Schultze and Sevenoak's Plane and Solid Geometry |
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Page 342
... parallelopiped is a prism whose bases are paral- lelograms ; hence one , all of whose faces are parallelograms . 569. DEF . A right parallelopiped is a parallelopiped whose lateral edges are perpendicular to the bases . Obviously a ...
... parallelopiped is a prism whose bases are paral- lelograms ; hence one , all of whose faces are parallelograms . 569. DEF . A right parallelopiped is a parallelopiped whose lateral edges are perpendicular to the bases . Obviously a ...
Page 347
... parallelopiped may be taken as bases . Ex . 1501. In a rectangular parallelopiped , lettered as the preceding figure , find the length of the diagonal AC ' , if AB = 9 , BC = 12 , CC ′ = 8 . Ex . 1502. In a right parallelopiped lettered ...
... parallelopiped may be taken as bases . Ex . 1501. In a rectangular parallelopiped , lettered as the preceding figure , find the length of the diagonal AC ' , if AB = 9 , BC = 12 , CC ′ = 8 . Ex . 1502. In a right parallelopiped lettered ...
Page 348
... parallelopipeds having equal ses are to each other as their altitudes . M B M ' D C A Given AB and CD , the altitudes of parallelopipeds м and м ' which have equal bases . To prove M : M ' AB ... parallelopiped are 348 SOLID GEOMETRY.
... parallelopipeds having equal ses are to each other as their altitudes . M B M ' D C A Given AB and CD , the altitudes of parallelopipeds м and м ' which have equal bases . To prove M : M ' AB ... parallelopiped are 348 SOLID GEOMETRY.
Page 349
... parallelopiped are the three edges that meet at the same vertex . 587. COR . The preceding theorem may be stated : Two rectangular parallelopipeds which have two dimensions in common are to each other as the third dimension ...
... parallelopiped are the three edges that meet at the same vertex . 587. COR . The preceding theorem may be stated : Two rectangular parallelopipeds which have two dimensions in common are to each other as the third dimension ...
Page 350
... parallelopipeds have equal altitudes and bases whose dimensions are 4 and 7 , and 5 and 9 respectively . Find the ratio of their volumes . Ex . 1506 . What is the ratio of the volumes of ... parallelopiped with base 350 SOLID GEOMETRY.
... parallelopipeds have equal altitudes and bases whose dimensions are 4 and 7 , and 5 and 9 respectively . Find the ratio of their volumes . Ex . 1506 . What is the ratio of the volumes of ... parallelopiped with base 350 SOLID GEOMETRY.
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Common terms and phrases
altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle LAOB lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism produced PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices
Popular passages
Page 82 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 222 - Two triangles having 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 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 208 - The area of a rectangle is equal to the product of its base and altitude.
Page 67 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.
Page 177 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 25 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 70 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 188 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 409 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...