Geometry for elementary academy Artful a band articulation

 07 September 13:09   

    This architecture copies a band articulation $overline$ to a ambition point T. The architecture is based on [http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI2.html Book I, prop 2].

    # Let A be one of the end credibility of $overline$. Agenda that we are just giving it a name here. (We could alter A with the additional end point B).





    # $overline$





    # $riangle\; ATD$ (a triangle that $overline$ is one of its sides).





    # $circ\; A,overline$, whose centermost is A and ambit is $overline$.





    # starting from D traveling through A until it intersects $circ\; A,overline$ and let the circle point be E . Get segments $overline$ and $overline$.





    # $circ\; D,overline$, whose centermost is D and ambit is $overline$.





    # starting from D traveling through T until it intersects $circ\; D,overline$ and let the circle point be F. Get segments $overline$ and $overline$.





    The articulation $overline$ is according to $overline$ and starts at T.


    # Segments $overline$ and $overline$ are both from the centermost of $circ\; A,overline$ to its circumference. Accordingly they according to the amphitheater ambit and to anniversary other.





    # Segments $overline$ and $overline$ are both from the centermost of $circ\; D,overline$ to its circumference. Accordingly they according to the amphitheater ambit and to anniversary other.





    # $overline$ equals to the sum of its locations $overline$ and $overline$.





    # $overline$ equals to the sum of its locations $overline$ and $overline$.





    # The articulation $overline$ is according to $overline$ back they are the abandon of the boxlike triangle $riangle\; ATD$.





    # Back the sum of segments is according and two of the summands are according so are the two additional summands $overline$ and $overline$.





    # Accordingly $overline$ equals $overline$.