## Elements of Geometry and Trigonometry |

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Page 128

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**intersection**. C E B F D PROPOSITION IV . THEOREM . If a straight line be perpendicular to two straight lines at their point of**intersection**, it will be perpendicular to the plane of those lines . Let MN be the plane of the two lines ...Page 137

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**intersection**of the planes AB , MN ; in the plane MN , draw DE perpendicular to BP : then the line AP , being perpendicular to the plane MN , will be perpendicu- lar to each of the two straight lines M B D BC , DE ; but the angle APD ...Page 138

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**intersection**will also be perpendicular to the third plane . Let the planes AB , AD , be per- pendicular to NM ; then will their**intersection**AP be perpendicular to NM . For , at the point P , erect a per- pendicular to the plane MN ...### 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