## Elements of Geometry |

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### Common terms and phrases

ABCD adjacent angles angles are equal apothem base and altitude bisector bisects centre chord circumference circumscribed coincide cone of revolution conical surface construct Def.-The Defs.-A diagonals diameter diedral angles distance divided draw equivalent Exercise.-The exterior angle figure frustum given line given point given straight line GIVEN TO PROVE Hence Hint.-Apply homologous homologous sides hypotenuse included angle intersection isosceles triangle lateral area lateral edges lateral faces locus middle point number of sides parallel planes parallelogram parallelopiped perimeter perpendicular plane MN polyedral angles polyedron prismatic surface PROPOSITION XI Q. E. D. PROPOSITION quadrilateral radii radius ratio of similitude rectangle regular inscribed regular polygon respectively equal right angles right section right triangle segment similar slant height sphere spherical polygon spherical triangle surface symmetrical tangent THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume

### Popular passages

Page 242 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.

Page 12 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.

Page 73 - A line perpendicular to a radius at its extremity is tangent to the circle.

Page 253 - The volume of a triangular pyramid is equal to one-third the product of its base and altitude.

Page 238 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.

Page 177 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.

Page 287 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...

Page 126 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 61 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.

Page 256 - The areas of two triangles which have 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.