Elements of Geometry and Trigonometry |
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Page 173
... cone being S. Hence this surface will be measured as we have said . This measure will always hold good , even when the point D falls on S , and thus forms a whole cone ; and also when the line AD is parallel to the axis , and thus forms ...
... cone being S. Hence this surface will be measured as we have said . This measure will always hold good , even when the point D falls on S , and thus forms a whole cone ; and also when the line AD is parallel to the axis , and thus forms ...
Page 174
... cone's base , H its alti- tude ; the solidity of the cone will be R2x H , or 1⁄4μR3H . PROPOSITION VI . THEOREM . The solidity of the frustum of a cone is equal to the sum of the solidities of three cones whose common altitude is the ...
... cone's base , H its alti- tude ; the solidity of the cone will be R2x H , or 1⁄4μR3H . PROPOSITION VI . THEOREM . The solidity of the frustum of a cone is equal to the sum of the solidities of three cones whose common altitude is the ...
Page 178
... cone described by the triangle ADC · is the third part of the cylinder de- B D scribed by the rectangle ADCE ; hence the sum of the two cones , or the solid described by ABC , is the third part of the two cylinders taken together , or ...
... cone described by the triangle ADC · is the third part of the cylinder de- B D scribed by the rectangle ADCE ; hence the sum of the two cones , or the solid described by ABC , is the third part of the two cylinders taken together , or ...
Page 179
... cones described by ABD and ACD ; but at the same time , the cylinder de- scribed by BCEF will be the difference of the two cylinders described by AFBD and AECD . Hence the solid , described by the revolution of the triangle , will still ...
... cones described by ABD and ACD ; but at the same time , the cylinder de- scribed by BCEF will be the difference of the two cylinders described by AFBD and AECD . Hence the solid , described by the revolution of the triangle , will still ...
Page 180
... cone descri- bed by ACM is equal to .AM2.CM , and the cone described by BCN to AM2 CN . Add the first two solids and take away A B M N the third ; we shall have the solid described by ABC equal to 7.AM2 . ( MN + CM - CN ) : and since CN ...
... cone descri- bed by ACM is equal to .AM2.CM , and the cone described by BCN to AM2 CN . Add the first two solids and take away A B M N the third ; we shall have the solid described by ABC equal to 7.AM2 . ( MN + CM - CN ) : and since CN ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex