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 888888 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 888888 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 line AB is the shortest dis- tance 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 line AB is the shortest dis- tance 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 Q E F 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 Q E F 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 centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex