# Elements of Geometry, After Legendre, with a Selection of Geometrical Exercises, and Hints for the Solution of the Same

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### Contents

 INTRODUCTION 7 PLANE GEOMETRY 19 BOOK II 54 BOOK III 97 BOOK IV 152 BOOK V 180
 BOOK VI 216 APPENDIX To Book VI The Regular Polyedrons 249 BOOK VII 255 BOOK VIII 287 HINTS TO SOLUTIONS OF EXERCISES 321

### Popular passages

Page 253 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Page 49 - 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 46 INTERCEPTS BY PARALLEL LINES.
Page 20 - Parallel straight lines are such as are in the same plane, and which, being produced ever so far both ways, do not meet.
Page 54 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 45 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 67 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 105 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 298 - The volume of a frustum of a cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the bases of the frustum.
Page 274 - Scholium. The spherical ungula, bounded by the planes AMB, ANB, is to the whole solid sphere, as the angle A is to four right angles. For, the lunes being equal, the spherical ungulas will also be equal ; hence two spherical ungulas are to each other, as the angles formed by the planes which bound them. PROPOSITION XVIII.
Page 9 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.