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236

263

279

F.volution, or the extracting of Roots,

217

Extraction of the Square Root,

218

Rules for the square root of Vulgar Fractions and mix-

ed numbers,

Application and use of the Square Root,

222

Extraction of the Cube Root,

226

Application and use of the Cube Root,

233

Extraction of the Biquadrate Root,

235

of the surfolids by approximation,

A general rule for extracting the Roots of all Powers, 237

Proportion in general,

239

Arithmetical Proportion,

241

Progression,

242

Geometrical Proportion,

248

Progression,

: 249

Simple interest,

258

by Decimals,

Discount,

277

Barter,

Lors and Gain,

283

Equation of Payment,

291

Comulion, or Factorage,

393

Brokerage,

294

Buying and selling stocks,

295

Policies of Insurance,

296

Compound Interest,

299

by Decimals,

30%

Discount by Compound Intereit,

207

Aonaties, or Pensions in arrears at Compound Interest, 308

Present worth of annuities, at Compound Interest,

3FI

Annuities in Reversion, at Compound Interest, 314

Table shewing the amount of £1 from one year to 40, 319

Thewing the present worth of £r from a year to 40, 320

--thewing the amount of £i annuity,

311

--hewing the present worth of £i annuity, 322

-hewing the annuity which £ I will purchase, 323

Alligation Medial,

324

- Alternate,

325

Single Polition,

331

Double Polition,

33.4

Permutations and Combinations,

The use of Logarithms,

342

Tables of Exchange,

345

directing to buy and fell by the Hundred Weight, 347

--to reduce Troy to Avoirdupois,

to reduce Avoirdupois to Troy,

Appendix,

ABRIDGED.

A

RITHMETICK is the Art or Science of com

puting by numbers, and is comprised under five priocipal or fundamental Rules, viz. NOTATION or Nua MERATION, Addition, SUBTRACTION, MULTIPLICA. Fion 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. Lo is called a cypher, and all the rest are called figures or digits.

2. Befides the simple value of figures as above noted, they have each a local value, according to the follow, iog law ; viz. In a combination of figures, reckoning from right to left, the figrire, in the first place represents its primitive simple value ; that in the second place, ten times its simple value, and so on the value of the figdure, in each succeeding place, being tea 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 fecond place, figni -fies 6. tens, or fixty ; 4, in the third place, four hundreds 3; in the fourth place, three thousand ; and the whole, taken together, is read thus ; three thousand four huadred and sixty feven,

4. А

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

To enumerate any parcel of figures, observe the fol lowing Rule.

First, Commit the words at the head of the Table viz. units, tens, handreds, &c. to memory ; then, to the fimple value of each figare, 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 ad, 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, &ça as iodices, over the 2d, 3d, 4th, &c. period : Thefe 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 milljons of millioos.)

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3 943, 208;000, 341,620, 0573219. 356;809 379;1 20, 406;129.763

Thousands

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NOTE T. Billions is substituted for millions of mill ions ; 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 fo often involved as their indices respec• tively denote.

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

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THE APPLICATION.

Write down, ia proper figures, the following numbers.

Fifteen.
Two hundred and seventy-nine.
Three thousand, four hundred and three.
Thirty seven thousand, five hundred and fixty féven.
Four hundred, one thousand and twenty 'eight.
Nine millions, seventy two thousand and two hundređ.
Fifty five millions, three hundred nine thousand and

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

five. Two thousand, five hundred and forty three millions,

four hundred and thirty one thousand, seven hundred

and two

Write down in words at longes, the following numbers. 8

437 709040 3476194 7584397647 17

3010 879066 84094007 49163189186 129 **76506 4091875 690748591 500098422700

Notution

Notation by Roman Letters. 1. One.

ÅL. Forty. 14. Two.

L. Fifty. III. Three.

LX. Sixty. IV. Four.

LXX. Seventy. V. Five.

LXXX. Eighty VI. Six.

XC. Ninety. VII. Seven.

C. Hundred VIII, Eight.

CC. Two Hundred. IX. Nine.

CCC. Three Hundred.
X. Ten.

CCCC. Four Hundred.
XI. Eleven. D or l]. Five Hundred.
XII. Twelve. DC. Six Hundred.
XIII. Thirteen. DCC. Seven Hundred.
XIV. Fourteen. DCCC. Eight Handred.
XV. Fifteen. DCCCC. Nirie Hundred.
XVI. Sixteen. M or CIO One Thousand.
XVII. Seventeen. 15. Five Thousand.
XVIII. Eighteen.

1953. Fifty Thousand. XIX. Nineteen. 1ɔɔɔlɔɔɔ. Five hund. thou. XX. Twenty.

MDCCCVII. One thousand XXX. Thirty

eight hundred and seven.

A lefs literal number, placed after a greater, always augments the value of the greater ; if put before, it di. minishes it. Thas, VI is 0; IV is 4 ; XI is it ; IX

is 9, &c.

ADDITION

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

SIMPLE ADDITION

Is the adding of several integers or whole numbers ikie gether, which are all of one kind, or fort ; as, 7 pour 1 2 pounds and 20 pounds, being added together, th.

gregate, or fum total, is 39 pounds.

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