Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα 287
... Lateral faces of a prism are all the faces except the bases . 508. DEF . The Lateral or Con- vex Surface of a prism is the sum of its lateral faces . 509. DEF . The Lateral edges of a prism are the intersections of its lateral faces ...
... Lateral faces of a prism are all the faces except the bases . 508. DEF . The Lateral or Con- vex Surface of a prism is the sum of its lateral faces . 509. DEF . The Lateral edges of a prism are the intersections of its lateral faces ...
Σελίδα 288
... 155 Q. E. D. 523. COROLLARY . Any section of a prism parallel to the base is equal to the base ; and all right sections of a prism are equal . PROPOSITION II . THEOREM . 524. The lateral area of 288 BOOK VII . GEOMETRY . -
... 155 Q. E. D. 523. COROLLARY . Any section of a prism parallel to the base is equal to the base ; and all right sections of a prism are equal . PROPOSITION II . THEOREM . 524. The lateral area of 288 BOOK VII . GEOMETRY . -
Σελίδα 291
... lateral edge of the oblique prism . F J ' A B F J H E D A C B Let A D ' be an oblique prism , and FI a right section . Complete the right prism FI ' , making its edges equal to those of the oblique prism . We are to prove oblique prism ...
... lateral edge of the oblique prism . F J ' A B F J H E D A C B Let A D ' be an oblique prism , and FI a right section . Complete the right prism FI ' , making its edges equal to those of the oblique prism . We are to prove oblique prism ...
Σελίδα 299
... lateral edge of the oblique prism ) . Through the edge IL make the right section ILPO , and complete the right parallelopiped IL PO - HG QR , and we have a rectangular parallelopiped equivalent to HIJ N - GLK M , $ 529 and hence ...
... lateral edge of the oblique prism ) . Through the edge IL make the right section ILPO , and complete the right parallelopiped IL PO - HG QR , and we have a rectangular parallelopiped equivalent to HIJ N - GLK M , $ 529 and hence ...
Σελίδα 300
... lateral edge A A ' , and the several diagonals of the base will divide the given prism into triangular prisms , which have for a common altitude the altitude of the prism . Hence , the volume of the entire prism is the product of the ...
... lateral edge A A ' , and the several diagonals of the base will divide the given prism into triangular prisms , which have for a common altitude the altitude of the prism . Hence , the volume of the entire prism is the product of the ...
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AABC ABCD altitude apothem arc A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide cone of revolution conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped pass perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section S-ABC SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume