Modern Methods in Elementary GeometryMacmillan, 1868 - 112 σελίδες |
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Σελίδα 36
... . It will be seen that every chord divides the circumference into two arcs ACB , ADB ; and the circle into two segments denoted by the same letters . THEOREM I. The diameter EOC , drawn per- pendicular to BOOK II. ...
... . It will be seen that every chord divides the circumference into two arcs ACB , ADB ; and the circle into two segments denoted by the same letters . THEOREM I. The diameter EOC , drawn per- pendicular to BOOK II. ...
Σελίδα 37
... diameter , and if one semi - circumference be turned about the diameter till it fall on the other , the two will coincide throughout , each point coinciding with its corresponding point . THEOREM II . The shortest line that can be drawn ...
... diameter , and if one semi - circumference be turned about the diameter till it fall on the other , the two will coincide throughout , each point coinciding with its corresponding point . THEOREM II . The shortest line that can be drawn ...
Σελίδα 38
... diameter ; and as be- fore is greater than any other line AE . Thus the diameter is the greatest line that can be drawn in a circle . H E A THEOREM III . Of two straight lines AD , AE 38 ELEMENTARY GEOMETRY .
... diameter ; and as be- fore is greater than any other line AE . Thus the diameter is the greatest line that can be drawn in a circle . H E A THEOREM III . Of two straight lines AD , AE 38 ELEMENTARY GEOMETRY .
Σελίδα 45
... diameter through A , and would therefore be greater than CD ; and if the arc AB were less than the arc CD , the chord AB would be less than the chord CD . [ II . 4. Cor . 2 . Conversely ; if AOB be greater than , equal to , or less than ...
... diameter through A , and would therefore be greater than CD ; and if the arc AB were less than the arc CD , the chord AB would be less than the chord CD . [ II . 4. Cor . 2 . Conversely ; if AOB be greater than , equal to , or less than ...
Σελίδα 53
... diameter through that point , shew that they are equal . 5. The same if the point be without the circumference . 6. Find the longest and shortest lines that can be drawn between two given circumferences . 7. If two equal circumferences ...
... diameter through that point , shew that they are equal . 5. The same if the point be without the circumference . 6. Find the longest and shortest lines that can be drawn between two given circumferences . 7. If two equal circumferences ...
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A'BC Algebra alternate angle altitude angle equal arc CD ARITHMETIC BC² bisect BROOKE FOSS WESTCOTT CA² Cambridge centre chord circle touching circumference cloth coincide congruent CONIC SECTIONS contain convex angle convex polygon Crown 8vo diagonals diameter dicular divide Edward Thring ELEMENTARY TREATISE equal angles equally distant equally remote equiangular equiangular and similar equilateral triangle Examples exterior angle Fcap Find the locus GEOMETRY given angle given circle given line given point given straight line greater Hence intersect isosceles John's College late Fellow Let ABCD line drawn MATHEMATICAL measure meet middle point opposite sides parallel to CD parallelogram perpen perpendicular polygon produced quadrilateral figure radius rectangle right angles right-angled triangle Schools Second Edition segments Shew shortest line similar triangles student tangent THEOREM THEOREM VII Third Edition trapezium triangle ABC vertex