# 1853 Elements Analytical Geometry Differential Calculus

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Differential and Integral Calculus

Elias Loomis, A.M.

New York : Harper & Brothers, Publishers --- 1853

Description: This hard cover book measures 6 1/8” across by 9 3/8” tall and contains 278 pages, followed by several pages of advertisements for other books by the author. is part of the description from the preface: The following treatise on Analytical Geometry and the Calculus constitutes the fourth volume of a course of Mathematics designed for Colleges and High Schools, and is prepared upon substantially the same model as the preceding volumes. It was written, not for mathematicians, nor for those who have a peculiar talent or fondness for the mathematics, but rather for the mass of college students of average abilities. I have, tfore, labored to smooth down the asperities of the road so as not to discourage travelers of moderate strength and courage ; but have purposely left some difficulties, to arouse the energies and strengthen the faculties of the beginner. In a course of liberal education, the primary object in studying the mathematics should be the discipline of the mental powers. This discipline is alike important to the physician and the divine, the jurist and the statesman, and it is more effectually recurred by mathematical studies

But, in order to secure the desired advantage, it is indispensable that the student should comprehend the reasons of the processes through which he is conducted. How can he be expected to learn the art of reasoning well, unless he see clearly the foundations of the principles which are taught? This remark applies to every branch of mathematical study, but perhaps to none with the same force os to the Differential and Integral Calculus. The principles of the Calculus are further removed from the elementary conceptions of the mass of mankind than either Algebra, Geometry, or Trigonometry, and they require to be developed with corresponding care. It is quite possible for a student to learn the rules of the Calculus, and attain considerable dexterity in applying them to the soulution of difficult problems, without having acquired any clear idea of the meaning of the terms Differential and Differential Coefficient.

Contents are divided under these main headings:Analytical Geometry Application of Algebra to Geometry Construction of Equations On the Point and Straight Line On the Circle On the Parabola On the Ellipse On the Hyperbola Classification of Algebraic Curves Transcendental Curves Differential Calculus

Definitions and First Principles --- Differentiation of Algebraic Functions Successful Differentials – MacLaurin’s Theorem --- Taylor’s Theorem --- Functions of Several Independent variables Signification of the First Differential Coefficient --- Maxima and Min. Transcendental Functions Application of the Differential Calculus to the Theory of Curves Radius of Curvature --- Evolutes of Curves Analysis of Curve Lines Integral Calculus

Integration of Monomial Differentials --- of Binomial Differentials --- of the Differentials of Circular Arcs Applications of the Integral Calculus

Miscellaneous Examples

Condition of book: Poor cover, fair contents. Considering that this book is 157 years old, it is in pretty good shape. The leather cover is still attached by the strings of the binding . The cover is split along both hinges and it is quite worn along the edges. The pages are very foxed (brown spots) and have lots of notes and problems worked in pencil. Several pages have folded corners. T are also a couple pieces of paper with math problems that I left in the book as found; one seems to be attached to the inside margin, near the gutter. Binding of textblock is very secure, although, as mentioned above, the cover itself is quite loose. An interesting old book.

Condition of dust jacket: No dus...

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