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 OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Página 120
... hour circles ; because the sun in his apparent diurnal motion passing over 360 ° of a circle parallel to the equator ... angle formed at the body by two great circles , one passing through the pole of the equator , the other through the pole ...
... hour circles ; because the sun in his apparent diurnal motion passing over 360 ° of a circle parallel to the equator ... angle formed at the body by two great circles , one passing through the pole of the equator , the other through the pole ...
Página 123
... hour cir- cle will be repre- sented by its dia- meter which is the axis PP ' , making with the horizon R Z ' E " the angle PCO = the height of the pole LMNT the latitude L : the equator will be projected into its diameter eq , making ...
... hour cir- cle will be repre- sented by its dia- meter which is the axis PP ' , making with the horizon R Z ' E " the angle PCO = the height of the pole LMNT the latitude L : the equator will be projected into its diameter eq , making ...
Página 125
... hour angle sin D sin L + cos D COS L COS H .... ( 6. ) 90 ° — D , E = 90 ° - then will the last equation become L , and z = 90 ° ⋅ cos z = cos △ cos E + sin A sin E cos H , ― A ; which accords precisely with the fundamental equation ...
... hour angle sin D sin L + cos D COS L COS H .... ( 6. ) 90 ° — D , E = 90 ° - then will the last equation become L , and z = 90 ° ⋅ cos z = cos △ cos E + sin A sin E cos H , ― A ; which accords precisely with the fundamental equation ...
Página 136
... hour lines for every variety of dial . And since the earth it- self compared ... hour circles , be placed upon any part of the earth's surface , so that its ... angle included between the style and the sub- style is called the elevation ...
... hour lines for every variety of dial . And since the earth it- self compared ... hour circles , be placed upon any part of the earth's surface , so that its ... angle included between the style and the sub- style is called the elevation ...
Página 137
... angle which it makes with a vertical plane . 12. The intersection of the plane of the dial and that of the meridian passing through the style is called the meridian of the ... hour angles , and let the plane on which General Problem . 137.
... angle which it makes with a vertical plane . 12. The intersection of the plane of the dial and that of the meridian passing through the style is called the meridian of the ... hour angles , and let the plane on which General Problem . 137.
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 251 - New General Atlas ; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Página 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.
Página 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.
Página 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...
Página 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.
Página 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'.
Página 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.