## Elements of Geometry |

### From inside the book

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Page vii

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**cone**, and the cylinder . The measure of the surfaces and solidities of these bodies is deter- mined by a method analogous to that of Archimedes , and found- ed , as to surfaces , upon the same principles , which we have endeavoured to ... Page 175

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**cone**, and the hypothenuse SB de- scribes the convex surface of the**cone**. The point S is called the vertex of the**cone**, SA the axis or alti- tude , and SB the side . Every section HKFI , made perpendicularly to the axis , is a circle ... Page 176

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**cones**are similar , when their axes are to each other as the diameters of their bases . 511. If , in the circle ACD ( fig ...**cone**and the sphere are the three round bodies , which are treated of in the elements . Preliminary Lemmas upon ... Page 177

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**cone**and cylin- der . It should be observed moreover , that the denomination of convex surface is not confined to curved surfaces ; it comprehends polyedral faces , or surfaces composed of several planes , also sur- faces that are in ... Page 182

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**cone**is equal to surf . AO SO . 1. Let surf . AO × SO be supposed to be the solidity of a greater**cone**, of a**cone**, for example , whose altitude is always SO , but of which BO , greater than AO , is the radius of the base . About the ...### 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