Elements of Geometry and Trigonometry: With Notes |
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Page 129
... prism is a solid bounded by several plane parallel- ograms , which are terminated at both ends by two plane poly- gons equal and parallel . K 60 A B d To construct this solid , let ABCDE be any polygon ; then if in a plane parallel to ...
... prism is a solid bounded by several plane parallel- ograms , which are terminated at both ends by two plane poly- gons equal and parallel . K 60 A B d To construct this solid , let ABCDE be any polygon ; then if in a plane parallel to ...
Page 130
... prism . V. The equal and parallel polygons ABCDE , FGHIK_are called the bases of the prism ; the plane parallelograms taken together constitute the lateral or convex surface of the prism ; the equal straight lines AF , BG , CH , & c ...
... prism . V. The equal and parallel polygons ABCDE , FGHIK_are called the bases of the prism ; the plane parallelograms taken together constitute the lateral or convex surface of the prism ; the equal straight lines AF , BG , CH , & c ...
Page 135
... prisms are equal when a solid angle in each is contained by three planes which are similarly placed , and ... prism abci . F 9 Id BRIGE BA For , lay the base ABCDE upon its equal abcde ; these two bases will coincide . But the ...
... prisms are equal when a solid angle in each is contained by three planes which are similarly placed , and ... prism abci . F 9 Id BRIGE BA For , lay the base ABCDE upon its equal abcde ; these two bases will coincide . But the ...
Page 136
... prisms , which have equal bases and equal al- titudes , are equal . For , since the side AB is equal to ab , and the altitude BG to bg , the rectangle ABGF will be equal to abgf ; so also will the rectangle BGHC be to bghc ; and thus ...
... prisms , which have equal bases and equal al- titudes , are equal . For , since the side AB is equal to ab , and the altitude BG to bg , the rectangle ABGF will be equal to abgf ; so also will the rectangle BGHC be to bghc ; and thus ...
Page 137
... prism ABDE / F / H ' such that it be symmetrical with the prism ABDEFH . According to what has been already proved ( 2. VI . ) , the plane ABF / E / must be equal to ABFE , and the plane ADH / E to E સ ADHE : but comparing the prism ...
... prism ABDE / F / H ' such that it be symmetrical with the prism ABDEFH . According to what has been already proved ( 2. VI . ) , the plane ABF / E / must be equal to ABFE , and the plane ADH / E to E સ ADHE : but comparing the prism ...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
Common terms and phrases
ACē adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cosē cosine cylinder demonstration determined diagonal diameter draw drawn equal angles equation equivalent faces figure formulas frustum greater homologous sides hypotenuse inclination inscribed intersection isosceles join less likewise manner measure multiplied number of sides opposite parallel parallelepipedon parallelogram perpendicular plane MN polyedron prism PROBLEM Prop PROPOSITION quadrilateral quantities radii radius ratio rectangle rectilineal triangle regular polygon right angles right-angled triangle SABC Scholium sector segment shew shewn side BC similar sinē sines solid angle sphere spherical polygon spherical triangle square straight line suppose tang tangent THEOREM third side three angles three plane angles triangle ABC triangular pyramids vertex vertices
Popular passages
Page 152 - AMB be a section, made by a plane, in the sphere, whose centre is C. From the...
Page 24 - THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 62 - Similar triangles are to each other as the squares of their homologous sides.
Page 211 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Page 187 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 140 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Page 150 - The radius of a sphere is a straight line, drawn from the centre to any point...
Page 168 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 135 - XII.) ; in like manner, the two solids AQ, AK, having the same base, AOLE, are to each other as their altitudes AD, A M.