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 115
... vertex . This being premised , draw BL bisecting the angle OBA , and we shall have this proportion , AL : LO :: AB : ОВ ( В. III . , Т. ХІІ . ) . But since the angle LBO = LBA = LOB = 3 , and consequently ALB = 2LOB = 1 , the two ...
... vertex . This being premised , draw BL bisecting the angle OBA , and we shall have this proportion , AL : LO :: AB : ОВ ( В. III . , Т. ХІІ . ) . But since the angle LBO = LBA = LOB = 3 , and consequently ALB = 2LOB = 1 , the two ...
Page 138
... vertex . Three planes , at least , are necessary for forming a polyedral angle . In the case of three planes , the angle is called a triedral angle . THEOREM I. One part of a straight line cannot be in a plane , and another part out of ...
... vertex . Three planes , at least , are necessary for forming a polyedral angle . In the case of three planes , the angle is called a triedral angle . THEOREM I. One part of a straight line cannot be in a plane , and another part out of ...
Page 150
... vertex S , is equiva- lent to the sum of the angles of an equal number of triangles AOB , BOC , etc. , formed about ... vertex is in O , is less than the sum of all the angles at the bases of the triangles whose common vertex is in ...
... vertex S , is equiva- lent to the sum of the angles of an equal number of triangles AOB , BOC , etc. , formed about ... vertex is in O , is less than the sum of all the angles at the bases of the triangles whose common vertex is in ...
Page 153
... vertex , taken together , constitute the lateral surface of the pyramid . The perpen- dicular distance from the vertex to the base is called its altitude . A VII . A pyramid is triangular , quadrilateral , pentagonal , etc ...
... vertex , taken together , constitute the lateral surface of the pyramid . The perpen- dicular distance from the vertex to the base is called its altitude . A VII . A pyramid is triangular , quadrilateral , pentagonal , etc ...
Page 170
... plane FAC , and there will remain the solid FACDE , which may be considered as a quadrangular pyramid whose vertex is F , and base the parallelogram ACDE . Draw E D the diagonal AD , and extend the plane FAD , 170 GEOMETRY .
... plane FAC , and there will remain the solid FACDE , which may be considered as a quadrangular pyramid whose vertex is F , and base the parallelogram ACDE . Draw E D the diagonal AD , and extend the plane FAD , 170 GEOMETRY .
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Common terms and phrases
ABē 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 GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle 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