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PLANE AND SPHERICAL,
WITH ITS APPLICATION то
NAVIGATION AND SURVEYING, NAUTICAL AND PRACTICAL
LOGARITHMIC, TRIGONOMETRICAL, AND NAUTICAL
FOR THE USE OF SCHOOLS AND COLLEGES.
A NEW EDITION, WITH EXTENSIVE ADDITIONS AND IMPROVEMENTS.
REV. CHARLES W. HACKLEY, S.T.D.,
Prof. of Mathematics and Astronomy in Columbia College.
GEORGE P. PUTNAM, 155 BROADWAY.
M DCCC LI.
HARVARD UNIVERSITY LIBRARY 046*172
ENTERED according to Act of Congress, in the year 1850, by
CHARLES W. HACKLEY,
in the Clerk's office of the District Court the Southern District of New York
B. Craighead, Printer and Stereotypor, 112 Fulton st, N, Y.
PREFACE TO THE FIRST EDITION.
ANALYTICAL TRIGONOMETRY has always been to the majority of students a dry and difficult study. A conviction that it might be rendered easy and interesting to all who have a tolerable acquaintance with Algebra and Geometry, has led to the production of the present work. The faults of former treatises on this subject, which have detracted from their usefulness as books of instruction, appear to be these:
1. A too sudden transition from Geometry to Trigonometry, in consequence of which, the first efforts of the learner are in the dark as to the object of his pursuit.
2. A tedious succession of general formulas at the commencement, the use and application of which are so long delayed as to produce weariness and discouragement before there is any apparent fruit to reward labor.
3. Too much abridgment in the demonstration, and particularly in the derivation of the algebraic results.
The author is aware of the importance attached to the exercise of intellect required to discover the connexion between propositions whose mutual dependence is shown by intermediate links which the mind must supply unaided, but it will be admitted on the other hand, that the ordinary term of study is too limited, and the field of knowledge in this department too extensive, to afford the loss of time which such a mode occasions. Besides, there will be abundant scope for this kind of exercise, in a more matured familiarity with mathematical reasoning, for which the shortening of labor here, will leave additional room.