THE PRIVATE INSTRUCTOR, OR MATHEMATICS SIMPLIFIED. COMPRISING EVERY THING NECESSARY IN ARITHMETIC, BOOK- TO FORM AND COMPLETE THE MAN OF BUSINESS. THE WHOLE UPON AN IMPROVED PLAN, NOT ONLY ADAPTED TO PRIVATE INSTRUCTION, BUT ALSO TO THE USE OF SCHOOLS. “He that is ignorant of numbers is scarce half a man.” CHARLES XII, OF SWEDEN. BY JASON M, MAHAN, MATHEMATICIAN, NEW ITALY, CHESTER COUNTY, PENNSYLVANIA. Harrisburg: 1839. Entered according to the act of Congress, in the year 1836, by Jason M. MAHAN, in the clerk's office of the District Court of the Eastern District of Pennsylvania. '1126 PREFACE. 09-11-50 ADE The following work has been in contemplation for a long time. Several years' experience as a teacher confirmed me in the opinion, that a work of this kind would be serviceable, particularly to such as are to receive but a small proportion of schooling. Its utility must be obvious to every one who considers that the opportunity for improvement with many is limited ; and that many of the treatises on Arithmetic, Mensuration, &c. are not altogether calculated to give that instruction in so short a time as one intended for business ought to receive. In order that the pupil may acquire a competent knowledge of the different branches, in as short a time and at as little expense as possible, I have carefully excluded all irrelevant matter, and have given only what I deemed necessary to prepare him for business. One of the most difficult questions in each rule is wrought out at full length, and by comparing these with the rules, which are laid down in a plain and familiar manner, any person who has the least knowledge of figures, or inclination to learn, may understand them, either with or without the aid of a teacher ; so that the work is not only adapted to private instruction, but also to the use of schools. With these impressions, and hoping that the work may be useful, it is now offered to the public, by The public's most humble servant, JASON M. MAHAN. New Italy, January 2, 1839. CONTENTS. Page. Page. Custom-house allowances, 140 Addition of Integers, 11 Vulgar Fractions, 145 Subtraction of Integers, 14 Reduction of Vulgar Frac- Multiplication of Integers, 18 Addition of Vulgar Frac- Addition, Subtraction and tions, Multiplication, 24 Subtraction of Vulgar Decimal Fractions, 28 Fractions, Addition of Decimals, 29 Division of Vulgar Frac- Subtraction of Decimals, 30 tions, Multiplication of Decimals, 30 The Single Rule of Three Compound Subtraction, 67 Contracted Multiplica- Compound Multiplication, 74 tion of Decimals, 162 Compound Division, 79 Contracted Division of Practical Questions, 83 Contracted Division, Single Rule of Three, 86 Equation of Payments, Double Rule of Three, 91 Alligation, Questions for exercise, 95 Double Position, 100 Arithmetical Progression, 180 |