# A New and Complete System of Arithmetick: Composed for the Use of the Citizens of the United States

William S. Parker & Son, 1832 - 528 СЕКъДЕР

### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 Problems resulting from the preceding Ru 57 450 66 Vulgar Fractions 71 Decimal Fractions 90 iDecimal Tables 101 Division 108 Reduction of Coins 114 Duodecimals or Cross Multiplication 126 The method of making Taxes in a Note 136 Single Rule of Three Direct and Inverse 144 Conjoined Proportion 152 Double Fellowship 159 Form of a Bill of Parcels 184 Extraction of the Square Roo 190 Having the Chord and Versed Sine of a Segment to find the 1i 196 Extraction of the Cube Root 197 Application and use of the Cube Root 203 Surds 210 Proportion in General 217 Geometrical Proportion 233 Simple Interest 253 Simple Interest by Decimals 261 in Connecticut 270 Duties 281 Equation of Payments 289 Policies of Insurance 297 Compound Interest 304 Discount by Compound Interest 312
 Table shewing the number of Days from any day in one month to any 401 Tables reducing Troy Weight to Avoirdupois and the contrary 407 of Measures of Length Capacity c of various countries 419 An Account of the Gregorian Calendar or New Style 425 Table to find Easter from the year 1753 to 4199 439 To measure a Sector 45s 26 To measure the Segment of a Circle 458 To measure an Ellipsis 460 Of Solids 461 To measure a Parallelopipedon 463 Having the Side of a Square Solid to find what Length will mnke a Solid Foot 465 Having the Diameter of a Cylinder given to find what length will make a Solid Foot 466 To measure a Prism 467 To measure the Frustum of a Pyramid or Come 469 To measure a Sphere or Globe 472 To measure a Frustum or Segment of a Globe 473 To measure a Spheroid 474 To measure the lower Frustum of a Parabolick Conoid 475 To measure a solid Ring 47t 46 To measure the Solidity of any irregular Body whose Dimensions cannot be taken 476 Of the five Regular Bodies 477 To measure a 1etraedron 478 To measure a Dodecaedron 479 To gauge a Mash Tub 480 To ullage a Cask lying on one side by the Gauging Rod 431 481 The Proportions and Tonnage of Noahs Ark 482 Questions in Mensuration 483 Book Keeping by Single Entry 488 Double Entry 508

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 199 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
сЕКъДА 239 - Write down a few of the leading terms of the series, and begin the indices with a cypher : Thus, 0, 1, 2, 3, &c. 2. Add together the most convenient indices to make an index less by 1 than the number expressing the place of the term sought.
сЕКъДА 197 - RULE. 1. Separate the given number into periods of three figures each, by putting a point over the unit figure and every third figure beyond the place of units. 2. Find the greatest cube in the left hand period, and put its root in the quotient. 3.
сЕКъДА 275 - The present worth of any sum, due some time hence, is such a sum, as, if put to interest, would in that time, and at the rate per cent. for which the discount is to be made, amount to the sum or debt then due.
сЕКъДА 221 - PROBLEM II. The first term, the last term, and the number of terms given, to find the common difference. RULE. — Divide the difference of the extremes by the number of terms less 1 , and the quotient will be the common diffcrenct.
сЕКъДА 78 - Multiply all the numerators together for a new numerator, and all the denominators for a new denominator; and they will form the fraction required.
сЕКъДА 372 - A hare starts 12 rods before a hound ; but is not perceived by him till she has been up 45 seconds ; she scuds away at the rate of 10 miles an hour ; and the dog, on view, makes after her at the rate of 16 miles an hour ; how long will the course hold, and what space will be run over, from the spot where the dog started ? Ans.
сЕКъДА 383 - As the distance between the body to be raised, or balanced, and the fulcrum, or prop, is to the distance between the prop and the point where the power is applied, so is the power to the weight which it will balance.
сЕКъДА 84 - To reduce any given quantity to the fraction of any greater denomination of the same kind. RULE. — Reduce the given quantity to the lowest term mentioned for a.
сЕКъДА 77 - To reduce a whole number to an equivalent fraction, having a given denominator. RULE. Multiply the whole number by the given denominator v place the product over the said denominator, and it will