Elements of Geometry |
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Page 124
... pyramid is a solid formed by several triangular planes proceeding from the same point and terminating in the sides of a Fig . 196. polygon ABCDE ( fig . 196 ) . Fig . 202 . The polygon ABCDE is called the base of the pyramid , the point ...
... pyramid is a solid formed by several triangular planes proceeding from the same point and terminating in the sides of a Fig . 196. polygon ABCDE ( fig . 196 ) . Fig . 202 . The polygon ABCDE is called the base of the pyramid , the point ...
Page 125
... triangular pyramids , which have for their common base the above triangle ; and these several pyramids will determine . the positions of the several solid angles of the polyedron with respect to the base . This being supposed ; Two ...
... triangular pyramids , which have for their common base the above triangle ; and these several pyramids will determine . the positions of the several solid angles of the polyedron with respect to the base . This being supposed ; Two ...
Page 140
... pyramids that have a common vertex , and whose altitudes are the same , or ... triangular pyramid , of which S is the vertex and ABC the base ; if the ... pyramids S - DEF , E - GBI . Demonstration . It follows from the construction ...
... pyramids that have a common vertex , and whose altitudes are the same , or ... triangular pyramid , of which S is the vertex and ABC the base ; if the ... pyramids S - DEF , E - GBI . Demonstration . It follows from the construction ...
Page 141
Adrien Marie Legendre. also a prism . Now we say that these two triangular prisms ... pyramids S - DEF , E - GBI ; now we say that these two pyramids are equal to ... triangular pyramid is greater than the fourth part of the product of its ...
Adrien Marie Legendre. also a prism . Now we say that these two triangular prisms ... pyramids S - DEF , E - GBI ; now we say that these two pyramids are equal to ... triangular pyramid is greater than the fourth part of the product of its ...
Page 142
... pyramid D - AGH equal to the pyramid S - DEF ; for the base DEF may be placed upon ... triangular pyramid is less than half of the product of its base by its ... pyramids S - DEF , E - GBI . Now the solidity of the prism AGH - FDE is DEF ...
... pyramid D - AGH equal to the pyramid S - DEF ; for the base DEF may be placed upon ... triangular pyramid is less than half of the product of its base by its ... pyramids S - DEF , E - GBI . Now the solidity of the prism AGH - FDE is DEF ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence