## Trigonometry: For Schools and Colleges |

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angle increases angle of elevation axis Calculus celestial longitude celestial sphere cents College cos a sin cos2 cos2a cos2b cosecant cosine ctn a ctn ctn Ra dec inc dec declination dicular ecliptic equal equations equinoctial Examples exclude formulas geometry given angle Greenwich mean horizontal hypotenuse inc dec inc inc inc inequalities integer introduction latitude length limit longitude Mailing price matics measure-units miles Oberlin Oblique observed obtained perpen perpendicular decreases polar triangle poles positive angle positive or negative preceding results Professor of Mathematics Quadrantal Triangles radians radius ratio reference for f represented respectively right ascension right triangles secant sides Similarly sin a sin sin b cos sin2 sin2a sin2b sin2c sine solution Spherical Right spherical triangle student subtends taken tan2 terminal line text-book tions tower triangle of reference trigonometric functions values vertical x-axis

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Page 93 - Its peculiarities are the rigorous use of the Doctrine of Limits, as a foundation of the subject, and as preliminary to the adoption of the more direct and practically convenient infinitesimal notation and nomenclature ; the early introduction of a few simple formulas and methods for integrating ; a rather elaborate treatment of the use of infinitesimals in pure geometry ; and the attempt to excite and keep up the interest of the student by bringing in throughout the whole book, and not merely at...

Page 95 - Taylor's Calculus was found to be in use in about sixty colleges. The Nation, New York: In the first place, it is evidently a most carefully written book. . . . We are acquainted with no textbook of the Calculus which compresses so much matter into so few pages, and at the same time leaves the impression that all that is necessary has been said. In the second place, the number of carefully selected examples, both of those worked out in full in illustration of the text, and of those left for the student...

Page 76 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 96 - ... forming clear notions of things. In doing this all the higher faculties are brought into play. It is this formation of concepts, therefore, that is the essential part of mental training. And it is in line with this idea that the present treatise has been composed. Professors of mathematics speak of it as the most exhaustive work on the subject yet issued in America ; and in colleges where an easier textbook is required for the regular course, this will be found of great value for post-graduate...

Page 98 - ... however, its rate at any instant is determined essentially in the same manner, viz. : by letting it change at the rate it had at the instant in question and observing what this change is. It is this change which the Calculus enables us to determine, however complicated the law of variation may be. From the author's experience in presenting the Calculus to beginners, the method of rates gives the student a more intelligent, that is, a less mechanical, grasp of the problems within its scope than...

Page 97 - SERIES of nearly three hundred examples with answers, sys•^ tematically arranged and grouped under the different cases, and accompanied by concise rules for the solution of each case. Selden J. Coffin, Prof, of Astron- 1 ance is most timely, and it supplies omy, Lafayette College : Its appear- | a manifest want.

Page 97 - Trigonometry alone, as the work contains but 29 pages of textThe Plane portion is compact, and complete in itself. Examples of Differential Equations. By GEORGE A. OSBORNE. Professor of Mathematics in the Massachusetts Institute of Technology, Boston. 12mo. Cloth, vii + 50 pages. Mailing Price, 60 cents; for introduction, 50 cents.

Page 94 - Mailing price, $3.15; for introduction, $3.00. rPHIS book is intended as an introduction to the treatment of some of the important Linear Partial Differential Equations which lie at the foundation of modern theories in physics, and deals mainly with the methods of building up solutions of a differential equation from easily obtained particular solutions, in such a manner as to satisfy given initial conditions. John Perry, Technical College, Finsbury, London, England: Byerly's book is one of the most...

Page 93 - Peirce's Elements of Logarithms. With an explanation of the author's Three and Four Place Tables. By Professor JAMES MILLS PEIRCE, of Harvard University. 12mo. Cloth. 80 pages. Mailing price, 55 cents ; for introduction, 50 cents.

Page 95 - Many theorems are proved both by the method of rates and that of limits, and thus each is made to throw light upon the other. The chapter on differentiation is followed by one on direct integration and its more important applications. Throughout the work there are numerous practical problems in Geometry and Mechanics, which serve to exhibit the power and use of the science, and to excite and keep alive the interest of the student.