Modern Methods in Elementary GeometryMacmillan, 1868 - 112 σελίδες |
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Σελίδα 4
... equal , viz . AEC to DEB , and AED to BEC . AEC + AED = 2R , AED + DEB = 2R . Therefore = AEC + AED AED + DEB . Therefore Similarly , AEC DEB . = AED BEC . = THEOREM III . Any straight line AB is less than 4 ELEMENTARY GEOMETRY .
... equal , viz . AEC to DEB , and AED to BEC . AEC + AED = 2R , AED + DEB = 2R . Therefore = AEC + AED AED + DEB . Therefore Similarly , AEC DEB . = AED BEC . = THEOREM III . Any straight line AB is less than 4 ELEMENTARY GEOMETRY .
Σελίδα 5
... Produce AC to meet DB in E. E Then CB CE + EB . Therefore AC + CB < AE + EB . Again , AE < AD + DE . Therefore AE + EB < AD + DB . Much more then AC + CB < AD + DB . COR . Similarly , it may be shewn that any THE STRAIGHT LINE . ལ་
... Produce AC to meet DB in E. E Then CB CE + EB . Therefore AC + CB < AE + EB . Again , AE < AD + DE . Therefore AE + EB < AD + DB . Much more then AC + CB < AD + DB . COR . Similarly , it may be shewn that any THE STRAIGHT LINE . ལ་
Σελίδα 6
E. M. Reynolds. COR . Similarly , it may be shewn that any convex broken F D C E line ACDEB is less than another broken line AFGB by which it is enclosed . THEOREM V. The perpendicular is the shortest line that can be drawn FE D B- -C ...
E. M. Reynolds. COR . Similarly , it may be shewn that any convex broken F D C E line ACDEB is less than another broken line AFGB by which it is enclosed . THEOREM V. The perpendicular is the shortest line that can be drawn FE D B- -C ...
Σελίδα 8
... Similarly Again ( 2 ) = ( IV ) . ( I ) + ( 2 ) = ( 1 ) + ( 2 ) · = 2R . Similarly ( 3 ) + ( IV ) = 2R ELEMENTARY GEOMETRY .
... Similarly Again ( 2 ) = ( IV ) . ( I ) + ( 2 ) = ( 1 ) + ( 2 ) · = 2R . Similarly ( 3 ) + ( IV ) = 2R ELEMENTARY GEOMETRY .
Σελίδα 9
E. M. Reynolds. Similarly ( 3 ) + ( IV ) = 2R . The angles ( 1 ) and ( I ) are called exterior and interior angles . The angles ( 3 ) and ( 1 ) are called alternate angles . The angles ( 2 ) and ( I ) are called interior angles on the ...
E. M. Reynolds. Similarly ( 3 ) + ( IV ) = 2R . The angles ( 1 ) and ( I ) are called exterior and interior angles . The angles ( 3 ) and ( 1 ) are called alternate angles . The angles ( 2 ) and ( I ) are called interior angles on the ...
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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