Elements of Geometry and Trigonometry |
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Page 166
... cylinder , the side CD at the same time describing the convex surface . The immoveable line AB is called the axis of the cylinder . E M P N B C G Every section KLM , made in the cylinder , at right angles to the axis , is a circle equal ...
... cylinder , the side CD at the same time describing the convex surface . The immoveable line AB is called the axis of the cylinder . E M P N B C G Every section KLM , made in the cylinder , at right angles to the axis , is a circle equal ...
Page 167
... cylinder , is said to be inscribed in the cylin- der , or the cylinder to be circumscribed about the prism . The edges AF , BG , CH , & c . of the prism , being perpendicular to the plane of the base , are evidently included in the ...
... cylinder , is said to be inscribed in the cylin- der , or the cylinder to be circumscribed about the prism . The edges AF , BG , CH , & c . of the prism , being perpendicular to the plane of the base , are evidently included in the ...
Page 168
... Cylinder , the Cone , and the Sphere , are the three round bodies treated of in the Elements of Geometry . PROPOSITION I. THEOREM . The convex surface of a cylinder 168 GEOMETRY .
... Cylinder , the Cone , and the Sphere , are the three round bodies treated of in the Elements of Geometry . PROPOSITION I. THEOREM . The convex surface of a cylinder 168 GEOMETRY .
Page 169
... cylinder's base , and H its altitude : the circumference whose radius is CA being rep- resented by circ . CA , we are to show that the convex surface of the cylinder is equal to circ . CA × H. Inscribe in the circle any regular polygon ...
... cylinder's base , and H its altitude : the circumference whose radius is CA being rep- resented by circ . CA , we are to show that the convex surface of the cylinder is equal to circ . CA × H. Inscribe in the circle any regular polygon ...
Page 170
... cylinder is equal to area CA × H. Inscribe in the circle any regu- lar polygon BDEFGA , and con- struct on this polygon a right prism having its altitude equal H A G F B D KCI to H , the altitude of the cylinder : this prism will be ...
... cylinder is equal to area CA × H. Inscribe in the circle any regu- lar polygon BDEFGA , and con- struct on this polygon a right prism having its altitude equal H A G F B D KCI to H , the altitude of the cylinder : this prism will be ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex