4.2.342 PREFACE. - ancho AMONG the several branches of Education which are taught in Schools, that of Arithmetic is undoubtedly of the greatest importance ; and it is either studied by the rich as a necessary part of genteel education, or by those in the middle rank of life, in order to qualify them for their intended pursuits : indeed, the first of these classes may have their ambition fully satisfied by merely studying a system of theory, and the fundamental rules ; but the Mechanic, Merchant, Surveyor, Sailor, Soldier, and Engineer, cannot follow his profession to advantage, without being expert in every part of arithmetical computation. A short, plain and easy course is then to be considered as a desideratum for the use of scholars in every seminary of learning, and it is certainly great encouragement to emulation when the task appears to be short, nor is any thing more discouraging to a beginner than to be impressed with the idea, that the rules to be learned are long and tedious, hence the apparent length of labor and difficult study frequently sets proficiency as it were, at an inaccessible distance, and often does away every hope or wish to excel ; the natural desire for learning being thus blasted in the bud, it will be difficult afterwards to induce the scholar to study with ardor. To learn the rules and solve the examples at school is not enough, but they must be remembered, so as to enable practitioners to perform the calculations not only with ease to themselves, but also to the satisfaction of those who inay be interested in their accuracy. As this compendium has been composed expressly with the intention of answering these ends, it is not designed to hold out the expectation of new inventions ; but rather to collect and arrange all the useful rules in a convenient practia eal form, retaining only-such parts as have a direct application to the more general purposes in life. As works of this nature must necessarily be made up of matters that have in a manner become common property, and in a great measure, are contained in some shape or other, in most books of this kind, therefore it will not be imputed to the Author as a crime, that he has avaited himself of the materials of some of the best publications on this science, from whence he may have taken extracts, or which he may have imitated. It is nevertheless expected that something new may be found in this work, and here the Author hopes that he will not be too severely criticised if, through a desire of rendering it short and easy, he has in some instances deviated from the old custom of giving long and tedious rules, particularly in the beginning, where they can be of no avail to the learner unacquainted with the use of figures, but in every part where precepts can be of service either to the scholar in working the questions proposed, or to assist the memory of the teacher in the examination thereof, they will not be found wante ing. The arrangement is such in the Author's opinion, as seems the best calculated for instruction, commencing the practical part with that which is most easy, and by gradual and rising steps proceeding to that which is more complex, in such order that what is prior, paves the way for what is to follow. TABLE OF CONTENTS. ib. - } 64 Multiplication 16 The Rule of Three Direct 44 Rule of Three Direct ib. Repeating and Circula- Decimal Fractions 57 Compound Proportion 66 With Holland - io Arbitration of Exchanges 106 ib. page page Compound Fellowship 111 Alligation Total PATT IV. Root of Sixth Power ib. Equation of Payments 139 Eighth Power ib. Compound Interest - 140 Ninth Power ib. | Annuities, &c. in Arrears 141 Any Power ib. Present worth of Annuities ib. Arithmetical Progression ib. Annuities, &c. taken 134 Purchasing Real Estate 144 Simple Interest by Decimals ib. Purchasing do.in Reversion ab. Annuities, &c. in Arrears 136 Insurance ADVERTISEMENT. 4714 Explanation of the Characters made use of in this Compendium. = Equal. The sign of Equality; as 112 lb. 1 cwt. signifies, that 112 lb. are equal to 1 cwt. + Plus or more. The sign of Addition; as 5+5=10, that is, 5 added to 5 more is equal to 10. - Minus or less. The sign of Subtraction ; as 8=6, that is 8 minus 2 is equal to 6. X Multiplied by. The sign of Multiplication ; 4x7=28, that is, 4 multiplied by 7 is equal to 28. -Divided by. The sign of Division ; as 28+7=4, that is, 28 divided by 7 is equal to 4. Numbers placed like a fraction, also denote Division; the upper number being the divi dend and the lower the divisor. 6 ::: Proportion. The sign of Proportion ; as 3 : 6 :: 8: 16, that is, as 3 is to 6, so is 8 to 16. 7–2+5=10. Shews that the difference between 2 and 7 added to 5 is equal to 10. 9-2X5=2. Signifies that the sum of 2 and 5 taken from 9 is equal to 2. V Prefixed to any number, signifies the Square root of that number is required. Signifies the Cube Root is required. Denotes the Biquadrate, or Root of the fourth power is required. A Vinculum ; denoting the several quantities over which it is drawn, to be considered jointly as a simple quantity, The Index or Exponant 3 denotes the third power of 8, or 8 =512, that is, 8 multiplied into self three times, or 3 |