## Elements of Plane and Solid Geometry |

### Other editions - View all

### Common terms and phrases

A B C D AABC AACB ABCD AC² altitude arc A B axis base and altitude BC² bisect centre chord circle circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B middle point number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle prove pyramid Q. E. D. PROPOSITION radii radius equal ratio rect rectangles regular polygon right angles right section SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume

### Popular passages

Page 114 - To describe an isosceles triangle having each of the angles at the base double of the third angle.

Page 40 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 187 - In any proportion, the product of the means is equal to the product of the extremes.

Page 174 - Two triangles having 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.

Page 163 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 187 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.

Page 145 - BC : B'C' : : CD : C' D' etc. § 278 (the homologous sides of similar polygons arc proportional). ••• AB + BC, etc. : A'B' + B'C', etc. : : AB : A'B', § 266 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent). That is P : P

Page 321 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 73 - A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A.

Page 106 - Two sides of a triangle, and the angle opposite one of them, being given, to construct the triangle. Let A and B be the given sides, and C the given angle.