Elements of Geometry and Trigonometry |
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Page 173
... cylinder . In the first case DC would be nothing ; in the second , DC would be equal to AO and to IK . PROPOSITION V. THEOREM . The solidity of a cone is equal to its base multiplied by a third of its altitude . Let SO be the altitude ...
... cylinder . In the first case DC would be nothing ; in the second , DC would be equal to AO and to IK . PROPOSITION V. THEOREM . The solidity of a cone is equal to its base multiplied by a third of its altitude . Let SO be the altitude ...
Page 178
... 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 of the cylinder described by the rectangle BCEF . 1 7 F E If ...
... 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 of the cylinder described by the rectangle BCEF . 1 7 F E If ...
Page 179
... 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 be a third part of the cylinder described by the revolution ...
... 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 be a third part of the cylinder described by the revolution ...
Page 180
... cylinder described by AMNB is equal to " .AM2.MN ; the 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 ...
... cylinder described by AMNB is equal to " .AM2.MN ; the 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 ...
Page 183
... cylinder , including its bases , as 2 is to 3 : and the so- lidities of these two bodies are to each other in the ... cylinder circum- scribed about that sphere . A P The altitude AD of the cylinder is equal to the diameter PQ ; the base ...
... cylinder , including its bases , as 2 is to 3 : and the so- lidities of these two bodies are to each other in the ... cylinder circum- scribed about that sphere . A P The altitude AD of the cylinder is equal to the diameter PQ ; the base ...
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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