The Elements of Solid Geometry |
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Page 17
... Prisms are named from their bases ; if the bases are pentagons , as in the figure of ( 52 ) , the prism is called a pentangular prism . In like manner we have quadrangular prisms , triangular prisms , etc. 56. A right prism is one whose ...
... Prisms are named from their bases ; if the bases are pentagons , as in the figure of ( 52 ) , the prism is called a pentangular prism . In like manner we have quadrangular prisms , triangular prisms , etc. 56. A right prism is one whose ...
Page 24
... triangular prisms . D ' B ' H F D B Let the plane AC ' pass through the diagonally opposite edges AA ' and CC ' of ... prism ABC - 24 THE ELEMENTS OF SOLID GEOMETRY .
... triangular prisms . D ' B ' H F D B Let the plane AC ' pass through the diagonally opposite edges AA ' and CC ' of ... prism ABC - 24 THE ELEMENTS OF SOLID GEOMETRY .
Page 25
William C. Bartol. ume ( 65 ) . Hence the prism ABC - B ' is equivalent to the prism ADC - D ' . Q. E. D. 81 ... triangular prism is equal to the product of its base and altitude . Let a represent the altitude of ABC - B ' ; then ...
William C. Bartol. ume ( 65 ) . Hence the prism ABC - B ' is equivalent to the prism ADC - D ' . Q. E. D. 81 ... triangular prism is equal to the product of its base and altitude . Let a represent the altitude of ABC - B ' ; then ...
Page 27
... prism DG into triangular prisms . All the prisms thus 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 ) ...
... prism DG into triangular prisms . All the prisms thus 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 ) ...
Page 36
William C. Bartol. PROPOSITION XXI . 119. THEOREM . Triangular pyramids ... prisms abc - d , def - g , and ghk - o ; and in pyramid o ' construct the prisms d ... prism constructed on abc as a base . By increasing the number of equal parts ...
William C. Bartol. PROPOSITION XXI . 119. THEOREM . Triangular pyramids ... prisms abc - d , def - g , and ghk - o ; and in pyramid o ' construct the prisms d ... prism constructed on abc as a base . By increasing the number of equal parts ...
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Common terms and phrases
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
Popular passages
Page 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...
Page 46 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 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.
Page 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.
Page 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'.
Page 46 - The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Page 6 - Theorem: If a straight line is perpendicular to one of two parallel planes, it is perpendicular, also, to the other plane.
Page 9 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 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.