...Spherical Surface. (I.) By the principles of solid geometry it is proved that if a sphere be intersected by a plane, the section is a circle. If the plane pass through the centre of the sphere, the section is called a great circle; if not, it is a lesser circle. (2.) That diameter of the sphere,...

...any required distance from the centre. § 1. OF THE SECTIONS OF A SPHERE BY A PLANE. THEOREM I. 30. If a sphere be cut by a plane, the section is a circle. Let AB С D be a sphere cut by a plane ; the section ABС is a circle. The intersecting plane may pass...

...semi-circumferences is equal to the circle whose diameter is DB. THEOREM III. Every section of a sphere by a plane is a circle. If the plane pass through the centre of the sphere, it is manifest that the section is a circle, having the same diameter as the generating semicircle....

...our station to the heaven, and bounding the hemisphere visible above the earth. It is a circle ; for if a sphere be cut by a plane the section is a circle. " The Meridian is a circle passing through the poles of the sphere, and at right angles to the horizon....

...all diameters of a sphere are equal. 3. It will be proved that every section of a sphere by a plane is a circle. If the plane pass through the centre of the sphere, the circle is called a great circle; if not, a small circle. Corottary.—The diameter of a great circle is also...

...universe, and separates off the segment which we see above the earth. The horizon is a circle; for, // a sphere be cut by a plane, the section is a circle. Let the name "meridian circle" be given to the circle through the poles which is at right angles to...