...sector, as DCF or FCH, describes a solid, which is named a spherical sector. PROPOSITION I. THEOREM. 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 point C, draw CO perpendicu-...

...this volume, is used to denote because; when applied in algebraic notation. 4 PROPOSITION I. THEOREM. Every section of a sphere, made by a plane, is a circle. Let j\MB be a section, made by a plane, in 'the sphere, whose centre is C. From the point G, draw CO perpend...

...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 EDF be any such section of a sphere, of which the centre is O. Draw OC from O perpendicular to the...

...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....be the section, made by a plane in the sphere whose B/ centre is C. From the point C, draw CO perpendicularly to the plane AMB ; and draw lines CM, CM...

...a sphere are equal ; and all its diameters are also equal, and double of the radius. 419. Theorem. Every section of a sphere made by a plane is a circle. Proof. From the centre C (fig. 178) of the sphere draw the perpendicular CO to the section AMB and...

...all the diameters are equal, and each double of the radius. 3. It will be demonstrated (Prop. 1) that every section of a sphere made by a plane is a circle ; this being assumed, A great circle of a sphere is the section made by a plane passing through the...

...110 XIII. Examples Ill SPHERICAL TRIGONOMETRY. CHAPTER I. Р1ОЖ I. Definition of a sphere . 115 II. Every section of a sphere made by a plane is a circle 116 III. In a spherical triangle, any side is less than the sumí of the other two ) IV. The sum of...

...PD.i; since AO x PD." is a mean proportional between OA"." and PD*.n PROPOSITION VII. THEOREM. xeciion 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 point C, draw CU perpendicular...

...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....sphere whose centre is C. From the point C, draw CO perpendicularly to the plane AMB ; and draw lines CM, CM to different points of the curve AMB, which...