...ELEMENTARY PRINCIPLES OP SPHERICAL TRIGONOMETRY. 1. A SPHERE is a solid bounded by a curve surface, every point of which is at the same distance from a point within, called the centre. Cor. 1. A sphere may be conceived to be generated by the revolution of a semicircle,...

...same proportions as the diameters of their bases. 11. A sphere is a solid bounded by a curve surface, every point of which is at the same distance from a point within, called the centre. 12. The diameter of a sphere is any right line passing through the centre and terminated...

...longer ? You have broken the conditions of a lake ; and it ceases to be one. What is a circle ? It is a line every point of which is at the same distance from a point within it called the centre. Suppose you change that, and have some part of the circle not the same distance from the centre...

...vertex is cut off by a plane parallel to the base. 11. A Sphere is a solid bounded by a curved surface, every point of which is at the same distance from a point within, called the center. The diameter of a sphere is a straight line passing through the center and having...

...the other side containing the right angle is the base. A sphere is a solid every point on the surface of which is at the same distance from a point within it, called its centre. A sphere may also be defined as a solid described by the revolution of a semicircle about...

...distance from the centre, the following may be given as an alternative definition : A sphere is a surface every point of which is at the same distance from a point within it called the centre. SECTIONS OF SPHERES. 74. PROP. 52. The common section of a plane and a sphere is a circle....

...a point is position without magnitude, a straight line is the shortest distance between two points, a circle is a plane figure bounded by one curved line every point of which is equally distant from a point within the circle known as its center." The axioms of geometry are propositions...

...containing the right angle is the base of the cone. A sphere is a solid every point on the surface of which is at the same distance from a point within it called its centre. A sphere may also be defined as a solid described by the revolution of a semicircle about...

...straight edge, the latter preferably not marked in units. 41. Definitions. A circumference is a closed curved line every point of which is at the same distance from a point within called the center. A part of a circumference is called an arc. The area enclosed by a circumference...

...number of coins of each denomination. CIRCLES 40. A circle is a figure on a flat surface made by a curved line every point of which is at the same distance from a point within called the center. The curved line of the circle is sometimes called the circumference. Any circle...