Elements of Geometry and Trigonometry: With Notes |
From inside the book
Results 6-10 of 32
Page 138
... NOPQR , STVXY are equal polygons . A N E B 10 Cor . Every section in a prism , if drawn parallel to the base , is also equal to that base . PROPOSITION VIII . THEOREM . The two symmetrical triangular prisms 138 GEOMETRY .
... NOPQR , STVXY are equal polygons . A N E B 10 Cor . Every section in a prism , if drawn parallel to the base , is also equal to that base . PROPOSITION VIII . THEOREM . The two symmetrical triangular prisms 138 GEOMETRY .
Page 139
... triangular prism ABDEFH will be equivalent to the right triangular prism aBdeFh . And since those two prisms have a part ABDheF in common , it will only be requisite to prove that the remaining parts , namely , the solids BaADd , FeEHh ...
... triangular prism ABDEFH will be equivalent to the right triangular prism aBdeFh . And since those two prisms have a part ABDheF in common , it will only be requisite to prove that the remaining parts , namely , the solids BaADd , FeEHh ...
Page 140
... triangular prism D AEIDHM is equal to the triangular prism BFKCGL . Since AE is parallel to BF , and HE to GF , the angle AEI - BFK , HEI = GFK , and HEA - GFB . Of these six angles the first three form the solid angle E , the last ...
... triangular prism D AEIDHM is equal to the triangular prism BFKCGL . Since AE is parallel to BF , and HE to GF , the angle AEI - BFK , HEI = GFK , and HEA - GFB . Of these six angles the first three form the solid angle E , the last ...
Page 146
... triangular prism is also equal to the product of its base ( half that of the paral- lelepipedon ) multiplied into its altitude . In the third place , any prism may be divided into as many triangular prisms of the same altitude , as ...
... triangular prism is also equal to the product of its base ( half that of the paral- lelepipedon ) multiplied into its altitude . In the third place , any prism may be divided into as many triangular prisms of the same altitude , as ...
Page 148
... triangular pyramids , having equivalent bases and equal altitudes , are equivalent , or equal in solidity . T 28 D G K N H E M m a Let SABC , sabc be those two pyramids , of which the two bases ABC , abc , conceived to be situated in ...
... triangular pyramids , having equivalent bases and equal altitudes , are equivalent , or equal in solidity . T 28 D G K N H E M m a Let SABC , sabc be those two pyramids , of which the two bases ABC , abc , conceived to be situated in ...
Other editions - View all
Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
Common terms and phrases
AC² adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cos² 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 sin² 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.