## Elements of Plane and Solid Geometry |

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### Common terms and phrases

A B C ABCDE altitude axis base bisect called centre chord circle circumference circumscribed coincide common cone construct contained 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 Geometry given greater Hence homologous sides inches included inscribed intersection joining less limit line drawn manner measured meet oblique opposite parallel parallelopiped pass perimeter perpendicular placed plane MN polyhedrons prism PROBLEM proportional PROPOSITION prove pyramid radii radius ratio rectangles regular polygon respectively right angles segment Show similar sphere spherical triangle square straight line surface symmetrical Take tangent THEOREM third triangle trihedral vertex vertices volume

### Popular passages

Page 132 - To describe an isosceles triangle having each of the angles at the base double of the third angle.

Page 140 - 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.

Page 206 - In any proportion, the product of the means is equal to the product of the extremes.

Page 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 353 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 179 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 192 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.

Page 150 - The areas of two triangles which have 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.