...any line passing through the centre and bounded by the surface is called a diameter of the sphere. 3. Every section of a sphere made by a plane is a circle. Let EOF be any such section of a sphere, of which the centre is 0. Draw OC from O perpendicular to the...

...passing through the center, and terminated each way by the surface. 3. It will be shown (Prop. I.), that every section of a sphere made by a plane is a circle. A great circle is a section made by a plane which passes through the center of the sphere. Any other...

...FG will, at the same time, be the diameter of the circumscribed circle. PROPOSITION VIII. THEOREM. Every section of a sphere, made by a plane, is a circle. Let AMB be the section, made by a plane in the sphere whose centre is C. From the point C, draw CO perpendicularly...

...follows that similar cylinders are to each other as the cubes of the linear dimensions. THEOREM XX. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular...

...follows that similar cylinders are to each other as the cubes of the linear dimensions. THEOREM XX. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular...

...All the radii of a sphere are equal; all the diameters are also equal, and double the radius. § ¿. Every section of a sphere made by a plane is a circle. If a sphere is cut by a plane which passes through the centre, the section is called a great circle...

...All the radii of a sphere are equal ; all the diameters are also equal, and double the radius. § £. Every section of a sphere made by a plane is a circle. If a sphere is cut by a plane which passes through the centre, the section is called a great circle...

...equal ; all the diameters are equal, and each is double the radius. 12. It will be shown (p. 7,) that every section of a sphere, made by a plane, is a circle : this granted, a great circle is a section which passes through the centre ; a small circle, is one...

...equal; all the diameters are equal, and each is double the radius. 12. It will be shown (p. 7,) that every section of a sphere, made by a plane, is a circle: this granted, a great circle is a section which passes through the centre; a small circle, is one which...

...follows that similar cylinders are to earfh other as the cubes of the linear dimensions. THEOREM XX. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular...