The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 289
... frustum of a pyramid is a trun- cated pyramid whose bases are parallel . The altitude is the perpendicular distance between the planes of the bases . EXERCISES . 15. Find the length of the diagonal of a rectangular parallelopiped whose ...
... frustum of a pyramid is a trun- cated pyramid whose bases are parallel . The altitude is the perpendicular distance between the planes of the bases . EXERCISES . 15. Find the length of the diagonal of a rectangular parallelopiped whose ...
Σελίδα 290
... frustum of a regular pyramid are equal trapezoids . A B ' D ' B Given AC ' a frustum of regular pyramid O - ABCDE . To Prove faces AB ' and BC ' equal trapezoids . Proof . We have AOAB = A OBC . ( § 507 , II ) We may then apply AOAB to ...
... frustum of a regular pyramid are equal trapezoids . A B ' D ' B Given AC ' a frustum of regular pyramid O - ABCDE . To Prove faces AB ' and BC ' equal trapezoids . Proof . We have AOAB = A OBC . ( § 507 , II ) We may then apply AOAB to ...
Σελίδα 291
... frustum of a regular pyramid are equal . 511. Def . The slant height of a frustum of a regular pyramid is the altitude of any lateral face . PROP . XVI . THEOREM . 512. The lateral area of a regular pyramid is equal to the perimeter of ...
... frustum of a regular pyramid are equal . 511. Def . The slant height of a frustum of a regular pyramid is the altitude of any lateral face . PROP . XVI . THEOREM . 512. The lateral area of a regular pyramid is equal to the perimeter of ...
Σελίδα 299
... frustum of any pyramid O - AC . To Prove vol . AC ' = ( B + b + √B × b ) × } H. Proof . Draw altitude OP , cutting A'C ' at Q. Now , vol . AC ' = vol . O - AC — vol . O - A'C ' - = B × } ( H + OQ ) − b × { OQ - = 1 · B × } H + B ...
... frustum of any pyramid O - AC . To Prove vol . AC ' = ( B + b + √B × b ) × } H. Proof . Draw altitude OP , cutting A'C ' at Q. Now , vol . AC ' = vol . O - AC — vol . O - A'C ' - = B × } ( H + OQ ) − b × { OQ - = 1 · B × } H + B ...
Σελίδα 301
... frustum of a regular quadrangular pyramid , the sides of whose bases are 17 and 7 , respectively , and whose altitude is 12 . Let ABB'A ' be a lateral face of the frustum , and O and O ' the centres of the bases ; draw lines OCLAB , O'C ...
... frustum of a regular quadrangular pyramid , the sides of whose bases are 17 and 7 , respectively , and whose altitude is 12 . Let ABB'A ' be a lateral face of the frustum , and O and O ' the centres of the bases ; draw lines OCLAB , O'C ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit axis base and altitude BC² bisector bisects centre chord circle circumference circumscribed coincide cone of revolution Converse of Prop diagonals diameter diedral angle distance Draw line equal respectively equally distant equilateral equivalent exterior angle faces Find the area frustum Given line given point Hence homologous homologous sides hypotenuse intersecting isosceles triangle lateral area lateral edges line drawn line joining middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedral polyedron prism Prove pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right triangle segment side BC similar slant height spherical polygon spherical triangle square tangent tetraedron THEOREM trapezoid triangle ABC triangular prism triedral vertex vertices volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 58 - 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.
Σελίδα 322 - A right circular cylinder may be generated by the revolution of a rectangle about one of its sides as an axis.
Σελίδα 371 - A zone is a portion of the surface of a sphere included between two parallel planes.
Σελίδα 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Σελίδα 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Σελίδα 151 - If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
Σελίδα 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 205 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Σελίδα 73 - A chord is a straight line joining the extremities of an arc ; as AB.
Σελίδα 202 - The circumferences of two circles are to each other as their radii. Given C and C" the circumferences of two © whose radii are R and R', respectively.