## Elements of Geometry and Trigonometry |

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Page 127

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**plane**, and partly out of it . For , by the definition of a**plane**, when a straight line has two points common with a**plane**, it lies wholly in that**plane**. Scholium . To discover whether a surface is**plane**, it is ne- cessary to apply ...Page 132

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**plane**MN , they will be par- allel ; for if they be not so , draw through the point D , a line parallel to AP , this par- allel will be perpendicular to the**plane**MN ; therefore M P A E D B through the same point D more than one ...Page 137

Adrien Marie Legendre Charles Davies. Let AP be perpendicular to the

Adrien Marie Legendre Charles Davies. Let AP be perpendicular to the

**plane**NM ; then will every**plane**passing through AP be perpendicu- lar to NM . Let BC be the intersection of the**planes**AB , MN ; in the**plane**MN , draw DE ...### 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