Elements of Geometry |
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Page 202
... polygons must be equal to 4 , taken as many times as there are solid angles ... spherical triangles formed with two given sides Fig . 276. CA , CB ( fig ... spherical triangle BCD , in which the angle DBC is also equal to the sum of the ...
... polygons must be equal to 4 , taken as many times as there are solid angles ... spherical triangles formed with two given sides Fig . 276. CA , CB ( fig ... spherical triangle BCD , in which the angle DBC is also equal to the sum of the ...
Page 203
... triangle CID ' , we have CI + ID ' > CD ' ; hence ID ' > CD— CI , or ID ' > ID . = = In the isosceles triangle CIB , bisect the angle I by the arc EIF , which will also bisect BC at right angles ... Spherical Isoperimetrical Polygons . 203.
... triangle CID ' , we have CI + ID ' > CD ' ; hence ID ' > CD— CI , or ID ' > ID . = = In the isosceles triangle CIB , bisect the angle I by the arc EIF , which will also bisect BC at right angles ... Spherical Isoperimetrical Polygons . 203.
Page 205
... spherical triangle has then increased to a hemisphere , but it has at the same time ceased to be a triangle . THEOREM . 563. Of all the spherical triangles , formed with a ... spherical polygons Of Spherical Isoperimetrical Polygons . 205.
... spherical triangle has then increased to a hemisphere , but it has at the same time ceased to be a triangle . THEOREM . 563. Of all the spherical triangles , formed with a ... spherical polygons Of Spherical Isoperimetrical Polygons . 205.
Page 206
... spherical polygons of the same perimeter and the same number of sides , that is the greatest which has its sides equal . The demonstration is the same as that of art . 301 . 566. Among spherical polygons formed of known sides and one ...
... spherical polygons of the same perimeter and the same number of sides , that is the greatest which has its sides equal . The demonstration is the same as that of art . 301 . 566. Among spherical polygons formed of known sides and one ...
Page 214
... spheres are to each other as the sides of the polyedrons . iv . If a regular polyedron is inscribed in a sphere , the ... spherical polygons , as the polyedron has faces all equal and similar among themselves . Improved Demonstration of ...
... spheres are to each other as the sides of the polyedrons . iv . If a regular polyedron is inscribed in a sphere , the ... spherical polygons , as the polyedron has faces all equal and similar among themselves . Improved Demonstration of ...
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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