## New Plane and Solid Geometry |

### From inside the book

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Page 265

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**SPHERICAL POLYGONS**AND SPHERICAL PYRAMIDS DEFINITIONS 539. A**spherical polygon**is a portion of the surface of a sphere bounded by three or more arcs of great circles ; as ABCD . The bounding arcs are called the sides of the spherical ... Page 266

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**spherical polygon**form a polyedral angle , O - ABCD , whose face & AOB , BOC , etc. , are measured by arcs AB , BC , etc. , respectively . A**spherical polygon**is called convex when the polyedral angle formed by the planes of its sides ... Page 269

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**spherical polygon**is less than 360 ° . B ་ D Given convex**spherical polygon**ABCD . To Prove AB + BC + CD + DA < 360 ° . ( By § 407 , sum of 4 AOB , BOC , COD , and DOA is < 360 ° . ) PROP . XIV . THEOREM 551. The sum of the THE SPHERE 269. Page 281

... polygon is equal to the sum of its angles , diminished by as many times two right angles as the figure has sides less two , multiplied by the area of a tri - rectangular ... sphere whose radius MEASUREMENT OF

... polygon is equal to the sum of its angles , diminished by as many times two right angles as the figure has sides less two , multiplied by the area of a tri - rectangular ... sphere whose radius MEASUREMENT OF

**SPHERICAL POLYGONS**281. Page 287

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**polygon**OACDB OE = area ACDB × OE . 4. If subdivisions of AB be bisected indefinitely , volume generated by**polygon**...**spherical**sector . Ex . 32. The angles of a**spherical**quadrilateral are 95 ° , 115 ° , 135 ° , and 110 ...### Other editions - View all

### Common terms and phrases

ABC and A'B'C adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisector bisects centre chord circle circumference circumscribed coincide construct Converse of Prop diagonals diameter diedral angle distance Draw line equal parts occur equal respectively equally distant equilateral triangle exterior angle faces frustum Given line given point homologous sides hypotenuse intersecting isosceles trapezoid isosceles triangle LAOB lateral area lateral edges line drawn lines be drawn measured by arc middle point number of sides oblique lines opposite parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism Proof proportional Prove pyramid quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle secant segments slant height spherical polygon spherical triangle square straight line surface tangent tetraedron THEOREM trapezoid triedral vertex vertices volume