Plane and Solid Geometry |
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Common terms and phrases
ABCD altitude axis bisector bisects called centre chord circumference circumscribed coincide construct curve cylinder denote diagonals diameter dihedral angles directrix distance divided Draw ellipse equiangular equidistant equilateral triangle equivalent feet Find the area Find the locus frustum given circle given line given point given straight line greater Hence homologous hyperbola hypotenuse inches inscribed intersection isosceles triangle lateral area lateral edges latus rectum limit middle point number of sides opposite parabola parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedron prism prismatoid Proof proportional prove Q. E. D. PROPOSITION radii radius ratio rectangle regular polygon respectively rhombus right angle right circular right triangle segments similar slant height sphere spherical triangle square surface tangent tetrahedron THEOREM trapezoid triangle ABC triangle is equal trihedral vertex vertices
Popular passages
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.
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 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 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 383 - 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.