## Elements of Plane and Solid Geometry |

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### Common terms and phrases

A B C ABCD altitude axis base bisect called centre chord circle circumference coincide common cone Cons construct COROLLARY corresponding cylinder denote describe diagonals diameter difference dihedral angle direction distance divided draw edges element equal equal respectively equally distant equilateral equivalent extremities faces fall figure foot formed four frustum given given point greater Hence homologous sides hypotenuse included inscribed intersection joining less limit line drawn manner measured meet middle point oblique opposite parallel parallelopiped pass perimeter perpendicular plane plane MN polyhedrons prism PROBLEM projection proportional PROPOSITION prove pyramid radii radius ratio rectangles regular polygon respectively right angles segment Show similar sphere square straight line surface symmetrical Take tangent THEOREM third triangle trihedral vertex vertices volume

### Popular passages

Page 120 - To describe an isosceles triangle having each of the angles at the base double of the third angle.

Page 42 - 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 191 - In any proportion, the product of the means is equal to the product of the extremes.

Page 178 - 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 165 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 191 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.

Page 151 - 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 325 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 75 - 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 110 - 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.