## Elements of Geometry |

### From inside the book

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**spherical**isoperimetrical**polygons**, and on the regular poly- L513 1300 485457 234126 edrons , are inserted in this , at the end. Page vii

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**sphere**and**spherical**triangles . This treatise does not ordina- rily make a part of the elements of geometry ; still we have thought it proper to consider so much of it as may form an intro- duction to**spherical**trigonometry . The ... Page 176

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**spherical polygons**intercepted between their planes or faces . The angle at the vertex of the pyramid , whose base ...**spherical polygon**, will give the measure of the corresponding solid angle . If , for example , the area of a ... Page 191

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**spherical**triangles , the ratio of which to the entire surface of the**sphere**has already been determined . In the ...**polygons**follows immediately from that of triangles , and it is moreover entirely determined by the proposition of art ... Page 201

... shall find their sum , or the surface of the

... shall find their sum , or the surface of the

**sphere**, represented by 8 , to be equal to the sum of all the angles of the GEOM . 26**polygons**, minus twice the number of their sides , Of**Spherical**Isoperimetrical**Polygons**. 201.### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence