Elements of Geometry and Trigonometry |
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Page 12
In both cases , the equal sides , or the equal angles , are named homologous sides or angles . Definitions of terms employed in Geometry . An axiom is a self - evident proposition . A theorem is a truth , which becomes evident by means ...
In both cases , the equal sides , or the equal angles , are named homologous sides or angles . Definitions of terms employed in Geometry . An axiom is a self - evident proposition . A theorem is a truth , which becomes evident by means ...
Page 68
Any two sides , or any two angles , which have like po- sitions in two similar figures , are called homologous sides or angles . 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal ...
Any two sides , or any two angles , which have like po- sitions in two similar figures , are called homologous sides or angles . 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal ...
Page 84
Two equiangular triangles have their homologous sides propor- tional , and are similar . -- Let ABC , CDE be two triangles which have their angles equal each to each , namely , BAC - CDE , ABC - DCE and ACB DEC ; then the homologous ...
Two equiangular triangles have their homologous sides propor- tional , and are similar . -- Let ABC , CDE be two triangles which have their angles equal each to each , namely , BAC - CDE , ABC - DCE and ACB DEC ; then the homologous ...
Page 85
When the homologous sides are de- termined , it is easy to form the proportions : AB : DC : AC : DE :: BC : CE . PROPOSITION XIX . THEOREM . Two triangles , which have their homologous sides proportional , are equiangular and similar .
When the homologous sides are de- termined , it is easy to form the proportions : AB : DC : AC : DE :: BC : CE . PROPOSITION XIX . THEOREM . Two triangles , which have their homologous sides proportional , are equiangular and similar .
Page 87
Two triangles , which have their homologous sides parallel , or perpendicular to each other , are similar . Let BAC , EDF , be two triangles . First . If the side AB is parallel to DE , and BC to EF , the angle ABC will be equal to DEF ...
Two triangles , which have their homologous sides parallel , or perpendicular to each other , are similar . Let BAC , EDF , be two triangles . First . If the side AB is parallel to DE , and BC to EF , the angle ABC will be equal to DEF ...
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ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole