Elements of Geometry |
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Page 13
... opposite side BC , draw the straight line AI , and produce it to C ' , mak- ing ACAB ; produce also AB to B ' , making AB ' double of AI . If we designate by A , B , C , the three angles of the triangle ABC , and by A ' , B ' , C ...
... opposite side BC , draw the straight line AI , and produce it to C ' , mak- ing ACAB ; produce also AB to B ' , making AB ' double of AI . If we designate by A , B , C , the three angles of the triangle ABC , and by A ' , B ' , C ...
Page 16
... opposite interior angles A and C ; for , by adding to each the angle ABC , the sums are each equal to two right angles . THEOREM . 64. The sum of all the interior angles of a polygon is equal to as many times two right angles as there ...
... opposite interior angles A and C ; for , by adding to each the angle ABC , the sums are each equal to two right angles . THEOREM . 64. The sum of all the interior angles of a polygon is equal to as many times two right angles as there ...
Page 18
... opposite interior angles MFN , MNF ( 63 ) , and these last are equal to each other , since they are oppo- site to the equal sides MN , FM ; consequently the angle AMF , or its equal MFG , is double of MFN ; therefore the straight line ...
... opposite interior angles MFN , MNF ( 63 ) , and these last are equal to each other , since they are oppo- site to the equal sides MN , FM ; consequently the angle AMF , or its equal MFG , is double of MFN ; therefore the straight line ...
Page 21
... opposite sides of a parallelogram are equal , and the opposite angles also are equal . Demonstration . Draw the diagonal BD ( fig . 44 ) ; the two Fig . 44 triangles ADB , DBC , have the side BD common ; moreover , on account of the ...
... opposite sides of a parallelogram are equal , and the opposite angles also are equal . Demonstration . Draw the diagonal BD ( fig . 44 ) ; the two Fig . 44 triangles ADB , DBC , have the side BD common ; moreover , on account of the ...
Page 22
... opposite to ADB is equal to the side DC opposite to the equal angle DBC , and likewise the third side AD is equal to the third side BC ;. there- fore the opposite sides of a parallelogram are equal . Again , from the equality of the ...
... opposite to ADB is equal to the side DC opposite to the equal angle DBC , and likewise the third side AD is equal to the third side BC ;. there- fore the opposite sides of a parallelogram are equal . Again , from the equality of the ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence