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### Innhold

 INTRODUCTION 3 PARALLEL LINES AND SYMMETRICAL FIGURES 15 TRIANGLES 32 PARALLELOGRAMS 60 PROBLEMS 66 BOOK II 73 MEASUREMENT 87 PROBLEMS OF DEMONSTRATION 106
 REGULAR POLYEDRONS 335 GENERAL THEOREMS ON POLYEDRONS 345 PROBLEMS FOR COMPUTATION 351 THE CONE 360 THE SPHERE 366 SPHERICAL ANGLES 378 POLAR TRIANGLES 390 MEASUREMENT OF SPHERICAL FIGURES 398

 PROBLEMS OF DEMONSTRATION 154 PROBLEMS FOR COMPUTATION 160 BOOK IV 170 PROBLEMS OF DEMONSTRATION 193 PROBLEMS OF CONSTRUCTION 196 BOOK V 202 PROBLEMS OF DEMONSTRATION 229 BOOK VI 235 PARALLEL LINES AND PLANES 246 DIEDRAL ANGLES AND PROJECTIONS 257 POLYEDRAL ANGLES 270 PROJECTIONS 282 PRISMS AND PARALLELOPIPEDS 288 PYRAMIDS 308 SIMILAR POLYEDRONS 326
 PROBLEMS OF DEMONSTRATION 408 THE CONE 420 THE SPHERE 430 PROBLEMS FOR COMPUTATION 445 MAXIMA AND MINIMA OF PLANE FIGURES 456 EXERCISES 465 BOOK IV 472 MAXIMA AND MINIMA 491 SOME PROPERTIES OF CIRCLES 497 RADICAL AXIS AND COAXAL CIRCLES 504 POLES AND POLARS 511 PERSPECTIVE 515 INVOLUTION 523 TABLE OF WEIGHTS AND MEASURES 533 RULES OF MENSURATION 539

### Populćre avsnitt

Side 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.
Side 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.
Side 434 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
Side 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...
Side 185 - To construct a square equivalent to the sum of any number of given squares.
Side 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...
Side 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.
Side 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.
Side 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.
Side 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.