Elements of geometry and trigonometry . ection which passes through the centre ; 3. small circle^is one which does not pass through the centre. 12. A plane is tangent to a sphere, when their surfaces havebut one point in common. 13. A zone is a portion of the surface of the sphere includedbetween two parallel planes, which form its hases. One ofthese planes may be tangent to the sphere ; in which case, thezone has only a single base. 14. A spherical segment is the portion of the solid sphere,included between two parallel planes which form its of these planes may be tangent to the sph
Elements of geometry and trigonometry . ection which passes through the centre ; 3. small circle^is one which does not pass through the centre. 12. A plane is tangent to a sphere, when their surfaces havebut one point in common. 13. A zone is a portion of the surface of the sphere includedbetween two parallel planes, which form its hases. One ofthese planes may be tangent to the sphere ; in which case, thezone has only a single base. 14. A spherical segment is the portion of the solid sphere,included between two parallel planes which form its of these planes may be tangent to the sphere ; in whichcase, the segment has only a single base. 15. The altitude of a zone or of a segment is the distancebetween the two parallel planes, which form the bases of thezone or segment. Note. The Gylinder, the Gone, and the Sphere, are thethree round bodies treated of in the Elements of Geometry. BOOK VIII. PROPOSITION I. THEOREM. The convex surface of a cyVuidcr is equal to the circumference ofits base multiplied by its Let CA be the radius of thegiven cylinders base, ami H itsaltitude : the circunilerencewhose radius is CA being rep-resented by circ, CA, we are toshow that the convex surface ofthe cvhnder is equal to circ, Q\X H. Inscribe in the circle anyregular polygon, BDEFGA, andconstruct on this polygon a rightprism having its altitude equal to II, the altitude of the cylin-der : this prism will be inscribed in the cylinder. The convexsurface of the prism is equal to the perimeter of the polygon,multiplied by the altitude II (Book Vll. Prop. I.). Let nowthe arcs which subtend the sides of the polygon be continuallybisected, and the number of sides of the polygon indefinitelyincreased : the {)erimeterof the polygon will then become equalto circ. CA (Book V. Prop. VIII. Cor. 2.), and the convex sur-face of the prism will coincide witii the convex surface of thecylindei*. But the convex surface of the prism is equal to theperimeter of its base multiplied by
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