten Twentieths, or the Half of a Pound, is esteem'd a Fraction. С НА Р. |