Elements of Geometry and Trigonometry |
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Page 17
... remaining three are also respectively equal , namely , the side EF = BC , the angle E = B , and the angle F = C PROPOSITION VI . THEOREM . If two triangles have two angles and the included side of the one , equal to two angles and the ...
... remaining three are also respectively equal , namely , the side EF = BC , the angle E = B , and the angle F = C PROPOSITION VI . THEOREM . If two triangles have two angles and the included side of the one , equal to two angles and the ...
Page 24
... remaining parts will also be equal , each to each , and the triangles themselves will be equal . A In the two right angled triangles BAC , EDF , let the hypothenuse AC = DF , and the side BA = ED : then will the side BC = EF , the angle ...
... remaining parts will also be equal , each to each , and the triangles themselves will be equal . A In the two right angled triangles BAC , EDF , let the hypothenuse AC = DF , and the side BA = ED : then will the side BC = EF , the angle ...
Page 33
... remaining sides will also be equal and parallel , and the ยท figure will be a parallelogram . Let ABCD be a quadrilateral , having D the sides AB , CD , equal and parallel ; then will the figure be a parallelogram . For , draw the ...
... remaining sides will also be equal and parallel , and the ยท figure will be a parallelogram . Let ABCD be a quadrilateral , having D the sides AB , CD , equal and parallel ; then will the figure be a parallelogram . For , draw the ...
Page 37
... remaining terms will be propor- tional . PROPOSITION V. THEOREM . If four quantities be in proportion , they will be in proportion when taken inversely . Let M : N :: P : Q ; then will N : M :: Q : P . For , from the first proportion we ...
... remaining terms will be propor- tional . PROPOSITION V. THEOREM . If four quantities be in proportion , they will be in proportion when taken inversely . Let M : N :: P : Q ; then will N : M :: Q : P . For , from the first proportion we ...
Page 60
... remaining angle HEF will be the third angle required ; be- D cause those three angles are XXV ) . C E H F together equal to two right angles ( Book I. Prop . I. and PROBLEM VII1 . Two sides of a triangle , and the angle which they ...
... remaining angle HEF will be the third angle required ; be- D cause those three angles are XXV ) . C E H F together equal to two right angles ( Book I. Prop . I. and PROBLEM VII1 . Two sides of a triangle , and the angle which they ...
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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