Euclid book IV proposition 6, 7 and 8

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HJH
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Euclid book IV proposition 6, 7 and 8

HJH
This post was updated on .
https://www.tate.org.uk/art/artworks/turner-lecture-diagram-euclids-elements-of-geometry-book-4-propositions-6-7-and-8-d17000

Euclide book IV propositions 6,7 and 8

https://mathcs.clarku.edu/~djoyce/elements/bookIV/propIV6.html

To inscribe a square in a given circle.

Draw two diameters AC and BD of the circle ABCD at right angles to one another, and join AB, BC, CD, and DA.




 | c ptM ptA ptB ptC ptD circle rayAM segCA bisector |

 c := DrGeoCanvas new.

 "Given is a circle M with radius MA"
 ptM := c point: 0@0.
 ptM name: 'M'.

 ptA := c point:  1@0.
 ptA name: 'A'.

 circle := c circleCenter: ptM to: ptA.

 rayAM := c ray: ptA to: ptM.
 rayAM hide.
 
 ptC := c altIntersectionOf: circle and: rayAM.
 ptC name: 'C'.

 segCA := c segment: ptC to: ptA.
 bisector := c perpendicularBisector: segCA.


 ptB := c altIntersectionOf: circle and: bisector.
 ptB name: 'C'.

 ptB := c altIntersectionOf: circle and: bisector.
 ptB name: 'B'.

 ptD := c intersectionOf: circle and: bisector.
 ptD name: 'D'.

 c segment: ptA to: ptB.
 c segment: ptB to: ptC.
 c segment: ptC to: ptD.
 c segment: ptD to: ptA.

Euclide book IV proposition 6 -- DrGeo result
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Re: Euclid book IV proposition 6, 7 and 8

Hilaire Fernandes
Administrator
Le 09/10/2018 à 22:06, HJH [via Dr. Geo Forum] a écrit :
https://mathcs.clarku.edu/~djoyce/elements/bookIV/propIV6.html

To inscribe a square in a given circle.

Draw two diameters AC and BD of the circle ABCD at right angles to one another, and join AB, BC, CD, and DA.

Of course your sketch designed with DrGeo's DSL should dynamically true.

Hilaire

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