## Elements of Geometry and Trigonometry |

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Page 182

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

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

**sphere**, and the semi - polygon a solid which has for its measure лƠI2 × 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

The sum of the three sides of a

The sum of the three sides of a

**spherical triangle**is less than the circumference of a great circle . Let ABC be any spherical trian- angle ; produce the sides AB , AC , till they meet again in D. The arcs ABD , ACD , will be semicir- ... Page 192

If from the vertices of the three angles of a

If from the vertices of the three angles of a

**spherical triangle**, as poles , three arcs be described forming a second triangle , the vertices of the angles of this second triangle , will be respectively poles of the sides of the first ...### 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 construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole