Elements of Geometry and Trigonometry |
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Page 12
... 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 of a train of reasoning called a demonstration ...
... 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 of a train of reasoning called a demonstration ...
Page 68
... angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 2. Any two sides , or any two angles , which have like po- sitions in two similar figures , are called homologous sides ...
... angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 2. Any two sides , or any two angles , which have like po- sitions in two similar figures , are called homologous sides ...
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
... sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC , DCE . When the homologous sides ...
... sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC , DCE . When the homologous sides ...
Page 87
Adrien Marie Legendre. PROPOSITION XXI . THEOREM . 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 ...
Adrien Marie Legendre. PROPOSITION XXI . THEOREM . 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 ...
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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