The Elements of Solid GeometryLeach, Shewell & Sanborn, 1893 - 95 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 30.
Σελίδα 19
... base are to each other as their altitudes . G F E D L H с K b 82 a C A B Let the right prisms AF and AL have the common base AC , and the altitudes CF and CL respectively ; then will AF : AL :: CF : CL . Let us suppose that CF and CL ...
... base are to each other as their altitudes . G F E D L H с K b 82 a C A B Let the right prisms AF and AL have the common base AC , and the altitudes CF and CL respectively ; then will AF : AL :: CF : CL . Let us suppose that CF and CL ...
Σελίδα 21
... base we may write , AF : AL :: BD : BP ... ( 71 ) . Regarding AP as a common ... volume of a cuboid is equal to the product of its three dimensions . For , let KN ... altitude . PROPOSITION XV . 76. THEOREM . An oblique parallelopiped is ...
... base we may write , AF : AL :: BD : BP ... ( 71 ) . Regarding AP as a common ... volume of a cuboid is equal to the product of its three dimensions . For , let KN ... altitude . PROPOSITION XV . 76. THEOREM . An oblique parallelopiped is ...
Σελίδα 22
... base and altitude are equal respectively to a right section and a lateral edge of the oblique parallelopiped ... base , LO is a right parallelopiped whose base JQ equals a right section of the oblique parallelopiped AF ; and the altitude ...
... base and altitude are equal respectively to a right section and a lateral edge of the oblique parallelopiped ... base , LO is a right parallelopiped whose base JQ equals a right section of the oblique parallelopiped AF ; and the altitude ...
Σελίδα 23
... volume of any parallelopiped is equal to the product of its base and altitude . Regard CF , JO , and NS , as the bases of the parallelo- pipeds to which they belong . Represent the common alti- tude of the three solids by a .. ( 25 ) ...
... volume of any parallelopiped is equal to the product of its base and altitude . Regard CF , JO , and NS , as the bases of the parallelo- pipeds to which they belong . Represent the common alti- tude of the three solids by a .. ( 25 ) ...
Σελίδα 25
... volume of any triangular prism is equal to the product of its base and altitude . Let a represent the altitude of ABC - B ' ; then will the volume of ABC - B ' be equal to ( ABC ) ( a ) . ( 1 ) . For , vol . BD ' = ( 2 ) ( ABC - B ...
... volume of any triangular prism is equal to the product of its base and altitude . Let a represent the altitude of ABC - B ' ; then will the volume of ABC - B ' be equal to ( ABC ) ( a ) . ( 1 ) . For , vol . BD ' = ( 2 ) ( ABC - B ...
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.