Elements of Geometry |
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Page iv
... pyramid by M. Queret of St. Malo , received too late for insertion in its proper place , is subjoined at the end . Cambridge , June 4 , 1825 . ། PREFACE . THE method of the ancients is very generally iv Advertisement .
... pyramid by M. Queret of St. Malo , received too late for insertion in its proper place , is subjoined at the end . Cambridge , June 4 , 1825 . ། PREFACE . THE method of the ancients is very generally iv Advertisement .
Page 124
... pyramid , the point S its vertex , and the triangles ASB , BSC , & c . , compose the lateral or convex surface of the pyramid . 376. The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base ...
... pyramid , the point S its vertex , and the triangles ASB , BSC , & c . , compose the lateral or convex surface of the pyramid . 376. The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base ...
Page 125
... 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 polyedrons are ...
... 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 polyedrons are ...
Page 139
... pyramid S - ABCDE ( fig . 214 ) is cut by a plane a b d , Fig , 214 , parallel to the base , 1. The sides SA , SB , SC , ..... and the altitude SO , will be divided proportionally in a , b , c , ..... and o ; 2. The section abcde will ...
... pyramid S - ABCDE ( fig . 214 ) is cut by a plane a b d , Fig , 214 , parallel to the base , 1. The sides SA , SB , SC , ..... and the altitude SO , will be divided proportionally in a , b , c , ..... and o ; 2. The section abcde will ...
Page 140
... pyramid S - ABC may be considered as com- posed of two prisms AGH - FDE , EGI - CFH , equivalent to each other , and two equal pyramids S - DEF , E - GBI . Demonstration . It follows from the construction , that ED is parallel to BA ...
... pyramid S - ABC may be considered as com- posed of two prisms AGH - FDE , EGI - CFH , equivalent to each other , and two equal pyramids S - DEF , E - GBI . Demonstration . It follows from the construction , that ED is parallel to BA ...
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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