Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page 153
... frustum of a pyramid . The altitude of a frustum of a pyramid is the perpendicular distance between its bases . The slant height of a frustum of a right pyra- mid is the portion of its slant height included between its bases . XI . Two ...
... frustum of a pyramid . The altitude of a frustum of a pyramid is the perpendicular distance between its bases . The slant height of a frustum of a right pyra- mid is the portion of its slant height included between its bases . XI . Two ...
Page 168
... frustum of a regular pyra- mid is measured by half the sum of the perimeters of its two bases multiplied by its slant height . For , since the frustum is formed from a regular pyramid , the two bases are similar and regular polygons ( T ...
... frustum of a regular pyra- mid is measured by half the sum of the perimeters of its two bases multiplied by its slant height . For , since the frustum is formed from a regular pyramid , the two bases are similar and regular polygons ( T ...
Page 172
... frustum of a pyramid is equivalent to three pyramids having the common altitude of the frustum , and for bases , the lower base of the frustum , the upper base , and a mean proportional between them . We will represent the lower base ...
... frustum of a pyramid is equivalent to three pyramids having the common altitude of the frustum , and for bases , the lower base of the frustum , the upper base , and a mean proportional between them . We will represent the lower base ...
Page 173
... frustum , which is the differ- ence of these pyramids by V , we shall have V 1 3 Až α 11h , 글 A 1 α which becomes V = ( A + a + A2 a3 ) × 1 h = A × 1 h + .a × } h + √ A × a × 3 h , which establishes the Theorem . THEOREM XX . Two ...
... frustum , which is the differ- ence of these pyramids by V , we shall have V 1 3 Až α 11h , 글 A 1 α which becomes V = ( A + a + A2 a3 ) × 1 h = A × 1 h + .a × } h + √ A × a × 3 h , which establishes the Theorem . THEOREM XX . Two ...
Page 175
... frustum of a cone . We may conceive it to be described by the revolution of a trapezium ABHG , whose angles A and C are right , about the side AG . The immovable line AG is called the axis or altitude of the frus- tum ; the circles BDC ...
... frustum of a cone . We may conceive it to be described by the revolution of a trapezium ABHG , whose angles A and C are right , about the side AG . The immovable line AG is called the axis or altitude of the frus- tum ; the circles BDC ...
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Common terms and phrases
a+b+c altitude apothem bisect centre chord circumference circumscribed cone consequently corresponding cosec Cosine Cotang cube cubic cylinder decimal denote diameter dicular divided draw drawn equation equivalent exterior angles feet figure frustum Geom give greater half hence hypotenuse inches intersection logarithm measure multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid solve the triangle sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism volume ΙΟ
Popular passages
Page 35 - 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 80 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 139 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 17 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Page 176 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 182 - Every section of a sphere, made by a plane, is a circle.
Page 28 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C ' with Proof STATEMENTS Apply A A'B'C ' to A ABC so that A'B
Page 165 - ... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes.
Page 29 - ... to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side of the first is.
Page 13 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.