Elements of Geometry and Trigonometry |
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Page 4
... manner of treating the subjects of Plane and Spherical Trigonometry . It has also been thought best to publish with the present edition a table of logarithms and logarithmic sines , and to apply the principles of geometry to the ...
... manner of treating the subjects of Plane and Spherical Trigonometry . It has also been thought best to publish with the present edition a table of logarithms and logarithmic sines , and to apply the principles of geometry to the ...
Page 17
... manner , since the angle F is equal to the angle C , the line FD will take the direction CA , and the point D will be found somewhere in the line CA. Hence , the point D , falling at the same time in the two straight lines BA and CA ...
... manner , since the angle F is equal to the angle C , the line FD will take the direction CA , and the point D will be found somewhere in the line CA. Hence , the point D , falling at the same time in the two straight lines BA and CA ...
Page 20
... manner it may be shown that the angle E is equal to B , and the angle F to C : hence the two triangles are equal ( Prop . VI . Sch . ) . Scholium . It may be observed that the equal angles lie op- posite the equal sides : thus , the ...
... manner it may be shown that the angle E is equal to B , and the angle F to C : hence the two triangles are equal ( Prop . VI . Sch . ) . Scholium . It may be observed that the equal angles lie op- posite the equal sides : thus , the ...
Page 27
... manner it may be proved that OGA + GOC is equal to two right angles . Cor . 1. If OGB is a right angle , GOD will be a right angle also therefore , every straight line perpendicular to one of two parallels , is perpendicular to the ...
... manner it may be proved that OGA + GOC is equal to two right angles . Cor . 1. If OGB is a right angle , GOD will be a right angle also therefore , every straight line perpendicular to one of two parallels , is perpendicular to the ...
Page 29
... manner , since AE , CB , are parallel , and AB cuts them , the alternate angles ABC , BAE , will be equal : hence the three angles of the triangle ABC make up the same sum as the three angles CAB , BAE , EAD ; hence , the sum of the ...
... manner , since AE , CB , are parallel , and AB cuts them , the alternate angles ABC , BAE , will be equal : hence the three angles of the triangle ABC make up the same sum as the three angles CAB , BAE , EAD ; hence , the sum of the ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex