## Elements of Geometry |

### From inside the book

Results 1-5 of 16

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 177

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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 describes the convex surface of the**cylinder**. The fixed line AB is called the axis of the ... Page 178

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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 180

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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 is ... Page 181

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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 of ...### 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