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

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ABCD adjacent altitude apply base Book called centre chord circle circumference circumscribed common cone Construct contained Conversely convex surface cylinder demonstration described determine diagonals diameter diedral difference distance divided draw drawn edges equal equilateral equivalent Exercises exterior extremities faces feet figure Find follows formed four Geometric give given line given point greater half Hence homologous inscribed intersection join less limit locus manner mean measure meet middle point multiplied opposite parallel parallelogram parallelopipedon pass perimeter perpendicular placed plane polyedron polygon prism problem Prop proportional PROPOSITION pyramid radii radius ratio reason rectangle regular respectively right angles SCHOLIUM segment sides similar solid angle solution sphere spherical square straight line Suppose surface tangent tetraedron THEOREM third triangle triangle ABC triedral vertex vertices volume whole

### Popular passages

Page 255 - 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 107 - 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 300 - 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 276 - 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.