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ON THE INDUCTIVE PLAN.
A SEQUEL TO THE PROGRESSIVE PRIMARY ARITHMETIC, CONTAINING
MANY ORIGINAL FORMS OF ANALYSIS APPLICABLE TO A
GREAT VARIETY OF PRACTICAL QUESTIONS.
AND DESIGNED FOR
THE MORE ADVANCED CLASSES
COMMON SCHOOLS AND ACADEMIES.
DANIEL W. FISH, A.M.
IVISON, BLAKEMAN AND COMPANY,
NEW YORK AND CHICAGO.
Graded to the wants of Primary, Intermediate, Grammar, Normal, and High Schools, Academies, and Colleges,
Progressive Table Book.
Progressive Primary Arithmetic.
Rudiments of Written Arithmetic.
JUNIOR-CLASS ARITHMETIC, Oral and Written. NEW.
Progressive Practical Arithmetic.
Key to Practical Arithmetic.
Progressive Higher Arithmetic.
Key to Higher Arithmetic.
Key to New Elementary Algebra.
Key to New University Algebra.
New Geometry and Trigonometry. In one vol.
Geometry, Plane and Solid. In separate vol.
New Surveying and Navigation.
New Differential and Integral Calculus.
University Astronomy-Descriptive and Physical.
Key to Geometry and Trigonometry, Analytical Geometry and Conic Sections, Surveying and Navigation.
Entered, according to Act of Congress, in the year 1858, and again in the year 1863, by
DANIEL W. FISH, A.M.,
In the Clerk's Office of the District Court of the United States, for the Northern District of New York.
ARVARD COLLEGE LIBRARY
GIFT OF THE
GRADUATE SOLO FOUCATION
May 8, 1930
THE importance, and the practical benefit to be derived from the study of Intellectual Arithmetic, not only as a preparation for business life, but as a means of developing and strengthening the 1inking and reasoning powers, and of thorough mental culture, an not be over-estimated. Not only is it a necessary study for young pupils, but indispensable to the more advanced student, as a preparation for the prompt and accurate business man. And it is believed that, as a general rule, the most critical, correct, and ready students of mathematics are those who have been most thoroughly drilled in intellectual arithmetic.
This work has been prepared more especially for advanced classes, and is designed for those who have first been well taught in the primary book, and for such as are pursuing the study of written arithmetic, or algebra, and who have never been thoroughly exercised in this branch of study.
Only a few of the many points of difference between this and other similar works, and which, it is believed, renders this superior to them, will be referred to.
It is more complete, comprehensive, and progressive in its character. The arrangement and classification are more strictly systematic, and in accordance with the natural order of mathematical science. The development of principles, and their applications, are shown by a more numerous selection, and greater variety of appropriate examples, progressively arranged, commencing with those that are simple and easy, and advancing to those more complex and difficult.
At intervals, and especially in the closing sections of each chaptr, examples are given containing such a combination of principles, and forms of analysis, as to require a knowledge of almost every principle previously taught, thus affording the pupil a thorough review, as well as requiring him to classify his knowledge of what he has been over.
One of the most important, and, it is thought, one of the most original and useful features of this work, is the full, concise, and uniform system of ANALYSIS it contains, the result of long expe
rience in the school-room.
Particular attention is invited to the subjects of Fractions, Percentage, and Interest; their treatment is peculiar, and adapted to obviate many of the difficulties, and greatly abbreviate most of the operations in them.
The chapter of Miscellaneous Examples will afford a valuable and thorough drill to the advanced student of arithmetic or algebra. They contain a great variety of principles, and while they may be considered difficult, yet the full analysis given of every principle, and the selection of numbers so adapted to the conditions of the question as to produce results free from large and difficult fractions, will render a mental solution of them comparatively easy. In conclusion, we may be allowed to express the belief, tht in this work the thorough teacher will find a desideratum long sought in this department of science,-the means of mental discipline and development such as has been furnished by 10 similar treatise.
SUGGESTIONS TO TEACHERS.
Pupils of nearly the same degree of advancement should be classed together. Regular exercises should be assigned to the class, and sufficient time allowed them to thoroughly examine their lesson before being called upon to recite.
The use of the book at the time of recitation should be strictly prohibited, except, perhaps, in some of the more difficult lessons in the latter part of the work.
Each example should be read but once, slowly and distinctly, the pupils called upon promiscuously, who should arise, stand erect, repeat the example, and then give the analysis. This wil secure close attention.
Every question should be clearly and thoroughly analyzed, and. the pupil required to adhere strictly to the forms of solution given, unless better ones can be substituted; and in no case should he be allowed to omit the conclusion, commencing with "Therefore." The class should be encouraged to detect and correct errors in statement or analysis, to criticise and make proper inquiries, all of which should be signaled by the uplifted hand.
It is suggested that the class be occasionally exercised upon "Ringing the Changes," as explained in the Appendix, and which may be applied to a great number and variety of examples. It will not only afford a valuable drill, but a pleasant and enlivening exercise.