The Elements of Solid GeometryLeach, Shewell & Sanborn, 1893 - 95 σελίδες |
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Αποτελέσματα 1 - 5 από τα 23.
Σελίδα 21
... represent by U ; BK , BO , and BP , each represent- ing the linear unit ; then , AF : U ( BA ) ( BM ) ( BD ) : 1 x 1 x 1 ... ( 73 ) ( BA ) ( BM ) ( BD ) AF i.e. , U 1 x 1 x 1 AF But is the volume of AF ( 70 ) . U Hence , volume AF ...
... represent by U ; BK , BO , and BP , each represent- ing the linear unit ; then , AF : U ( BA ) ( BM ) ( BD ) : 1 x 1 x 1 ... ( 73 ) ( BA ) ( BM ) ( BD ) AF i.e. , U 1 x 1 x 1 AF But is the volume of AF ( 70 ) . U Hence , volume AF ...
Σελίδα 23
... Represent the common alti- tude of the three solids by a .. ( 25 ) ; then will the volume of AF be equal to ( a ) ( CF ) . For CF , JO , and NS are equivalent ( 363 ) ; then , multi- plying each of the above by a , we obtain ( a ) ( CF ) ...
... Represent the common alti- tude of the three solids by a .. ( 25 ) ; then will the volume of AF be equal to ( a ) ( CF ) . For CF , JO , and NS are equivalent ( 363 ) ; then , multi- plying each of the above by a , we obtain ( a ) ( CF ) ...
Σελίδα 24
... represent equivalence . PROPOSITION XVI . 80. THEOREM . A plane passed through the diagonally opposite edges of a parallelopiped divides it into two equiva- lent triangular prisms . D ' B ' H F D B Let the plane AC ' pass through the ...
... represent equivalence . PROPOSITION XVI . 80. THEOREM . A plane passed through the diagonally opposite edges of a parallelopiped divides it into two equiva- lent triangular prisms . D ' B ' H F D B Let the plane AC ' pass through the ...
Σελίδα 25
... 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 ' ) . . . ( 80 ) , ( 2 ) . And , area DB = ( 2 ) ( ABC ) ... ( 359 ) , ( 3 ) . But , vol . BD ...
... 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 ' ) . . . ( 80 ) , ( 2 ) . And , area DB = ( 2 ) ( ABC ) ... ( 359 ) , ( 3 ) . But , vol . BD ...
Σελίδα 27
... represented by B , a , and V , respectively ; then will V = ( B ) ( a ) . Through the edge AB and the vertices E , K , etc. , pass planes AF , AL , etc. , dividing the prism DG into triangular prisms . All the prisms thus constructed ...
... represented by B , a , and V , respectively ; then will V = ( B ) ( a ) . Through the edge AB and the vertices E , K , etc. , pass planes AF , AL , etc. , dividing the prism DG into triangular prisms . All the prisms thus constructed ...
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.