Euclid book IV proposition 15

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Euclid book IV proposition 15

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| c ptA ptB ptC
circleA circleB
ptD ptE ptF ptG ptH
segAB rayBA rayFA
lineAB lineAC lineCB |

 c := DrGeoCanvas new.

 "Given is a segment AB"
 ptA := c point: -1@0.
 ptA name: 'A'.

 ptB := c point: 1@0.
 ptB name: 'B'.

 segAB := c segment: ptA to: ptB.

 "Use two circles to get point C"
 circleA := c circleCenter: ptA to: ptB.
 circleB := c circleCenter: ptB to: ptA.

 ptC := c intersectionOf: circleB and: circleA.
 ptC name: 'C'.


"second intersection point of the circles"
 ptF := c altIntersectionOf: circleB and: circleA.
 ptF name: 'F'.



 "-- get additional points D, E, F and H with hidden helper lines"
 rayBA := c ray: ptB to: ptA.
 ptD := c altIntersectionOf: circleA  and: rayBA.
 ptD name: 'D'.
 rayBA hide.


 lineAC := c line: ptA to: ptC.
 ptG := c intersectionOf: circleA  and: lineAC.
 ptG name: 'G'.
 lineAC hide.


 rayFA := c ray: ptF to: ptA.
 ptH := c altIntersectionOf: circleA  and: rayFA.
 ptH name: 'H'.
 rayFA hide.

 c segment: ptB to: ptC.
 c segment: ptC to: ptH.
 c segment: ptH to: ptD.
 c segment: ptD to: ptG.
 c segment: ptG to: ptF.
 c segment: ptF to: ptB.

 c segment: ptC to: ptG.
 c segment: ptH to: ptF.
 c segment: ptD to: ptB.


 circleB hide.


Euclid book IV Proposition 15


https://mathcs.clarku.edu/~djoyce/elements/bookIV/propIV15.html

https://en.wikipedia.org/wiki/Euclid%27s_Elements#/media/File:HexagonConstructionAni.gif

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