Elements of Geometry |
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Page 17
... Scholium . If we would apply this proposition to poly- gons , which have any re - entering * angles , each of these angles is to be considered as greater than two right angles . But , in order to avoid confusion , we shall confine ...
... Scholium . If we would apply this proposition to poly- gons , which have any re - entering * angles , each of these angles is to be considered as greater than two right angles . But , in order to avoid confusion , we shall confine ...
Page 20
... Scholium . The angles of which we have been speaking , compared , two and two , take different names . We have already called the angles AGH , GHC , interior upon the same side ; the angles BGH , GHD , have the same name ; the angles ...
... Scholium . The angles of which we have been speaking , compared , two and two , take different names . We have already called the angles AGH , GHC , interior upon the same side ; the angles BGH , GHD , have the same name ; the angles ...
Page 21
... Scholium . There is a restriction in this proposition , name- ly , that the side EF be directed the same way as AC , and ED the same way as AB : the reason is this ; if we produce FE toward H , the angle DEH would have its sides ...
... Scholium . There is a restriction in this proposition , name- ly , that the side EF be directed the same way as AC , and ED the same way as AB : the reason is this ; if we produce FE toward H , the angle DEH would have its sides ...
Page 23
... Scholium . In the case of the rhombus , the sides AB , BC , being equal , the triangles AOB , OBC , have the three sides of the one equal to the three sides of the other , each to each , and are consequently equal ; whence it follows ...
... Scholium . In the case of the rhombus , the sides AB , BC , being equal , the triangles AOB , OBC , have the three sides of the one equal to the three sides of the other , each to each , and are consequently equal ; whence it follows ...
Page 26
... chord AH be greater than AD , it may be inferred , from the same triangles , that the angle ACH is greater than ACD , and that thus the arc AH is greater than AD . 104. Scholium . The arcs , of which we have 26 Elements of Geometry .
... chord AH be greater than AD , it may be inferred , from the same triangles , that the angle ACH is greater than ACD , and that thus the arc AH is greater than AD . 104. Scholium . The arcs , of which we have 26 Elements of Geometry .
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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