Elements of Geometry |
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Page vii
... 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 ...
... 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
... 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 of the ...
... 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 of the ...
Page 176
... 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 ...
... 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
... 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 ...
... 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 179
... 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 ...
... 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 ...
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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