The Elements of Solid Geometry |
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Results 1-5 of 13
Page 12
... equal to all the parts of the other , each to each , are said to be mutually equal in all their parts , or , with re- spect to all their parts . B C A FIG . 1 . B ' 40. If the equal parts of the one are arranged in the same order as the ...
... equal to all the parts of the other , each to each , are said to be mutually equal in all their parts , or , with re- spect to all their parts . B C A FIG . 1 . B ' 40. If the equal parts of the one are arranged in the same order as the ...
Page 15
... equal to the three face angles of the other , each to each , the two triedral angles are mutually equal in all their parts . 444 In the triedral angles o and o ' , let the face angles aob , boc , coa , be equal to the face angles a'o'b ...
... equal to the three face angles of the other , each to each , the two triedral angles are mutually equal in all their parts . 444 In the triedral angles o and o ' , let the face angles aob , boc , coa , be equal to the face angles a'o'b ...
Page 16
... equal to the corresponding diedral angles of o ' , each to each . Q. E. D. 47 . SCHOLIUM . The triedral angles o and ... mutually equal in all their parts . Prove the above theorem , using the diagram and method of ( 46 ) . 49. THEOREM ...
... equal to the corresponding diedral angles of o ' , each to each . Q. E. D. 47 . SCHOLIUM . The triedral angles o and ... mutually equal in all their parts . Prove the above theorem , using the diagram and method of ( 46 ) . 49. THEOREM ...
Page 25
... mutually equal in all their parts ; however , not being superposable , they are not equal solids but symmetrical ( 41 and 42 ) . 82. COROLLARY . The volume of any triangular prism is equal to the product of its base and altitude . Let a ...
... mutually equal in all their parts ; however , not being superposable , they are not equal solids but symmetrical ( 41 and 42 ) . 82. COROLLARY . The volume of any triangular prism is equal to the product of its base and altitude . Let a ...
Page 34
... equals ABC ... ( 19 ) . And in like manner we can prove that the section and the base have corresponding angles equal ... mutually equiangular , as we have shown ; hence they are similar . Q. E. D. 116. SCHOLIUM : The lateral edges and the ...
... equals ABC ... ( 19 ) . And in like manner we can prove that the section and the base have corresponding angles equal ... mutually equiangular , as we have shown ; hence they are similar . Q. E. D. 116. SCHOLIUM : The lateral edges and the ...
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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.