A treatise on special or elementary geometry (1877)
Olney, Edward, 1827-1887, Olney, Edward, 1827-1887. Elements of trigonometry, plane and spherical · New York : Sheldon · leaf 253
PROPOSITION xxyni. 60t, Theorem.—The area of a lune is to the area of the surfaceof the sphere on lohich it is situated, as the angle of the lune is tofour right angles. Dem.—Let ACEB be a mne whose angle is the spherical angle CAB, or what 232 ELEMENTARY SOLID GEOiZETRY. … is tlie same thing, the plane angle BOC measuredby the arc CB, of which A is the pole; then is lune ACEB : surface of spCiere :: CAB : 4 right angles. For, suppose the arc CB commensurable with thecircumference BCwD;i, and suppose that they areto each other as 5 : 24. Dividing BC into 5 equalarcs,…
Geometry · Trigonometry
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