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Western District of Pennsylvania, to wit:

BE IT REMEMBERED, That on the eleventh day of September, in the fifty-fourth year of the Independence of the United States of America, A. D. 1829, Cramer & Spear, of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors in the words

following, to wit: Connolly's Arithmetic, or the Ohio Accomptant, being a plain practical treatise, with a complete system of Mensuration. By James L. Connolly."

In conformity to the act of the congress of the United States, entitled, “An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned;" and also to the act, entitled, “An act supplementary to an act, entitled, 'An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned;' and extending the benefits there. of to the arts of designing, engraving, and etching historical and other prints."

E. J. ROBERTS, Clerk of the Western District of Pennsylvania

Midland

11-6-39
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ARNANETICAL TABLES

10 Vulgar Fractions

64

Simple Addition

14 Reduction of Fractions

64

Addition of Money

16 Addition of Fraetions

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

33

cation
Fq'iation 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 ealculate interest on Bonds,

Reduction

105

41 Notes, &c.

Reduction ascending

41 Compound Interest

112

Questions to exercise Reduction 42 Commission

113

Questions to exercise the foregoing 46 Insurance

11%

Mechanics' & Farmers' Arith-

115

Brokerage

metic and Accompts

48

Rebate or Discount

115

A Tailor's account

48 Annuities or Pensions by Sim-

A Shoemaker's account

49 ple Interest

117

A Tanner's account

49 Annuities or Pensions at Com.

A Saddler's account

50 pound Interest

A Blacksmith's account

50 Permutation

123

A Wheel wright'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

137

The Rule of Three Direct 54 Decimal Fractions

139

Inverse 58 Addition of Decimal Fractions 140

Questions in Direct and Loverse Subtraction of the same

14L

60

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 Chimonies

181

Square Root

148 Of Plasterers' work

182

Cube Root

-152 Rendering

183

Daodecimals

159 Of Joiners' work

183

Mensuration of Superficies 163 Masons' work

18S

Of a Square

163 Mensuration of boards & timber 184

Parallelogram

163|Of boards

184

Rhombus

164 squared timber

184

Rhomboides

164

unequal squared timber 185

Triangle

164 of round timber, whose bases

Trapeziom

165

185

are equal

Of Irregular Figures

165 Of round timber, whose bases

165

Regular Polygons

186

are unequal

a Circle

166 Of the Five Regular Bodies 186

a Semicircle

171|Of a Tetraedron

186

a Quadrant

172 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 Pendulums

205

Parallelopipedon

174 the Lever

206

Triangular Prism

175 the Wheel and Axletree 206

Pyramid

175

Water

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

frustum of a reetangled

212

pyramid

Of the frustum of a cone

176 Chronological Cycles

Of a Sphere or Globe

177 A Perpetual Almanack

218

Spheroid

178

A table of the 19 Epacts

219

Parabolic 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

179

Po measure a Still

222

Roofing

179 A Key to Mensuration and the 223

Of Bricklayers' work

180 Practical Questions

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PREFACE.

ISHALL 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.

I'ne 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 reter 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.

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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, ou these subjects, in the United States.

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

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