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 82
... angles COB , COA , & c . Here it is 1st , evident that the three sides of a spherical triangle are together less than a circle , or , a + b + c < 360 ° . For the solid angle at o is contained by three plane angles , which ( Euc . xi ...
... angles COB , COA , & c . Here it is 1st , evident that the three sides of a spherical triangle are together less than a circle , or , a + b + c < 360 ° . For the solid angle at o is contained by three plane angles , which ( Euc . xi ...
Página 101
... Solid Angles . Theorem I. 43. In every spherical triangle , the following propor- tion obtains , viz . as four right angles , ( or 360 ° ) , to the surface of a hemisphere ; or , as two right angles ( or 180 ° ) , to a great circle of ...
... Solid Angles . Theorem I. 43. In every spherical triangle , the following propor- tion obtains , viz . as four right angles , ( or 360 ° ) , to the surface of a hemisphere ; or , as two right angles ( or 180 ° ) , to a great circle of ...
Página 104
... angles of any spheric polygon , is always less than 2n right angles , but greater than ( 224 ) right angles , n denoting the number of angles of the polygon . Nature and Measure of Solid Angles . 45. A solid angle is defined by Euclid ...
... angles of any spheric polygon , is always less than 2n right angles , but greater than ( 224 ) right angles , n denoting the number of angles of the polygon . Nature and Measure of Solid Angles . 45. A solid angle is defined by Euclid ...
Página 105
... solid angles bear just the same relation to the surfaces which comprise them , as plane angles do to the lines by which they are included :. so that , as in the latter , it is not the magnitude of the lines , but their mutual ...
... solid angles bear just the same relation to the surfaces which comprise them , as plane angles do to the lines by which they are included :. so that , as in the latter , it is not the magnitude of the lines , but their mutual ...
Página 106
... solid angle made by the planes at their common point of meeting : for no change can ' be conceived in the relative position of those planes , that is , in the magnitude of the solid angle , without a corresponding and proportional ...
... solid angle made by the planes at their common point of meeting : for no change can ' be conceived in the relative position of those planes , that is , in the magnitude of the solid angle , without a corresponding and proportional ...
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Términos y frases comunes
altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent 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 hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² 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