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ABRIDGED.

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RITHMETICK is the Art or Science of com puting by numbers, and is comprised under five principal or fundamental Rules, viz. NOTATION or NuMERATION, ADDITION, SUBTRACTION, MULTIPLICA TION and DIVISION

NUMERATION

Teaches the different value of figures by their different places and to read or write any sum or number by these ten characters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.0 is called. a cypher, and all the rest are called figures or digits.

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2. Befides the simple value of figures as above noted, they have each a local value, according to the following law; viz. In a combination of figures, reckoning from right to left, the figure, in the first place reprefents. its primitive simple value; that in the second place, ten, times its fimple value, and so on the value of the figure, in each fucceeding place, being ten times the value of it, in that immediately preceding it.

3. The values of the places are estimated according to their order: the first is denominated the place of units;. the second, tens: the third, hundreds, and so on, as in, the Table. Thus, in the number 3467: 7 in the first place, fignifies only seven; 6 in the second place, figni fies 6 tens, or fixty; 4, in the third place, four hundred 3, in the fourth place, three thousand; and the whole, taken together, is read thus; three thousand four hundred and fixty seven.

4. A cypher, though of no fignification itself, yet it poffefsses a place, and when set on the right hand of figures, in whole numbers, increases their value in the same tenfold proportion; thus, 9 fignifies only nine ; but, if a cypher is placed on its right hand, thus, 90, it then becomes ninety,

To enumerate any parcel of figures, observe the following Rule.

First. Commit the words at the head of the Table viz. units, tens, hundreds, &c. to memory; then, to the fimple value of each figure, join, the name of its place, beginning at the left hand, and reading towards the right-More particularly-1. Place a dot under the right hand figure of the 2d, 4th, 6th, 8th, &c. half periods, and the figure over such dot will, universally, have the name of thousands.-2. Place the figures 1, 2, 3, 4, &c. as indices, over the 2d, 3d, 4th, &c. period: These indices, will then show the number of times the millions are involved the figure under 1, bearing the name of millions, that under 2, the name of billions (or millions of millions) that under 3, trillions (or millions of millions of millions.).

Thousands

EXAMPLE.

Sextill. Quintili. Quatrill. Trillions. Eillions. Millions. Units.

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th. un. th. un. th. un.. th. un. th. un. th. un. c.x.t.c.x.u.

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913,208,000, 341,620,0573219,356,809 379;120, 406;129.763

Thousands

Thousands

Thousands

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Thousands

Thousands

Thousands

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NOTE

NOTE 1. Billions is substituted for millions of millions; Trillions, for millions of millions of millions: Quatrillions, for millions of millions of millions of millions.

Quintillions, Sextillions, Septillions, Octillions, Nonmillions Decillions, Undecillions, Duodecillions &c. an. fwer to millions so often involved as their indices refpec tively denote.

NOTE 2. The right hand figure of each half period has the place of units, of that half period; the middle one, that of tens, and the left hand one, that of hundreds.

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Write down, in proper figures, the following numbers.

Fifteen.

Two hundred and feventy-nine.

Three thousand, four hundred and three.

Thirty seven thousand, five hundred and fixty seven.
Four hundred, one thousand and twenty eight.

Nine millions, seventy two thousand and two hundred.
Fifty five millions, three hundred nine thousand and

nine.

Eight hundred millions, fourty four thousand, and fifty five.

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Two thousand, five hundred and forty three millions, four hundred and thirty one thousand, seven hundred and two.

Write down in words at length, the following numbers. 8437 709040 3476194 7584397647 879066 84094007 40163189186 12976506 4091875 690748591 500098422700 Notation

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3010

I. One.

H. Two.

III. Three.

IV. Four.

V. Five.

VI. Six.

Notation by Roman Letters.

VII. Seven. VIII. Eight. IX. Nine. X. Ten. XI. Eleven. XII. Twelve. XIII. Thirteen. XIV. Fourteen. XV. Fifteen. XVI. Sixteen. XVII. Seventeen. XVIII. Eighteen. XIX. Nineteen. XX. Twenty. XXX. Thirty.

XL. Forty. L. Fifty. LX. Sixty. LXX. Seventy. LXXX. Eighty. XC. Ninety. C. Hundred. CC. Two Hundred. CCC. Three Hundred. CCCC. Four Hundred. D or I. Five Hundred. DC. Six Hundred. DCC. Seven Hundred. DCCC. Eight Hundred. DCCCC. Nine Hundred. M or CIO. One Thousand. I. Five Thousand. I. Fifty Thousand. 1. Five hund. thou. MDCCCVII. One thousand

eight hundred and seven.

A less literal number, placed after a greater, always augments the value of the greater; if put before, it diminishes it. Thus, VI is 6; IV is 4; XI is II; IX is 9, &c.

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ADDITION

Is the putting together of two or more numbers, or fums, to make them one total, or whole fum.

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Is the adding of several integers or whole numbers

gether, which are all of one kind, or fort; as, 7 poun 12 pounds and 20 pounds, being added together, the.. aggregate, or fum total, is 39 pounds.

RULE.

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