## Elements of Geometry |

### Contents

3 | |

15 | |

32 | |

60 | |

66 | |

81 | |

85 | |

106 | |

287 | |

288 | |

308 | |

326 | |

335 | |

345 | |

351 | |

353 | |

108 | |

154 | |

160 | |

170 | |

180 | |

193 | |

196 | |

202 | |

229 | |

235 | |

246 | |

257 | |

270 | |

282 | |

360 | |

366 | |

378 | |

390 | |

413 | |

456 | |

493 | |

500 | |

508 | |

515 | |

523 | |

529 | |

538 | |

### Other editions - View all

### Common terms and phrases

ABCD allel altitude angles are equal apothem base and altitude bisecting bisector centre chord circumference circumscribed coincide cone conical surface construct cylinder Def.-The Defs.-A diagonals diameter diedral angles distance divided draw drawn equilateral triangle equivalent Exercise.-The face angles figure Find the area frustum given line given point given straight line GIVEN TO PROVE given triangle Hence homologous homologous sides hypotenuse intersection lateral area lateral edges lateral faces locus measured by arc middle points number of sides parallel planes parallelogram parallelopiped pass a plane perimeter PLANE GEOMETRY plane MN polyedral angle polyedron prismatic surface Q. E. D. PROPOSITION quadrilateral radii radius ratio of similitude rectangle regular polygon right angles right triangle segment similar slant height sphere spherical polygon square surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume

### Popular passages

Page 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.

Page 5 - If of three quantities the first is greater than the second and the second greater than the third, then the first is greater than the third.

Page 434 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.

Page 393 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 185 - To construct a square equivalent to the sum of any number of given squares.

Page 390 - 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 67 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 70 - The three medians of any triangle intersect in a common point which is two-thirds of the distance from each vertex to the middle of the opposite side.

Page 476 - The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides.

Page 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.