Plane and Solid Geometry |
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Plane and Solid Geometry Virgil Snyder,C. A. B. 1863 Hart,J. H. B. 1861. editor Tanner No preview available - 2016 |
Common terms and phrases
ABCD adjacent angles altitude ARGUMENT REASONS bisector bisects chord circumference circumscribed Construct a triangle cube denoted diagonals diameter dihedral angles divided Draw drawn equilateral triangle equivalent exercise exterior angles face feet figure Find the area Find the locus Find the volume frustum geometry given circle given line given point given triangle HINT homologous hypotenuse inches inscribed isosceles triangle lateral area limit line joining measure measure-number mid-points number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular Plane Geometry plane MN polyhedron prism prismatoid Prop PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon rhombus right angles right circular cone right triangle segments similar slant height sphere spherical polygon spherical triangle square straight line student surface tangent THEOREM third side trapezoid triangle ABC trihedral vertex vertices
Popular passages
Page 85 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.
Page 445 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (g'). If A'B'C' is the polar triangle of ABC, that is, if A, -B, and С are the poles of the arcs a', b', and c', respectively, then, conversely, А B С is the polar triangle of A'B'C'.
Page 451 - The volumes of two spheres are to each other as the cubes of their radii or as the cubes of their diameters.
Page 66 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 61 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Page 169 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.
Page 345 - The lateral area of a prism is equal to the product of the perimeter of a right section of the prism by a lateral edge. Let AD...
Page 152 - ... ratios ; or which will leave the product of the means equal to the product of the extremes.
Page iii - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 343 - If two pyramids have equal altitudes and equivalent bases, sections made by planes parallel to the bases, and at equal distances from the vertices, are equivalent.