Elements of Geometry and Trigonometry |
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Page 5
... Third Books , BOOK IV . The Proportions of Figures and the Measurement of Areas , . Problems relating to the Fourth Book , 41 57 68 8888 98 BOOK V. Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid ...
... Third Books , BOOK IV . The Proportions of Figures and the Measurement of Areas , . Problems relating to the Fourth Book , 41 57 68 8888 98 BOOK V. Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid ...
Page 12
... third to the third , and so on . The phrase , mutually equian- gular , has a corresponding signification , with respect to the angles . In both cases , the equal sides , or the equal angles , are named homologous sides or angles ...
... third to the third , and so on . The phrase , mutually equian- gular , has a corresponding signification , with respect to the angles . In both cases , the equal sides , or the equal angles , are named homologous sides or angles ...
Page 17
... third side EF , will coincide with the third side BC ( Ax . 11. ) : therefore , the triangle EDF is equal to the triangle BAC ( Ax . 13. ) . Cor . When two triangles have these three things equal , namely , the side ED = BA , the side ...
... third side EF , will coincide with the third side BC ( Ax . 11. ) : therefore , the triangle EDF is equal to the triangle BAC ( Ax . 13. ) . Cor . When two triangles have these three things equal , namely , the side ED = BA , the side ...
Page 18
... third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short- est distance between the points A and B ( Def . 3. ) ; hence AC + CB is ...
... third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short- est distance between the points A and B ( Def . 3. ) ; hence AC + CB is ...
Page 19
... third side BC of the first triangle is greater than the third side EF of the second ; then will the an- gle BAC of the first triangle , be greater than the angle EDF of the second . CE E H For , if not , the angle BAC must be equal to ...
... third side BC of the first triangle is greater than the third side EF of the second ; then will the an- gle BAC of the first triangle , be greater than the angle EDF of the second . CE E H For , if not , the angle BAC must be equal to ...
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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