Plane and solid geometry . determining the areasof these figures. For this purpose the entire surface of a sphereis thought of as being divided into 720 equal parts, and eachone of these parts is called a spherical degree. Hence: 986. Def. A spherical degree is y^ of the surface of a sphere. Now if the area of a lune or of a spherical triangle can be ob-tained in spherical degrees, the area can easily be changed tosquare units. For example, if it is found that the area of aspherical triangle is 80 spherical degrees, its area is J^, -i-of the entire surface of the sphere. On the sphere who
Plane and solid geometry . determining the areasof these figures. For this purpose the entire surface of a sphereis thought of as being divided into 720 equal parts, and eachone of these parts is called a spherical degree. Hence: 986. Def. A spherical degree is y^ of the surface of a sphere. Now if the area of a lune or of a spherical triangle can be ob-tained in spherical degrees, the area can easily be changed tosquare units. For example, if it is found that the area of aspherical triangle is 80 spherical degrees, its area is J^, -i-of the entire surface of the sphere. On the sphere whoseradius is 6 inches, the area of the given triangle will be \ of144 TT square inches, 16 tt square inches. The followingtheorems are for the purpose of determining the areas of figureson the surface of a sphere in terms of spherical degrees. 452 SOLID GEOMETRY Proposition XXIV. Theorem 987. The area of a lune is to the area of the surface ofthe sphere as tlve number of degrees in tlxe angle of thelune is to 360. N N. Q E
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
