## Elements of Geometry and Trigonometry |

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Page 171

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**cone**is equal to the circumference of its base , multiplied by half its side . Let the circle ABCD be the base of a**cone**, S the vertex , SO the altitude , and SA the side then will its convex sur- face be equal to circ . OA × SA . For ...Page 173

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**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

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**cone's**base , H its alti- tude ; the solidity of the**cone**will be R2x4H , or πR2Н . 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 ...### Contents

BOOK | 7 |

Problems relating to the First and Third Books 57 | 57 |

BOOK IV | 68 |

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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 consequently convex surface cosine Cotang 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex