Euclid book I proposition 10 - bisect a given finite straight segment.

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HJH
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Euclid book I proposition 10 - bisect a given finite straight segment.

HJH
This post was updated on .
https://mathcs.clarku.edu/~djoyce/elements/bookI/propI10.html

Let AB be a given straight segment.

| c ptA ptB ptC ptD ptE
circleA circleB
segAB segCE  |

 c := DrGeoSketch minimal.

 "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'.

 ptE := c altIntersectionOf: circleB and: circleA.
 ptE name: 'E'.

 segCE := c segment: ptC to: ptE.
 ptD := c intersectionOf: segAB  and: segCE.
 ptD name: 'D'.


Euclid's elements book 1 proposition 10