## Plane and Solid Geometry |

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### Common terms and phrases

ABCD altitude angle approaches axis base bisector bisects called centre chord circle circular circumference circumscribed coincide common cone construct corresponding 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 272 - 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.

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

Page 66 - 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. Given A ABC and A'B'C...

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 169 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.

Page 358 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 71 - The sum of the perpendiculars dropped from any point in the base of an isosceles triangle to the legs, is equal to the altitude upon one of the arms.

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 71 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.

Page 381 - Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle.