Elements of Geometry |
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Page 145
... frustum , and whose bases are the inferior base of the frustum , its superior base , and a mean proportional between these bases . Demonstration . Let S - ABCDE ( fig . 217 ) be a pyramid cut Fig . 217 . by the plane abd parallel to the ...
... frustum , and whose bases are the inferior base of the frustum , its superior base , and a mean proportional between these bases . Demonstration . Let S - ABCDE ( fig . 217 ) be a pyramid cut Fig . 217 . by the plane abd parallel to the ...
Page 146
... frustum of a triangular pyramid . Let FGH - hfg be the frustum of a triangular pyramid ; through the points F , g , H , suppose a plane FgH to pass cutting off from the frustum the triangular pyramid g - FGH . This pyramid has for its ...
... frustum of a triangular pyramid . Let FGH - hfg be the frustum of a triangular pyramid ; through the points F , g , H , suppose a plane FgH to pass cutting off from the frustum the triangular pyramid g - FGH . This pyramid has for its ...
Page 147
... frustum of a triangular pyramid is equal to three pyramids , which have for their common altitude the altitude of the frustum , and whose bases are the inferior base of the frustum , its superior base , and a mean proportional between ...
... frustum of a triangular pyramid is equal to three pyramids , which have for their common altitude the altitude of the frustum , and whose bases are the inferior base of the frustum , its superior base , and a mean proportional between ...
Page 154
... frustum of a pyramid and let A , B , be the bases ; then AB will be the mean proportional between them , and the solidity of the frustum will be } H × ( A + B + √лB ) • Let B be the base of a truncated triangular prism , H , H ' , H ...
... frustum of a pyramid and let A , B , be the bases ; then AB will be the mean proportional between them , and the solidity of the frustum will be } H × ( A + B + √лB ) • Let B be the base of a truncated triangular prism , H , H ' , H ...
Page 175
... frustum of a cone . It may be conceived to be generated by the revolution of the trapezoid ABHG , of which the angles A and G are right angles , about the side AG . The fixed line AG is called the axis or altitude of the frustum , the ...
... frustum of a cone . It may be conceived to be generated by the revolution of the trapezoid ABHG , of which the angles A and G are right angles , about the side AG . The fixed line AG is called the axis or altitude of the frustum , the ...
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Common terms and phrases
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Popular passages
Page 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 7 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Page 76 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 160 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 203 - In every triangle the sum of the three angles is equal to two right angles.
Page 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 141 - If a pyramid is cut by a plane parallel to its base, the...