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 73
... homologous points , lines , or angles , are those which have like positions , in regard to the two figures . V. The area of a surface , or its superficial extent , is the nu merical ratio of this surface referred to its unit surface ...
... homologous points , lines , or angles , are those which have like positions , in regard to the two figures . V. The area of a surface , or its superficial extent , is the nu merical ratio of this surface referred to its unit surface ...
Page 78
... homologous angles equal , each to each . Let ABC and A'B'C ' be the two A similar triangles . Take AB " = A'B ... homologous sides . THEOREM VI . Two triangles , which have the angles of the one respectively equal to the angles of ...
... homologous angles equal , each to each . Let ABC and A'B'C ' be the two A similar triangles . Take AB " = A'B ... homologous sides . THEOREM VI . Two triangles , which have the angles of the one respectively equal to the angles of ...
Page 79
... homologous sides , AB and A'B ' , AC and A'C ' , BC and B'C ' , as we see , are opposite the equal angles C ' = C , B ' = B , A ' = A. THEOREM VII . Two triangles are similar when the sides of the one are respectively parallel or ...
... homologous sides , AB and A'B ' , AC and A'C ' , BC and B'C ' , as we see , are opposite the equal angles C ' = C , B ' = B , A ' = A. THEOREM VII . Two triangles are similar when the sides of the one are respectively parallel or ...
Page 80
... homologous sides proportion al , and the homologous angles respectively equal . For , by the similarity of the triangles ABC and A'B'C ' , ACD and A'C'D ' , ADE and E D F E D A'D'E ' , etc. , we deduce the following series of equal ra ...
... homologous sides proportion al , and the homologous angles respectively equal . For , by the similarity of the triangles ABC and A'B'C ' , ACD and A'C'D ' , ADE and E D F E D A'D'E ' , etc. , we deduce the following series of equal ra ...
Page 81
... homologous angles are equal ( T. V. ) , and consequently the respective angles of the two polygons are equal , since they are composed of angles equal each to each . Thus , A = A ' , B = B ' , C = C ' , D = D ' , etc. THEOREM X. Two ...
... homologous angles are equal ( T. V. ) , and consequently the respective angles of the two polygons are equal , since they are composed of angles equal each to each . Thus , A = A ' , B = B ' , C = C ' , D = D ' , etc. THEOREM X. Two ...
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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