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ABITHMETICAL TABLES

10 Vulgar Fractions

64

Simple Addition

14 Reduction of Fractions

Addition of Money

16 Addition of Fractions

71

Addition of divers denominations 17 Subtraction of Fractions

73

Questions to exercise Addition 19 Multiplication of Fractions

74

Simple Subtraction

21 Division of Fractions

74

Subtraction of Money

22 Rule of Three of Fractions 75

Subtraction divers denominations 23

Inverse do. 75.

Questions to exercise Subtraction 25 Practice

76

Simple Multiplication

27 Tare and Trett

78

Multiplication of Money

29 Barter

81

Multiplication of divers denomi. Profit and Loss

83

nations

30

Single Fellowship

87

Questions to exercise Multipli. Compound Fellowship

89

cation

33

Equation of Payments

91

Simple Division

34 Single Position

92

Division of Money

37 Double Position

94

Questions to exercise Division 38 Simple Interest

99

Division of divers denominations 39 To calculate interest on Bonds,

Reduction

Notes, &c.

Reduction ascending

41 Compound Interest

111

Questions to exercise Reduction 42 Commission

113

Questions to exercise the foregoing 46 Insurance

114

Mechanics' & Farmers' Arith Brokerage

115

metic and Accompts

48

Rebate or Discount

115

A Tailor's account

48 Annuities or Pensions by Sina.
A Shoemaker's account

49 ple Interest

A Tánner's account

49 Annuities or Pensions at Com.

A Saddler's account

50 pound Interest

119

A Blaeksmith's account

50 Permutation

123

A Wheelwright's account 51 Combination

125

A Carpenter's account

51 Arithmetical Progression 125

A Laborer's account

51 Geometrical Progression 129

A Farmer's account

52 Alligation Medial

132

Another

52

Alternate

133

Partial

135

Orders

53

Exchange

137

The Rule of Three Direct 54 Decimal Fractions

139

Inverse 58 Addition of Decimal Fractions 140

Questions in Direct and Inverse Subtraction of the same

60

141

Proportion

Multiplication of the same 141

Double Rule of Three Direct 61 Division of the same

141

Inverse 62 Contracted Multiplication of

Promiscuous Questions

63

the same

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Contracted Division of the same 144 Of Walling

180

Reduction of the same

146 Chimnies

181

Square Root

148 OF Plasterers' work

182

Cube Root

152 Rendering

183

Duodecimals

159 Of Joiners' work

183

Mensuration of Superficies 163 Masons' work

183

Of a Square

163 Mensuration of boards & timber 184

Parallelogram

163 Of boards

184

Rhombus

164

squared timber

Rhomboides

164

unequal squared timber 185

Triangle

161|Of round timber, whose bases

Trapezium

165

are equal

185

Of Irregular Figures

165 Of round timber, whose bases

Regolar Polygons

165 are unequal

186

a Circle

166 of the Five Regular Bodies 186

a Semicircle

171|of a Tetraedron

186

a Quadrant

Octaedron

186

the Sector of a Circle

172 Dodecaedron

187

the Segment of a Circle 173 Icosaedron

187

Compound Figures

173 of any irregular body

188

an Ellipsis

173 Practical Questions

188

a Parabola

174 Winter evening Questions 204

Mensuration of Solids

174 Appendix

205

Of a Cube
174 | Of Pindulums

205

Parallelopipedon

174

the Lever

206

Triangular Prism

175 the Wheel and Axletree 206

Pyramid

175

207

Cylinder

175 a Balloon

210

Cone

175 A table of specific gravities 211

Of the frustum of a pyramid 176 of the specific gravities of bodies 211

How to try spirituous liquors 212

pyraraid

176 To find the magnitnde of bodies 213 ·

Of the frustum of a cone

176 Chronological Cycles

214

Of a Sphere or Globe

177 A Perpetual Almanack

218

Spheroid

178

A table of the 19 Epacts

219

Parabolio Conoid

178

A table of the Dominical Letters 219

Parabolic Spindle

178

Useful tables

220

Artificers' Mensuration

179

Of Gauging

221

Of Carpenters' work

179

To measure a Cask

221

Flooring

179

To find the ullage of a Cask 222

Partitioning

170

To measure a Still

222

Roofing

179 A Key to Mensuration and the

Of Bricklayers' work

180 Practical Questions

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223

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I shall not amuse the reader with any pompous eulogium on the merits of this work; or endeavour, as is customary, to anticipate the public favour by a recital of excellencies, which, in the opinion of some, may be of a disputable nature. This much I may venture to say—the adding one to the number of treatises already extant, will not appear superfluous, when we consider the importance of the subject.

The design of this work is to furnish schools with a system of practical arithmetic, in which I have, according to my knowledge in this science, arranged the different branches in a judicious and perspicuous order.

I shall not here detail the particulars in this book, but refer the reader to the table of contents.

I have entirely omitted pounds, shillings, and pence, (except a few examples in exchange with England and Ireland,) as useless to the learner; and have introduced a complete system of Mensuration, (arithmetically, according to Euclid, and other celebrated authors.

This work is in two parts: the second part contains a useful appendix, and a key for Mensuration and the exercise questions.

Perfect accuracy, in a work of this size and nature, can hardly be expected: the author and the press are liable to

If any such are pointed out, it will be considered as a token of friendship and favour.

How far this treatise will answer the end intended, will, in some measure, be obvious to any judicious scholar, by taking a short view of the plan pursued.

JAMES L. CONNOLLY,

Schoolmaster. WASHINGTON, G. C. Ohio,

May 1st, 1828.

errors.

I HAVE carefully examined Mr. Connolly's system of Arithmetic and Mensuration, and have not the least hesitation in pronouncing it to be worthy of a place among the best authors, on these subjects, in the United States.

JOHN TAYLOR, E. M. Pittsburgh, Sept. 4th, 1828.

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