Elements of Geometry and Trigonometry |
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Page 12
... 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 of a train of reasoning called a demonstration . A problem is a ...
... 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 of a train of reasoning called a demonstration . A problem is a ...
Page 68
... homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc BC will be similar to DE ...
... homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc BC will be similar to DE ...
Page 84
... homologous sides , or the sides adjacent to the equal angles , will be proportional , so that we shall have BC : CE :: AB : CD : : AC : DE . B A E Place the homologous sides BC , CE in the same straight line ; and produce the sides BA ...
... homologous sides , or the sides adjacent to the equal angles , will be proportional , so that we shall have BC : CE :: AB : CD : : AC : DE . B A E Place the homologous sides BC , CE in the same straight line ; and produce the sides BA ...
Page 85
... homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC , DCE . When the homologous sides are de- termined , it is easy to form the proportions : AB : DC :: AC : DE :: BC : CE ...
... homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC , DCE . When the homologous sides are de- termined , it is easy to form the proportions : AB : DC :: AC : DE :: BC : CE ...
Page 87
... homologous sides are the perpendicular ones . Thus in the latter case DE is homologous with AB , DF with AC , and EF with BC . The case of the perpendicular sides might present a rela- tive position of the two triangles different from ...
... homologous sides are the perpendicular ones . Thus in the latter case DE is homologous with AB , DF with AC , and EF with BC . The case of the perpendicular sides might present a rela- tive position of the two triangles different from ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex