Euclid book I proposition 12

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HJH
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Euclid book I proposition 12

HJH
This post was updated on .
https://mathcs.clarku.edu/~djoyce/elements/bookI/propI12.html

To draw a straight line perpendicular to a given infinite straight line from a given point not on it.

HJH
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Re: Euclid book I proposition 12

HJH
"-------------------------------------------------"
" Construct what is given "
"-------------------------------------------------"

| c ptA ptB ptC segment |

c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 50.
ptA := c point: -4@0.
ptA name: 'A'.

ptB := c point: 5@0.
ptB name: 'B'.

ptC := c point: 0@4.
ptC name: 'C'.

segment := c segment: ptA to: ptB. 

c view area extent: 700@700.
c view area color: Color white.
c view area openInWorld.


Euclid book I proposition 12 step A
HJH
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Re: Euclid book I proposition 12

HJH
"-------------------------------------------------"
" Construct what is given "
"-------------------------------------------------"

| c ptA ptB ptC ptD segment |

c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 50.
ptA := c point: -4@0.
ptA name: 'A'.

ptB := c point: 5@0.
ptB name: 'B'.

ptC := c point: 0@4.
ptC name: 'C'.

segment := c segment: ptA to: ptB.

"-------------------------------------------------"
" Choose a point D on the other side  "
"-------------------------------------------------"

ptD := c point: 0.5@ -1.
ptD name: 'D'.


Euclide book I Proposition 12 step B
HJH
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Re: Euclid book I proposition 12

HJH
"Euclid Book 1 propostion 12, Step B"
"-------------------------------------------------"
" Construct what is given "
"-------------------------------------------------"

| c ptA ptB ptC ptD segment |

c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 40.
ptA := c point: -4@0.
ptA name: 'A'.

ptB := c point: 5@0.
ptB name: 'B'.

ptC := c point: 0@4.
ptC name: 'C'.

segment := c segment: ptA to: ptB.

"-------------------------------------------------"
" Choose a point D on the other side  "
"-------------------------------------------------"

ptD := c point: 0.5@ -1.
ptD name: 'D'.


"--------------------------------------------------------------------"
" Draw a circle with center PtC and radius CD"
"--------------------------------------------------------------------"

c circleCenter: ptC to: ptD.



Euclide book I Proposition 12 step C

HJH
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Re: Euclid book I proposition 12

HJH
"Euclid Book 1 propostion 12, Step B"
"-------------------------------------------------"
" Construct what is given "
"-------------------------------------------------"

| c ptA ptB ptC ptD segment circle ptE ptF |

c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 40.
ptA := c point: -4@0.
ptA name: 'A'.

ptB := c point: 5@0.
ptB name: 'B'.

ptC := c point: 0@4.
ptC name: 'C'.

segment := c segment: ptA to: ptB.

"-------------------------------------------------"
" Choose a point D on the other side  "
"-------------------------------------------------"

ptD := c point: 0.5@ -1.
ptD name: 'D'.


"--------------------------------------------------------------------"
" Draw a circle with center PtC and radius CD"
"--------------------------------------------------------------------"

circle := c circleCenter: ptC to: ptD.

"--------------------------------------------------------------------"
" Identify and name intersection points          "
"--------------------------------------------------------------------"

ptE := c intersectionOf: circle and: segment.
ptE name: 'E'.

ptF := c altIntersectionOf: circle and: segment.
ptF name: 'F'.


Euclide book I Proposition 12 step D
HJH
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Re: Euclid book I proposition 12

HJH
"Euclid Book 1 propostion 12, Step B"
"-------------------------------------------------"
" Construct what is given "
"-------------------------------------------------"

| c ptA ptB ptC ptD segment circle ptE ptF circle2 circle3 ptG |

c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 40.
ptA := c point: -4@0.
ptA name: 'A'.

ptB := c point: 5@0.
ptB name: 'B'.

ptC := c point: 0@4.
ptC name: 'C'.

segment := c segment: ptA to: ptB.

"-------------------------------------------------"
" Choose a point D on the other side  "
"-------------------------------------------------"

ptD := c point: 0.5@ -1.
ptD name: 'D'.


"--------------------------------------------------------------------"
" Draw a circle with center PtC and radius CD"
"--------------------------------------------------------------------"

circle := c circleCenter: ptC to: ptD.

"--------------------------------------------------------------------"
" Identify and name intersection points          "
"--------------------------------------------------------------------"

ptE := c intersectionOf: circle and: segment.
ptE name: 'E'.

ptF := c altIntersectionOf: circle and: segment.
ptF name: 'F'.


circle hide.
circle2 := c circleCenter: ptE to: ptC.
circle3 := c circleCenter: ptF to: ptC.

ptG := c intersectionOf: circle2 and: circle3.
ptG name: 'G'.

Euclide book I Proposition 12 step E
HJH
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Re: Euclid book I proposition 12

HJH
"Euclid Book 1 propostion 12, Step B"
"-------------------------------------------------"
" Construct what is given "
"-------------------------------------------------"

| c ptA ptB ptC ptD segment circle ptE ptF circle2 circle3 ptG |

c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 40.
ptA := c point: -4@0.
ptA name: 'A'.

ptB := c point: 5@0.
ptB name: 'B'.

ptC := c point: 0@4.
ptC name: 'C'.

segment := c segment: ptA to: ptB.

"-------------------------------------------------"
" Choose a point D on the other side  "
"-------------------------------------------------"

ptD := c point: 0.5@ -1.
ptD name: 'D'.


"--------------------------------------------------------------------"
" Draw a circle with center PtC and radius CD"
"--------------------------------------------------------------------"

circle := c circleCenter: ptC to: ptD.

"--------------------------------------------------------------------"
" Identify and name intersection points          "
"--------------------------------------------------------------------"

ptE := c intersectionOf: circle and: segment.
ptE name: 'E'.

ptF := c altIntersectionOf: circle and: segment.
ptF name: 'F'.


circle hide.
circle2 := c circleCenter: ptE to: ptC.
circle3 := c circleCenter: ptF to: ptC.

ptG := c intersectionOf: circle2 and: circle3.
ptG name: 'G'.


"hide circles, draw segment "
circle2 hide.
circle3 hide.

c segment: ptC to: ptG.
ptD hide.

Euclide book I Proposition 12 step F