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I need not point out the great utility of such a performance; it is sufficiently evident to all who are employed in this branch of education, especially such as have the care of a numerous school, and experience the difficulties that teachers in general labour under with respect to time; a grievance that must continue, while their remuneration is so very inadequate to their labours. I hope the gentlemen of the profession will do me the justice to believe, that my design in this performance was not to dictate to, but ease the master; and the skilful teacher will no doubt vary the work of the questions according to the nature of the several rules. The TUTOR'S GUIDE and its KEY furnish a Complete System of ARITH METIC, and will enable those, who are acquainted with the first principles, to attain (without the assistance of a master) a competent knowledge of the several Rules with ease and precision. The favourable reception the former editions have met with, encourages me to hope that the alterations and corrections which have been made in this, will merit the approbation of those gentlemen, who have kindly interested themselves in behalf of my former endeavours, to whom I return my most sincere thanks; and remain, With the utmost Esteem and Respect, Their and the Public's much obliged,

Obedient humble Servant,

CHARLES VYSE. London, 1807. (~~~~ ~~~~

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Multiplication - - - - - ....... 147 | Questions .................. 151

Division ............. ..... 148 -

PART III.

- DECIMAL FRACTIONS.

Notation .................. 155 l Present Worth of Annui-

Addition ...... ............ 150 ties ..................... 195

Subtraction ............... 157 Annuities, &c. taken in

Multiplication............ 158 Reversion ............... 197

Division ........see v.... 161 | Rebate-or-Discount...... 198

Reduction .....&..... 164 || Equation of Payments... 200

Extraction of the Square Compound Interest ...... 201

Root ........ .......... 170 || Aunuities, Pensions, in

Its Use ........................ 172 Arrears ............... 206

Extraction of the Cube Present Worth of Annui-

Oot..................... 177 ties ................... ... 210

Its Use................... ... 179 Annuities, Leases, &c.

- Single 181 taken in Reversion ... 216

Rule of Three } Double 185 | Rebate or Discount ....... 217

Vibrations of Pendulums 186 | Purchasing Freehold or

Fellowship ............... 186 Real Estates ......... 219

Simple linterest ............ 188 Ditto in Reversion ...... 220

Annuities, Pensions, &c. Questions ............... 221

in Arrears ............ 193 - -

- PART IV.

MENSURATION.

Definitions ............... 223 | Problems in Solids ...... 24.6

Problems in Superficials 226 | Questions for Exercise 259

Of Artificers’ Works...... 238 || Specific Gravity ......... 202

Questions for Exercise 242

PART V.

Chronology............... 266 Examples on the Celestial

Examples on the Ter- Globe .................. 275

restrial Globe ......... 273

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