Essentials of Solid Geometry |
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Σελίδα 76
If the length of a rectangular parallelepiped is 22 in . , the width 8 in . , and the
height 6 in . , what is the area of the total ... that is , iron is 7.2 times as heavy as
water . $$ 113-115 PYRAMIDS 77 II . PYRAMIDS 113. Pyramid . 76 BOOK VII
PRISMS.
If the length of a rectangular parallelepiped is 22 in . , the width 8 in . , and the
height 6 in . , what is the area of the total ... that is , iron is 7.2 times as heavy as
water . $$ 113-115 PYRAMIDS 77 II . PYRAMIDS 113. Pyramid . 76 BOOK VII
PRISMS.
Σελίδα 77
Pyramids classified as to Bases . Pyramids are said to be triangular ,
quadrangular , and so on , according as their bases are triangles , quadrilaterals ,
and so on . A triangular pyramid is also called a tetrahedron . 115. Regular
Pyramid .
Pyramids classified as to Bases . Pyramids are said to be triangular ,
quadrangular , and so on , according as their bases are triangles , quadrilaterals ,
and so on . A triangular pyramid is also called a tetrahedron . 115. Regular
Pyramid .
Σελίδα 78
Properties of Regular Pyramids . The proofs of the following obvious properties of
regular pyramids depend upon the theorems indicated : 1. The lateral edges of a
regular pyramid are equal ( $ 43 ) . For they meet the base at equal distances ...
Properties of Regular Pyramids . The proofs of the following obvious properties of
regular pyramids depend upon the theorems indicated : 1. The lateral edges of a
regular pyramid are equal ( $ 43 ) . For they meet the base at equal distances ...
Σελίδα 79
Lateral Area of a Pyramid 118. Theorem . The lateral area of a regular pyramid is
half the product of the slant height and the perimeter of the base . D С B Given V -
ABCDE , a regular pyramid ; L , the lateral area ; 1 , the slant height ; and p ...
Lateral Area of a Pyramid 118. Theorem . The lateral area of a regular pyramid is
half the product of the slant height and the perimeter of the base . D С B Given V -
ABCDE , a regular pyramid ; L , the lateral area ; 1 , the slant height ; and p ...
Σελίδα 81
If two pyramids have equal altitudes and equivalent bases , sections made by
planes parallel to the bases at equal distances from the vertices are ... The
perimeter of the base of a regular pyramid is 40 mm . and the lateral area is 320
sq . mm .
If two pyramids have equal altitudes and equivalent bases , sections made by
planes parallel to the bases at equal distances from the vertices are ... The
perimeter of the base of a regular pyramid is 40 mm . and the lateral area is 320
sq . mm .
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altitude base called chord circle circumscribed common compute cone congruent Consider construct Corollary corresponding cube cubic cylinder determine diagonal diameter dihedral angles dimensions distance divided Draw drawn edges equal equilateral equivalent Exercises faces figure Find the area Find the volume follows formed formula four frustum geometry given given line greater Hence inches included inscribed intersection lateral area lateral edges lateral faces length locus lune measured meet oblique opposite parallel parallel planes pass perpendicular plane polar pole polyhedral angles polyhedron prism projection Proof proportional Proposition Prove pyramid radii radius regular pyramid respectively segment shown shows sides similar Similarly slant height solid sphere spherical spherical triangle square straight line student surface symmetric tangent tetrahedron Theorem third total surface triangle triangular trihedral unit vertex vertices volume zone
Δημοφιλή αποσπάσματα
Σελίδα 7 - The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it.
Σελίδα 40 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.
Σελίδα 176 - The areas of two triangles which have 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.
Σελίδα 10 - 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...
Σελίδα 15 - 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.
Σελίδα 77 - The height of a cone is the perpendicular distance from the vertex to the plane of the base.
Σελίδα 3 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Σελίδα 24 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Σελίδα 16 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 15 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.