## Plane and Solid Geometry |

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ABCD altitude angle approaches axis base bisector bisects called centre chord circle circular circumference circumscribed coincide common cone construct contains curve cylinder denote describe diagonals diameter difference dihedral angles distance divided draw drawn edges ellipse equal equidistant equilateral equivalent faces fall feet figure Find formed frustum given line given point greater half height Hence homologous inches included inscribed intersection isosceles joining lateral legs length less limit locus measured meet middle point opposite parallel parallelogram pass perimeter perpendicular plane polygon prism PROBLEM Proof proportional PROPOSITION prove pyramid quantities radii radius ratio rectangle regular polygon respectively right angle segments sides similar sphere spherical square straight line surface tangent THEOREM third touches triangle vertex vertices volume

### Popular passages

Page 94 - Any two sides of a triangle are together greater than the third side.

Page 274 - If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.

Page 50 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.

Page 42 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first 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 360 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 89 - The tangents to a circle drawn from an external point are equal, and make equal angles with the line joining the point to the centre.

Page 156 - 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 41 - If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle.

Page 191 - 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.

Page 166 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.