The Elements of Solid GeometryLeach, Shewell & Sanborn, 1893 - 95 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 26
... inscribed prism , when the number of lateral faces of the prism is increased indefinitely . Thus if an inscribed prism of four lateral faces be changed to an inscribed prism of eight lateral faces , and then the prism of eight faces be ...
... inscribed prism , when the number of lateral faces of the prism is increased indefinitely . Thus if an inscribed prism of four lateral faces be changed to an inscribed prism of eight lateral faces , and then the prism of eight faces be ...
Σελίδα 28
... inscribed prism ; and accordingly the theorem of ( 90 ) must be true alike for the prism and for the cylinder ( 88 ) . 92. COROLLARY 2. Prisms are to each other as the pro- ducts of their bases and altitudes . When the altitudes are ...
... inscribed prism ; and accordingly the theorem of ( 90 ) must be true alike for the prism and for the cylinder ( 88 ) . 92. COROLLARY 2. Prisms are to each other as the pro- ducts of their bases and altitudes . When the altitudes are ...
Σελίδα 29
... the limiting case of the inscribed prism ( 88 ) ; and , accordingly , theorem ( 94 ) must be true alike for the prism and for the cylinder . 96. COROLLARY 2. The lateral surface of a right prism SOLIDS : PRISMS AND CYLINDERS . 29.
... the limiting case of the inscribed prism ( 88 ) ; and , accordingly , theorem ( 94 ) must be true alike for the prism and for the cylinder . 96. COROLLARY 2. The lateral surface of a right prism SOLIDS : PRISMS AND CYLINDERS . 29.
Σελίδα 39
... inscribed in a cone when the base of the pyramid is inscribed in the base of the cone and the two solids have a common vertex . The lateral edges of the pyramid are elements of the sur- face of the cone . 127. A cone may be regarded as ...
... inscribed in a cone when the base of the pyramid is inscribed in the base of the cone and the two solids have a common vertex . The lateral edges of the pyramid are elements of the sur- face of the cone . 127. A cone may be regarded as ...
Σελίδα 40
... any cone is equal to one - third the product of the base and altitude . For , in any cone A ' - BCDEF inscribe a pyramid A ' - BCDEF . By indefinitely increasing the number of its lateral faces the 40 THE ELEMENTS OF SOLID GEOMETRY .
... any cone is equal to one - third the product of the base and altitude . For , in any cone A ' - BCDEF inscribe a pyramid A ' - BCDEF . By indefinitely increasing the number of its lateral faces the 40 THE ELEMENTS OF SOLID GEOMETRY .
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC and DEF ABC-B altitude are equal axis base and altitude bases are equal bisecting centre circle circumference coincide common altitude common vertex conical surface COROLLARY cube cuboid DEFINITIONS diameter dicular diedral angle EDC-O equal with respect equivalent faces is called feet Find the volume frustum Hence inscribed prism intersection lateral edges lateral faces lateral surface Let the line line BA lune MN and PQ mutually equal O-ABCD oblique parallelopiped parallel planes parallelogram pass perimeter perpen perpendicular to MN plane angle plane MN plane PQ polar triangle polyedral angle prisms whose bases radii radius regular polyedrons regular polygon right angles right circular cone right prism right section SCHOLIUM sides slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tetraedron THEOREM triangles ABC triangular prism triangular pyramids triedral
Δημοφιλή αποσπάσματα
Σελίδα 48 - Assuming that 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 46 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Σελίδα 4 - 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 49 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Σελίδα 94 - Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.
Σελίδα 46 - The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Σελίδα 6 - Theorem: If a straight line is perpendicular to one of two parallel planes, it is perpendicular, also, to the other plane.
Σελίδα 9 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Σελίδα 56 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.