154 GREENLEAF'S MENTAL ARITHMETIC. of the first and second is equal to the third, and half the sum of the first and third is equal to the second; what are the numbers? 56. A farmer employed 3 men and 3 boys one day for $5, and another day, at the same wages, 4 men and 6 boys, for $8; what was the daily wages of each? 57. What number is that to which if 3 and 14 be separately added, the first sum will be second? of the 58. Three men, A, B and C, each, have a sum of money in their pockets; A has $3, A and C together have 3 times as much as B, and B and C together have 11 times as much as A; how much have B and C respectively? 59. Smith, Jones and Brown, each, have a sum of money at interest at 5 per cent., and these sums are to each other as, and, respectively; the annual income of the three sums taken together is $90; what is the principal that each one has at interest? 60. Three men hired a pasture for $77; at first A put in 4 horses and 8 cows; B 6 horses and 12 sheep; afterwards, when the grass was half eaten up, C put in 24 sheep; now, supposing every horse. eats, in a given time, as much as 4 sheep, and every cow as much as 3 sheep, what ought each man to pay? 61. Robinson, Savage and Harrison, agree together to do a piece of work; they are to receive for it $200, to be divided in the proportion of 5, 4 and 3, respectively, for the same amount of work; but Robinson, whose labor is worth most, is absent of the time, and Harrison, whose labor is worth least, is absent of the time; how should the money be justly divided among them? THE END. GREENLEAF'S SERIES OF MATHEMATICS. THE Publishers of this Series, in its present revised and much improved form, would call the attention of Teachers, School Directors, and others interested, to its several important distinctive characteristics: The ARRANGEMENT of its several parts and subjects is lucid, progressive, and strictly philosophical. The RULES, DEFINITIONS, and ILLUSTRATIONS, are expressed in language, simple, clear, concise, and accurate. The PROBLEMS are of a practical nature, tending to interest the pupil, exercise his ingenuity, and secure useful mental discipline. It is a CONSECUTIVE SERIES, adapted to Primary, Intermediate, Grammar, and High Schools; and is in accordance with the best modern methods of instruction. The MECHANICAL EXECUTION is neat and durable, an important consideration, too often disregarded. I. THE NEW PRIMARY ARITHMETIC Constitutes attractive and interesting First Lessons in numbers, and contains all the pupil needs as preparatory to the next book in the series. In order that the reasoning of some of the principal processes might be the more apparent to the beginner, pictures of objects have been, to some extent, introduced. After these, counters are employed, as unit marks; and then follow lessons without any such aids, that the learner may early acquire the habit of depending upon mental resources alone for the solution of problems. II. THE INTELLECTUAL ARITHMETIC, As an advanced course of exercises, inductive and analytic, it is thought, will fully meet the requirements of the highest standard of mental culture. It has been the constant aim of the author, in its preparation, to unfold inductively the science of numbers in such a series of progressive intellectual exercises as should awaken latent thought, encourage originality, give activity to invention, and develop the powers of discriminating justly, reasoning exactly, and of applying readily results to practical purposes. The advanced exercises in the fundamental processes of the science, given toward the end of the book, constitute a feature peculiar to this work. Greenleaf's Series of Mathematics. III. THE COMMON SCHOOL ARITHMETIC Contains all the important rules of common arithmetic, with their practical applications, and is ample to prepare the student for all ordinary business transactions. It is a complete system in itself, though not so extensive as the National Arithmetic. IV. THE HIGHER ARITHMETIC, or NATIONAL ARITHMETIC, Contains a greater amount and variety of matter strictly connected with the science, than will be found in any other treatise of the kind. It embraces a large amount of mercantile information, not usually included in works of this nature, but important to be possessed by all who are destined for the warehouse or counting-room. As a text-book for advanced and normal classes it has no equal. V. THE TREATISE ON ALGEBRA Furnishes what has been hitherto much desired, a thorough practical and theoretical text-book, suited to the wants of Advanced Schools, and Academies, in a single volume of convenient size. Very comprehensive in its plan and details, and progressive in its gradation of problems, it occupies the ground sometimes given to two different books. Its several demonstrations, especially those connected with the roots, the method of solving cubic equations by completing the square, and the very complete Table of Logarithms at the end of the volume, are among its useful distinctive features. The book has now been fully tested in the school-room, and the testimony of teachers is that its merit is fully equal to that of the arithmetics by the same author, and to which it proves the best and most appropriate sequel. VI. THE ELEMENTS OF GEOMETRY, Designed for Academies and High Schools, to form a volume of about 300 pp. 12mo., now being prepared with great care, it is believed, will fully meet the demands which it is intended to supply. KEYS TO THE COMMON SCHOOL, NATIONAL ARITHMETIC, AND ALGEBRA, containing Solutions and Explanations, for Teachers only. Two editions of the NATIONAL ARITHMETIC, and also of the COMMON SCHOOL ARITHMETIC, one containing the ANSWERS to the examples, and the other without them, are published. Teachers are requested to state in their orders which edition they prefer. Greenleaf's Arithmetics and Algebra are no untried books, or of doubtful reputation. No other works of the kind have, in the same time, secured so general an introduction, in all parts of the United States, or been as highly commended by eminent teachers and mathematicians. |