## Elements of Geometry |

### From inside the book

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Page vii

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**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 demonstrate ... Page 175

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**cylinder**the solid generated by the revolution of a rectangle ABCD ( fig . 250 ) , which may be conceived to Fig ...**cylinder**, and the side CD des- cribes the convex surface of the**cylinder**. The fixed line AB is called the axis ... Page 176

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**cylinder**, a polygon ABCDE be inscribed , and upon the base ABCDE a right prism be erected equal in altitude to the**cylinder**, the prism is said to be inscribed in the**cylinder**, or the**cylinder**to be circumscribed about the prism . It ... Page 178

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**cylinder**is equal to the product of its base by its altitude . Demonstration . Let CA ( fig . 258 ) be the radius of the base of the given**cylinder**, H its altitude ; and let surf . CA represent the surface of a circle whose radius ... Page 179

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**cylinder**by its altitude cannot be the measure of a less**cylinder**. We say , in the second place , that this same product cannot be the measure of a greater**cylinder**; for , not to multiply figures , let CD be the radius of the base ...### 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