## Elements of Geometry and Trigonometry |

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Page 160

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**third**of the prism . E B F Cut off the pyramid F - ABC from the prism , by the plane FAC ; there will remain the ...**third**part of the prism ABC - DEF , which has the same base and the same altitude . Cor . The solidity of a triangular ...Page 173

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**third**of its altitude . Let SO be the altitude of a cone , OA the radius of its base , and let the area of the base be designated by area OA : it is to be proved that the solidity of the cone is equal to area OA × SO . A F S B D E ...Page 178

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**third**part of the cylinder described by the rectan- gle AFBD ( Prop . V. Cor . ) ; also the cone described by the triangle ADC is the**third**part of the cylinder de- B A E D scribed by the rectangle ADCE ; hence the sum of the two cones ...### 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