Euclid's elements book I proposition 11

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HJH
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Euclid's elements book I proposition 11

HJH
From a given point (C) in a given right line (AB) to draw a right line.
Euclid's elements book 1 proposition 11
HJH
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Re: Euclid's elements book I proposition 11

HJH
This post was updated on .
"Draw a straight line at right angles to a given straight line from a given point on it.

"Straight line: AB"
"Point C on it"

"Construct a perpendicular going through C"

| c ptA ptB ptC segment|
c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 50.
ptA := c point: -2@0.
ptA name: 'A'.

ptB := c point: 3@0.
ptB name: 'B'.

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

segment := c segment: ptA to: ptB.

Segment AB with point C
HJH
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Re: Euclid's elements book I proposition 11

HJH
This post was updated on .

"Draw a straight line at right angles to a given straight line from a given point on it."

"Straight line: AB"
"Point C on it"

"TODO: Construct a perpendicular going through C" 


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

| c ptA ptB ptC segment|
c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 50.
ptA := c point: -2@0.
ptA name: 'A'.

ptB := c point: 3@0.
ptB name: 'B'.

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

segment := c segment: ptA to: ptB. 


"---------------------------------------------------------------------------------------------"
" Construct helper point D and E at the same distance from C "
"---------------------------------------------------------------------------------------------"


ptE := c point: 1.5@0.
ptE name: 'E'.

circle := c circleCenter: ptC to: ptE.
circle dotted.
ptD := c intersectionOf: circle and: segment.
ptD name: 'D'. 


"------------------------------------------------------------------------------------------------"
" Display (Squeak implementation)"
c app view area extent: 400@400.
c app view area color: Color white.
c app view area openInWorld.
"SREObjectInspector inspect: c app view."

Euclide book I Proposition 11 step II
HJH
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Re: Euclid's elements book I proposition 11

HJH
"Draw a straight line at right angles to a given straight line from a given point on it."

"Straight line: AB"
"Point C on it"

"TODO: Construct a perpendicular going through C" 


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

| c ptA ptB ptC segment circle 
circleWithCenterD circleWithCenterE |

c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 50.
ptA := c point: -2@0.
ptA name: 'A'.

ptB := c point: 3@0.
ptB name: 'B'.

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

segment := c segment: ptA to: ptB. 


"---------------------------------------------------------------------------------------------"
" Construct helper point D and E at the same distance from C "
"---------------------------------------------------------------------------------------------"


ptE := c point: 1.5@0.
ptE name: 'E'.

circle := c circleCenter: ptC to: ptE.
circle dotted.
ptD := c intersectionOf: circle and: segment.
ptD name: 'D'. 


"------------------------------------------------------------------------------------------------"
" Use D and E to find F which is at the same distance from them."
"------------------------------------------------------------------------------------------------"

circleWithCenterD := c circleCenter: ptD to: ptE.
circleWithCenterD color: Color green.

circleWithCenterE := c circleCenter: ptE to: ptD.
circleWithCenterE color: Color green.

ptF := c altIntersectionOf: circleWithCenterD and: circleWithCenterE.
ptF name: 'F'.


"------------------------------------------------------------------------------------------------"
" Display (Squeak implementation)"
c app view area extent: 500@500.
c app view area color: Color white.
c app view area openInWorld.
"SREObjectInspector inspect: c app view."

"------------------------------------------------------------------------------------------------"




Euclid book I Proposition 11 step C
HJH
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Re: Euclid's elements book I proposition 11

HJH
"Draw a straight line at right angles to a given straight line from a given point on it."

"Straight line: AB"
"Point C on it"

"TODO: Construct a perpendicular going through C" 


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

| c ptA ptB ptC segment circle 
circleWithCenterD circleWithCenterE
segmentDF segmentEF segmentFC |

c := DrGeoCanvas minimal.
c view extent: 500@500.
c scale: 50.
ptA := c point: -2@0.
ptA name: 'A'.

ptB := c point: 3@0.
ptB name: 'B'.

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

segment := c segment: ptA to: ptB. 


"---------------------------------------------------------------------------------------------"
" Construct helper point D and E at the same distance from C "
"---------------------------------------------------------------------------------------------"


ptE := c point: 1.5@0.
ptE name: 'E'.

circle := c circleCenter: ptC to: ptE.
circle dotted.
ptD := c intersectionOf: circle and: segment.
ptD name: 'D'. 


"------------------------------------------------------------------------------------------------"
" Use D and E to find F which is at the same distance from them "
"------------------------------------------------------------------------------------------------"

circleWithCenterD := c circleCenter: ptD to: ptE.
circleWithCenterD color: Color green.

circleWithCenterE := c circleCenter: ptE to: ptD.
circleWithCenterE color: Color green.

ptF := c altIntersectionOf: circleWithCenterD and: circleWithCenterE.
ptF name: 'F'.


"------------------------------------------------------------------------------------------------"
" Display result "
"------------------------------------------------------------------------------------------------"

circleWithCenterD hide.
circleWithCenterE hide.

segmentDF := c segment: ptD to: ptF.
segmentEF := c segment: ptE to: ptF.

segmentFC := c segment: ptF to: ptC.
segmentFC color: Color red.


"segmentDF dotted.
segmentEF dotted.  DOES NOT WORK YET in Squeak"

circle hide.



"------------------------------------------------------------------------------------------------"
" Display (Squeak implementation)"
c app view area extent: 500@500.
c app view area color: Color white.
c app view area openInWorld.
"SREObjectInspector inspect: c app view."

"------------------------------------------------------------------------------------------------"
Euclid book I Proposition 11 step D