## Elements of Geometry |

### From inside the book

Results 6-10 of 15

Page 178

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**convex surface**, which plane would be less than the surface CMD ; and thus the surface CND would be smaller than MN , which is contrary to the hypothesis , that MN is the smallest of all . Therefore the**convex surface**AB is less than ... Page 179

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**convex surface**of a right prism is equal to the perime- ter of its base multiplied by its altitude . Demonstration . This surface is equal to the sum of the rect- angles AFGB , BGHC , CHID , & c . ( fig . 252 ) , which compose it ... Page 180

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**convex surface**of a cylinder is greater than the**convex surface**of any inscribed prism , and less than the**convex surface**of any circumscribed prism . Demonstration . The**convex surface**of the cylinder and that of Fig 252. the inscribed ... Page 181

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**convex surface**of the prism is less than circ . CAx H. But circ . CA x H is , by hypothesis , the**convex surface**of a cylinder of which CD is the radius of the base , which cylinder is inscribed in the prism ; whence the convex ... Page 184

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**convex surface**of a cone is equal to the circumference of its base multiplied by half its side . Demonstration . Let AO ( fig . 259 ) , be the radius of the base of the given cone , S its vertex , and SA its side ; we say that the surface ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence