Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic Operations |
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Page v
... obtaining a thorough comprehension of the principal topics of research , and by seeing a little of their utility ... obtained by analytical processes ; and their utility is shown in the logarithmic and trigonometric solution of a great ...
... obtaining a thorough comprehension of the principal topics of research , and by seeing a little of their utility ... obtained by analytical processes ; and their utility is shown in the logarithmic and trigonometric solution of a great ...
Page 23
... obtained , with the analogous results in the preceding operations , will ma- nifestly establish the correctness of both . The sines and cosines of the degrees and minutes up to 30 ° , being determined by these or other processes ( some ...
... obtained , with the analogous results in the preceding operations , will ma- nifestly establish the correctness of both . The sines and cosines of the degrees and minutes up to 30 ° , being determined by these or other processes ( some ...
Page 25
... obtained by means of chap . ii . prop . 14 , where it is demonstrated that the sides of plane triangles are respectively proportional to the sines of their opposite angles . C In practice if a side be required , begin the Solution of ...
... obtained by means of chap . ii . prop . 14 , where it is demonstrated that the sides of plane triangles are respectively proportional to the sines of their opposite angles . C In practice if a side be required , begin the Solution of ...
Page 26
... obtain the logarithm of the fourth term . Or , adding the arith- metical complement of the logarithm of the first term to the logarithms of the other two , to obtain that of the fourth . Note 3. It is an excellent plan to accustom the ...
... obtain the logarithm of the fourth term . Or , adding the arith- metical complement of the logarithm of the first term to the logarithms of the other two , to obtain that of the fourth . Note 3. It is an excellent plan to accustom the ...
Page 35
... obtained , conformably with this rule , easier without logarithms than with them . For , Let ABC be a right angled ... obtain these expressions . B perp . 1 . = tan angle at base . base base 2 . tan angle at vertex . perp . hyp . 3 ...
... obtained , conformably with this rule , easier without logarithms than with them . For , Let ABC be a right angled ... obtain these expressions . B perp . 1 . = tan angle at base . base base 2 . tan angle at vertex . perp . hyp . 3 ...
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Common terms and phrases
altitude angled spherical triangle axis azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hour line hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith δα
Popular passages
Page 4 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 19 - In any plane triangle, as twice the rectangle under any two sides is to the difference of the sum of the squares of those two sides and the square of the base, so is the radius to the cosine of the angle contained by the two sides.
Page 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 251 - New General Atlas ; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Page 69 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Page 18 - AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Page 85 - 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 19 - ... will be — As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Page 70 - Required the horizontal distance of the mountain-top from the nearer station, and its height. Ans. Distance, 24840 yards; height, 1447 yards. 10. From the top of a light-house the angle of depression of a ship at anchor was observed to be 4° 52', from the bottom of the light-house the angle was 4° 2'.
Page 245 - XI- -A Treatise on Astronomy; in which the Elements of the Science are deduced in a natural Order, from the Appearances of the Heavens to an Observer on the Earth ; demonstrated on Mathematical Principles, and explained by an Application to the various Phenomena. By Olinthus Gregory, Teacher of Mathematics, Cambridge, 8vo.