## Plane and Solid Geometry |

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### Common terms and phrases

ABCD ACē adjacent angles altitude angle formed angles are equal apothem base and altitude bisector bisects centre chord circumference circumscribed cone of revolution construct a square cylinder diagonals diameter diedral angles distance divided draw equal angles equally distant equilateral triangle equivalent EXERCISES exterior angle faces Find the area four right angles frustum given angle given circle given line given point given straight line given triangle hence hypotenuse intersection isosceles triangle lateral area lateral edges line drawn lune mean proportional middle point number of sides opposite sides parallel planes parallelogram perimeter perpendicular polyedral angle polyedron prove pyramid Q.E.D. PROPOSITION quadrilateral radii rectangle rectangular parallelopiped regular hexagon regular inscribed regular polygon rhombus right triangle SCHOLIUM segments semiperimeter similar slant height sphere spherical polygon spherical triangle surface tangent THEOREM trapezoid triangle ABC triangles are equal vertex vertical angle volume

### Popular passages

Page 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.

Page 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.

Page 190 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 173 - The volume of a triangular prism is equal to the product of its base by its altitude. A~ Let V denote the volume, B the base, and H the altitude of the triangular prism CEA-E'.

Page 108 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 80 - In any proportion the terms are in proportion by Composition; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.

Page 81 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.

Page 30 - In an isosceles triangle, the angles opposite the equal sides are equal.

Page 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.