## Elements of Geometry and Trigonometry |

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Page 182

B A F D E If the semicircle and semi - polygon be -evolved about EA , the semicircle will C describe a

B A F D E If the semicircle and semi - polygon be -evolved about EA , the semicircle will C describe a

**sphere**, and the semi - polygon a solid which has for its measure ОI2 × EA ( Prop . XIII . ) ; and this will be true whatever be the ... Page 186

OF

OF

**SPHERICAL TRIANGLES**AND SPHERICAL POLYGONS . Definitions . 1. A**spherical triangle**is a portion of the surface of a sphere , bounded by three arcs of great circles . These arcs are named the sides of the triangle , and are always ... Page 187

In every

In every

**spherical triangle**, any side is less than the sum of the other two . Let O be the centre of the sphere , and ACB the triangle ; draw the radii OA , OB , OC . Imagine the planes AOB , AOC , COB , to be drawn ; these planes will ... Page 188

THEOREM The sum of all the sides of any

THEOREM The sum of all the sides of any

**spherical**polygon is less than the circumference of a great circle , E C Take the pentagon ABCDE , for example . Produce the sides AB , DC , till they meet in F ; then since BC is less than BF + ... Page 192

From the vertices A , B , C , as poles , let the arcs EF , FD , ED , be described , forming on the surface of the

From the vertices A , B , C , as poles , let the arcs EF , FD , ED , be described , forming on the surface of the

**sphere**, the**triangle**DFE ; then will the points D , E , and F , be respectively poles of the sides BC , E M AC , AB .### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole