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
... problems , classified under the particular heads of the several applications , as specified in the ta- ble of ... problem in reference to Dial- ling , and the comprehensive table of Differential Equa- tions for the variations of ...
... problems , classified under the particular heads of the several applications , as specified in the ta- ble of ... problem in reference to Dial- ling , and the comprehensive table of Differential Equa- tions for the variations of ...
Page xi
... problems XI . Minute variations of triangles , with a table of differential equations XII . Miscellaneous problems , in two sections Sect . 1. Problems with solutions Sect . 2. Problems without solutions 151 • 187 206 • . 232 ERRATA ...
... problems XI . Minute variations of triangles , with a table of differential equations XII . Miscellaneous problems , in two sections Sect . 1. Problems with solutions Sect . 2. Problems without solutions 151 • 187 206 • . 232 ERRATA ...
Page xii
... problem . 167 , line 9 from bottom , for limited , read limits 212 , last line but one , for + 2√p , read + 2√P . to the whole circumference . tween the versed sine of Right angled spherical triangles Oblique angled ditto Analogies of ...
... problem . 167 , line 9 from bottom , for limited , read limits 212 , last line but one , for + 2√p , read + 2√P . to the whole circumference . tween the versed sine of Right angled spherical triangles Oblique angled ditto Analogies of ...
Page 2
... problems . I. Knowing three of the six things , whether angles or sides , which enter the constitution of a rectilinear tri- angle , to determine the other three ; when it is possible . II . Knowing three of the six things which compose ...
... problems . I. Knowing three of the six things , whether angles or sides , which enter the constitution of a rectilinear tri- angle , to determine the other three ; when it is possible . II . Knowing three of the six things which compose ...
Page 25
... problem thus ex- pressed is unlimited . Our twenty varieties , therefore , only furnish three distinct cases , to the solution of which we shall now proceed . CASE I. 2. When a side and its opposite angle are among the given parts ...
... problem thus ex- pressed is unlimited . Our twenty varieties , therefore , only furnish three distinct cases , to the solution of which we shall now proceed . CASE I. 2. When a side and its opposite angle are among the given parts ...
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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 cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side gonal h cos h half Hence horizon hour angle 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 yards zenith δα δε дв
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 248 - SCIENTIFIC DIALOGUES ; intended for the Instruction and Entertainment of Young People ; in which the first principles of Natural and Experimental Philosophy are fully explained, by the Rev.
Page 225 - ... third of the excess of the sum of its three angles above two right angles...
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 249 - OSTELL'S NEW GENERAL ATLAS; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Page 34 - Call any one of the sides radius, and write upon it the word radius ; observe whether the other sides become sines, tangents, or secants, and write those words upon them accordingly. Call the word written upon each side the name of each side ; then say, As the name of the given side, Is to the given side ; So is the name of the required side, To the required side.
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 83 - 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...