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
... Dial- ling , and the comprehensive table of Differential Equa- tions for the variations of triangles , are taken , simply with such alterations as fitted them better for general usefulness , from the Chevalier Delambre's admirable ...
... Dial- ling , and the comprehensive table of Differential Equa- tions for the variations of triangles , are taken , simply with such alterations as fitted them better for general usefulness , from the Chevalier Delambre's admirable ...
Page 134
... dial , that is , a figure , the dif ferent lines of which , when the sun shines , indicate by the shadow of a style or gnomon the time of the day . 2. The general principles which serve as a basis to the theory of dialling , cannot be ...
... dial , that is , a figure , the dif ferent lines of which , when the sun shines , indicate by the shadow of a style or gnomon the time of the day . 2. The general principles which serve as a basis to the theory of dialling , cannot be ...
Page 135
... dial for London : for the shadow of the axis would fall upon each particular hour line of the dial , when it fell upon the like hour circle of the sphere . If the plane which intersects the sphere be imagined upright , and at the same ...
... dial for London : for the shadow of the axis would fall upon each particular hour line of the dial , when it fell upon the like hour circle of the sphere . If the plane which intersects the sphere be imagined upright , and at the same ...
Page 136
... dial . And since the earth it- self compared with its distance from the sun , may , in reference to this branch of ... dial , and the upper edge of which marks and bounds the shadow , is called the gnomon ; the superior edge of the said ...
... dial . And since the earth it- self compared with its distance from the sun , may , in reference to this branch of ... dial , and the upper edge of which marks and bounds the shadow , is called the gnomon ; the superior edge of the said ...
Page 137
... dial and that of the meridian passing through the style is called the meridian of the dial , or the hour line of 12 . 13. Those meridians passing through the style , which make angles of 15 ° , 30 ° , 45 ° , & c . with the meridian of ...
... dial and that of the meridian passing through the style is called the meridian of the dial , or the hour line of 12 . 13. Those meridians passing through the style , which make angles of 15 ° , 30 ° , 45 ° , & c . with the meridian of ...
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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.