## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |

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Page 216

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**cylinders**described within the hemis- phere , is exceeded by the hemisphere by a solid less than the**cylinder**I. D E K N F R G f q X S H P r gM h A C f B generated by the rectangle HB , that is , by 216 SUPPLEMENT TO THE ELEMENTS. Page 217

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**cylinder**generated by HB is less than W. In the same manner , it may be demonstrated , that the sum of the**cylinders**circumscribing the cone ICE is greater than the cone by a solid less than the**cylinder**generated by the rectangle DN ... Page 218

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**cylinder**described by DB , that is , to the**cylinder**having the same base and altitude with the hemisphere QE . D. PROP . XXI . Every sphere is two - thirds of the circumscribing**cylinder**. Let the figure be constructed as in the two ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore