n. round seed-vessel of cotton, flax,et cetera (и так далее) [Dutch]
... segment is a part of a ball , cut . off from it by a plane The formula for the volume of the ball segment is. obtained similarly to the formula for the volume of the.ball : where R is the radius of the ball , and H. is the height ... ... segment is. obtained similarly to the formula for the volume of the.ball : where R is the radius of the ball , and H. is the height of the ball segment ... (Stereometry)
... is. a circle The center of this circle is the base of the. perpendicular , which is lowered from the center of the ball .to the cutting plane Evidence Let α be a cutting plane and O be. the center of the ball We drop ... ... from the center of the ball . to the plane α and denote by O` the base .of this perpendicular Let X be an arbitrary point of the ball belonging . to the plane α According to the Pythagorean theorem Formula Since OX is not. larger than ... (Stereometry)
... than .a given one from a given point This point is called the center of the ball , and. this distance is the radius of the ball . The boundary of the ball is called a spherical surface . , or sphere ... ... from a given point This point is called the center of the ball , and. this distance is the radius of the ball . The boundary of the ball is called a spherical surface . , or sphere Thus , the points of the sphere ... (Stereometry)
... Theorem Any diametrical plane of the ball is its plane The center of the ball is its center of symmetry . Evidence Let α be the diametrical plane and X be an. arbitrary point of the ball ... ... `, it. follows that OX ` = OX Since OX ≤ R, then OX ` ≤ R, i e the point symmetric to the point X belongs to the. ball The first assertion of the theorem is proved Now let X`` be a point symmetric to X with. respect ... (Stereometry)
... , we . calculate the volume of the ball We introduce Cartesian coordinates , taking the center of the ball . to the origin The xy plane intersects the surface of a sphere of. radius R in a circle defined ... ... by the formula The .semicircle located above the x axis is given by the equation . Therefore , the volume of the ball is determined by the.formula ... (Stereometry)
... point . Theorem The tangent plane has only one common point with. the ball - the point of tangency Evidence Let α be the plane tangent to the ball ., and A the point of tangency Take ... ... OA is perpendicular and OX is inclined , OX > OA . = R Therefore , point X does not belong to the ball The theorem is proved ... (Stereometry)
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