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acute angle adapted to logarithmic altitude base celestial horizon celestial sphere chord circle of latitude Circular Functions colog complement cosecant cosine cosqp cotangent ctn A ctn ctn qp deduced denote difference distance ecliptic equator esc qp Example feet figures find the angle find the functions find the height formulas four-place functions of 90 Geometry given angle given logarithm horizon Hyperbolic Functions hypothenuse initial line interpolation IOOO'O less than 180 log ctn log esc log sin logarithmic computation Logarithms of Circular miles negative obtained perpendicular Plane Trig positive Prove quadrant radius right angle right ascension right triangle sec qp secant sin a sin sin2 sine and cosine solution solve spherical triangle substituting Table of Logarithms tan2 tana tangent terminal line triangle of reference trigonometric functions vernal equinox
Page x - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 48 - 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 51 - Notes on English Literature 1.00 English Literature Pamphlets: Ancient Mariner, .05; First Bunker Hill Address, .10; Essay on Lord Clive, .15; Second Essay on the Earl of Chatham, .15; Burke, I. and II.; Webster, I. and II.; Bacon; Wordsworth, I. and II.; Coleridge and Burns; Addison and Goldsmith Each...
Page 91 - From a station B at the base of a mountain its summit A is seen at an elevation of 60░; after walking one mile towards the summit up a plane making an angle of 30░ with the horizon to another station C, the angle BCA is observed to be 135░.
Page 49 - Plane and Spherical portions are arranged on opposite pages. The memory is aided by analogies, and it is believed that the entire subject can be mastered in less time than is usually given to Plane Trigonometry alone, as the work contains but 29 pages of textThe Plane portion is compact, and complete in itself.
Page 20 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 73 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 46 - By . . and . we have. — sin (a ▒ ▀) sin a cos ▀ ▒ cos a sin ▀ cos (a ▒ ▀) cos acoe▀ Т sin a sin ▀ Divide both numerator and denominator by cos a cos |3.
Page 69 - Having measured a distance of 200 feet, in a direct horizontal line, from the bottom of a steeple, the angle of elevation of its top, taken at that distance, was found to be 47░ 30'; from hence it is required to find the height of the steeple.
Page 48 - Mailing price, 55 cents ; for introduction, 50 cents. rPHE design of the author has been to give to students a more complete and accurate knowledge of the nature and use of Logarithms than they can acquire from the cursory study commonly bestowed on this subject.