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 174
... cone is a solid , which may be pro- duced or generated by the revolution of a right - angled triangle SAB , conceived to re- volve about the side SA . In this rotation , the side AB describes a circular plane BDCE , named the base of the ...
... cone is a solid , which may be pro- duced or generated by the revolution of a right - angled triangle SAB , conceived to re- volve about the side SA . In this rotation , the side AB describes a circular plane BDCE , named the base of the ...
Page 175
... cone SCDB , the cone SFKH be cut off by a section parallel to the base , the remaining solid CBHF is called a truncated cone , or the frustum of a cone . We may conceive it to be described by the revolution of a trapezium ABHG , whose ...
... cone SCDB , the cone SFKH be cut off by a section parallel to the base , the remaining solid CBHF is called a truncated cone , or the frustum of a cone . We may conceive it to be described by the revolution of a trapezium ABHG , whose ...
Page 176
... solid , which is named a spherical sector . NOTE . The cylinder , the cone , and the sphere , are the three round bodies treated of in the elements of geometry . THEOREM I. The lateral or convex surface of a cylinder 176 GEOMETRY .
... solid , which is named a spherical sector . NOTE . The cylinder , the cone , and the sphere , are the three round bodies treated of in the elements of geometry . THEOREM I. The lateral or convex surface of a cylinder 176 GEOMETRY .
Page 178
... cone , S its vertex , and SA its slant height . Then will the convex surface of the cone have for its measure circ . OA SA . A E S For , conceive a regular polygon in- scribed in the circle OA ; and on this polygon , as a base , a ...
... cone , S its vertex , and SA its slant height . Then will the convex surface of the cone have for its measure circ . OA SA . A E S For , conceive a regular polygon in- scribed in the circle OA ; and on this polygon , as a base , a ...
Page 179
... cone is equal to its side multiplied by half the sum of the circumferences of its two bases . In the plane SAB which ... cone SAB , which is measured by circ . AO × SA . For a like reason , the triangle SDH is equal to the surface of the ...
... cone is equal to its side multiplied by half the sum of the circumferences of its two bases . In the plane SAB which ... cone SAB , which is measured by circ . AO × SA . For a like reason , the triangle SDH is equal to the surface of the ...
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Common terms and phrases
a+b+c ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum given angle given line gives greater half hence hypotenuse inches included angle inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume
Popular passages
Page 113 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 31 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 112 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 33 - 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 15 - 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 174 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 107 - ... similar figures are to each other as the squares of their homologous sides.
Page 180 - Every section of a sphere, made by a plane, is a circle.