Elements of Geometry |
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Page 7
... namely , the angle A = D , the side AB DE , and the side AC = DF , we may thence infer , that the other three are also equal , namely , the angle B = E , the angle C = F , and the side BC EF . THEOREM . 38. Two triangles are equal ...
... namely , the angle A = D , the side AB DE , and the side AC = DF , we may thence infer , that the other three are also equal , namely , the angle B = E , the angle C = F , and the side BC EF . THEOREM . 38. Two triangles are equal ...
Page 8
... namely , BC = EF , B = E , and CF , we may thence infer that the other three are also equal , namely , AB = DE , AC DF , and A = D. = THEOREM . 40. One side of a triangle is less than the sum of the other two . Demonstration . The ...
... namely , BC = EF , B = E , and CF , we may thence infer that the other three are also equal , namely , AB = DE , AC DF , and A = D. = THEOREM . 40. One side of a triangle is less than the sum of the other two . Demonstration . The ...
Page 9
... namely , A = D , BE , and CF. - For , if the angle A were greater than the angle D , as the sides AB , AC , are equal to the sides DE , DF , each to each , the side BC would be greater than EF ( 42 ) ; and if the angle A were less than ...
... namely , A = D , BE , and CF. - For , if the angle A were greater than the angle D , as the sides AB , AC , are equal to the sides DE , DF , each to each , the side BC would be greater than EF ( 42 ) ; and if the angle A were less than ...
Page 18
... namely , 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 parallel to those of the angle BAC , but the two angles would not ...
... namely , 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 parallel to those of the angle BAC , but the two angles would not ...
Page 20
... namely , AB = CD , and AD = CB , the equal sides will be parallel , and the figure will be a parallelogram . Demonstration . Draw the diagonal BD ; the two triangles ABD , BDC , have the three sides of the one equal to the three † A re ...
... namely , AB = CD , and AD = CB , the equal sides will be parallel , and the figure will be a parallelogram . Demonstration . Draw the diagonal BD ; the two triangles ABD , BDC , have the three sides of the one equal to the three † A re ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence