The Elements of Solid GeometryLeach, Shewell & Sanborn, 1893 - 95 σελίδες |
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Αποτελέσματα 1 - 5 από τα 9.
Σελίδα 10
... Construct a second plane angle C'A'B ' , as before ; then CAB is equal to C'A'B ' . . . ( 19 ) . PROPOSITION IX . 31. THEOREM . If a line is perpendicular to a plane , any plane passing through the line is perpendicular to the plane ...
... Construct a second plane angle C'A'B ' , as before ; then CAB is equal to C'A'B ' . . . ( 19 ) . PROPOSITION IX . 31. THEOREM . If a line is perpendicular to a plane , any plane passing through the line is perpendicular to the plane ...
Σελίδα 20
... Construct a right prism ABC - c . Now , because CF and Ce are commensurable , then , AF : Ac :: CF : Cc ; and we have supposed AF : AL :: CF : Ca ; combine these proportions , Ac : AL :: Cc : Cx . Now , Ac is less than AL , being a part ...
... Construct a right prism ABC - c . Now , because CF and Ce are commensurable , then , AF : Ac :: CF : Cc ; and we have supposed AF : AL :: CF : Ca ; combine these proportions , Ac : AL :: Cc : Cx . Now , Ac is less than AL , being a part ...
Σελίδα 27
... constructed have the common altitude a . From ( 82 ) we may write the following equations : vol . ( DFB - C ) = ( DFB ) ( a ) . vol . ( FBL - A = ( FBL ) ( a ) . vol . ( BLH - K ) = ( BLH ) ( a ) . By axiom the sum of the first members ...
... constructed have the common altitude a . From ( 82 ) we may write the following equations : vol . ( DFB - C ) = ( DFB ) ( a ) . vol . ( FBL - A = ( FBL ) ( a ) . vol . ( BLH - K ) = ( BLH ) ( a ) . By axiom the sum of the first members ...
Σελίδα 36
... construct the prisms abc - d , def - g , and ghk - o ; and in pyramid o ' construct the prisms d'e'f ' - a ' and g'h'k ' - d ' . ( a ) . It is evident that the difference between the sum of the prisms of o and the sum of the prisms in o ...
... construct the prisms abc - d , def - g , and ghk - o ; and in pyramid o ' construct the prisms d'e'f ' - a ' and g'h'k ' - d ' . ( a ) . It is evident that the difference between the sum of the prisms of o and the sum of the prisms in o ...
Σελίδα 38
... constructed with the same base and altitude as the prism , has a volume one - third as great . Hence , the volume of a triangular pyramid is equal to one - third the product of its base and altitude . B DEFINITIONS . 122. A conical ...
... constructed with the same base and altitude as the prism , has a volume one - third as great . Hence , the volume of a triangular pyramid is equal to one - third the product of its base and altitude . B DEFINITIONS . 122. A conical ...
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.