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PRACTICALLY APPLIED,

FOR ADVANCED PUPILS,

AND FOR PRIVATE REFERENCE,

DESIGNED AS A

SEQUEL TO ANY OF THE ORDINARY TEXT-BOOKS ON THE SUBJECT.

BY HORACE MANN, LL.D.,

THE FIRST SECRETARY OF THE MASSACHUSETTS BOARD OF EDUCATION,

AND PLINY E. CHASE, A.M.,

AUTHOR OF 'THE COMMON-SCHOOL ARITHMETIC.'

PHILADELPHIA:

PUBLISHED BY E. H. BUTLER & CO.

HARVARD
CINEVERSITY
LTSKARY
047*179

Entered, according to the Act of Congress, in the year 1850, by

HORACE MANN AND PLINY E. CHASE.

in the Clerk's Office of the District Court of the United States, in and for the Eastern District of Pennsylvania.

JUST PUBLISHED,

THE ELEMENTS OF ARITHMETIC, PART FIRST, for Primary Schools. The SECOND PART, for Grammar Schools, which is in course of preparation, will complete the following Arithmetical Series:

ELEMENTS OF ARITHMETIC, PART FIRST. By HORACE MANN and PLINY E. CHASE.

ELEMENTS OF ARITHMETIC, PART SECOND. BY HORACE MANN and PLINY E. CHASE.

COMMON-SCHOOL ARITHMETIC. BY PLINY E. CHASE.

ARITHMETIC PRACTICALLY APPLIED. By HORACE MANN and PLINY E. CHASE.

E. B. MEARS,

STEREOTYPER.

C. SHERMAN, PRINTER.

MR. MANN'S PREFACE.

THE appearance of my name on the title page of this Arithmetic, requires me to state the extent of my connection with its authorship, and of my responsibility for its execution.

Believing the idea of the work to be original, I will attempt its elucidation. In seeking for the elements or materials of its questions, it proposes to take a survey of all the vocations of life, of all the facts of knowledge, and of all the truths of science, and to make a selection from each department of whatever may be most interesting and valuable. It does not confine itself to the playthings of the nursery, or to the commodities of the market place, and to the money they will cost, or make, or lose. On the contrary, the present work proposes to carry the student over the wide expanse of domestic and social employments; to introduce him to the various departments of human knowledge so far as that knowledge has been condensed into tables, or exhibited in arithmetical summaries, and to make him acquainted with many of the most wonderful results which mathematical science has revealed. Instead of groping along the mole-path of an irksome routine, with little other change than from dollars and cents, to pounds and pence, or some other familiar currency, and with little other variety than from cloth to corn, or some other common-place commodity, it derives its examples from biography, geography, chronology, and history; from educational, financial, commercial, and civil statistics; from the laws of light and electricity, of sound and motion, of chemistry and astronomy, and others of the exact sciences. Trades, handicrafts, and whatever pertains to the useful arts, so far as they are the subject of numerical statement, and their facts possess arithmetical relations, together with all the ascertained and determinate results of economical or political knowledge, and of scientific discoveries, are laid under contribution, and are made to supply appropriate elements for the questions on which the youthful learner may exercise his arithmetical faculties.

In this way, and without departing from the most rigid rules on which an arithmetical text-book should be constructed, I have supposed that a work may be prepared which shall exemplify in the best manner the science of numbers, and be full of useful knowledge also; and which, while it exercises the student's powers of calculation, shall enlarge his acquaintance with the varied business of the world, and with many of the most interesting results of applied science.

In a universe like this, where every star has been weighed in a mathematical balance, and all inter-stellar spaces have been measured by a mathematical line; where the orbits of all the planets have been traced as by a compass, and their velocities graduated to their distances by an unchanging law; where not only wind and tide, but every particle of dust in a hurricane, and every drop of water in a cataract, know their exact places by an infallible rule; where the gravitation of matter, the radiation of heat, and the diffusion of light, at all times and instantaneously, adjust their force to their distance with unerring precision; where every chemical combination is formed on some fixed prin ciple of proportion, and the atoms of every crystal arrange themselves around their nucleus in geometric lines; and where, whatever other contemplations or volitions occupy the Infinite Mind, it is still true, as was said by the old Greek philosopher, that 66 'God geometrizes;"-I say, in such a universe, built, weighed, measured, compounded, and arranged on mathematical principles, why should not the arithmetical exercises of those minds which have entered it, to dwell in it forever, embrace something more than the market price of commodities, the gain or loss in trade, and the interest and discount of banks?

Why, for instance, cannot a child be taught to count the bones in his hands, as well as the nuts in his pocket; to add together the number of bones in all the different parts of his body, or to subtract the number of those contained in his head or in his hands, from the number of those contained in his feet, as well as to add or subtract the number of apples or of cakes in the possession of James, John, and Joe; and why can he not, by such exercises, be led to enrich his mind with anatomical or physiological facts, instead of stimulating his imagination with the provocatives of appetite? Why cannot a child add together the population of the different States of this Union, or of the different nations of Europe or of the world, and thus learn the sum of the population of the whole earth and of its parts, as well as to

add naked columns of abstract figures? In addition, subtraction, multiplication, and division, why cannot the pupil use examples whose elements or data are drawn from the distance between different historical epochs, from the ages of distinguished men, from the date of one discovery or invention to that of another discovery or invention, or from the rise to the fall of dynasties, or from a comparison of the heights of different mountains, or the lengths of different rivers, or of degrees of longitude on different parallels of latitude, or the distance from city to city by land, or from port to port by sea; and thus live in the perpetual presence and company of most important truths pertaining to history, chronology, biography, and geography, and so familiarize himself with these classes of facts, without devoting special time or effort to their acquisition, just as he becomes familiar with the faces and the names of his school-fellows and his townsmen, merely because he has always lived amongst them? If the arithmetical exercises of the pupil direct his attention almost exclusively to the shop of the retailer or the countingroom of the merchant, then he does not enjoy even a pedlar's opportunity to become acquainted with men, events, times, places, and things,—with the great results of business and of civilization, as they now exist in the world. Instead of wearying the learner with endless reiterations about bales, boxes, barrels, and bushels, or dollars, dimes, cents, and mills, why not open before him some of the vast storehouses of truth, and display some specimens of their endless variety and beauty? Let the teacher, taking the learner by the hand, follow the farmer, the craftsman, the architect, the manufacturer, the road-maker, the mill-wright, the ship-wright, the watch-maker, and the long catalogue of others who are employed in the mechanic arts, or other branches of useful industry; or, rising into the sphere of the educated or professional laborer, let him observe the optician, the electrician, the mathematical instrument maker, the astronomical observer, the telegraph operator, and borrow from them all some of the curious facts pertaining to their respective arts and professions, and convert them into the pleasing and instructive elements of arithmetical problems. I can conceive of a work so replete with the facts of technology and science, that it shall be examined with interest and profit by any one who is only seeking after valuable information, and which, at the same time, shall be perfectly adapted to the mere student who only seeks after the best means of arithmetical practice.

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