EntityList[EntityClass["GeometricScene","EuclidsElements"]]
In[]:=
Out[]=
GeometricScene[{{A.,O.,B.,C.,D.,E.,F.,G.,H.},{}},{{CircleThrough[{A.},O.],Triangle[{D.,E.,F.}]},{GeometricAssertion[{Line[{G.,A.,H.}],CircleThrough[{A.},O.]},Tangent]},{C.∈CircleThrough[{A.},O.],Line[{A.,C.}],PlanarAngle[{C.,A.,H.}]PlanarAngle[{D.,E.,F.}]},{B.∈CircleThrough[{A.},O.],Line[{A.,B.}],PlanarAngle[{B.,A.,G.}]PlanarAngle[{D.,F.,E.}]},{Line[{B.,C.}]}},{GeometricAssertion[{Triangle[{A.,B.,C.}],Triangle[{D.,E.,F.}]},Similar]}]
In[]:=
RandomInstance[%500]
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In[]:=
EntityList["GeometricScene"]
In[]:=
Length[EntityList["GeometricScene"]]
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332
In[]:=
Length[EntityList[EntityClass["GeometricScene","EuclidsElements"]]]
Out[]=
196
In[]:=
EntityValue["GeometricScene","ProofDates"]
In[]:=
DateHistogram[DeleteMissing[Flatten[EntityValue["GeometricScene","ProofDates"]]],"Century"]
Out[]=
In[]:=
Histogram[ByteCount/@EntityValue[EntityClass["GeometricScene","EuclidsElements"],"Statement"]]
Out[]=
In[]:=
TakeLargestBy[EntityList[EntityClass["GeometricScene","EuclidsElements"]],ByteCount[#["Statement"]]&,5]
Out[]=
,,,,
In[]:=
EntityValue[%,"Statement"]
Out[]=
,,,,
Let be any point outside a circle and ,,,,,and be lines to the circumference of the circle. If passes through the center of the circle, is the production of in the opposite direction, and are drawn to the concave circumference, is closer to than is to , and are drawn to the convex circumference, and is closer to than is to , then , .
P
PA
PB
PC
PD
PE
PF
PA
PD
PA
PB
PC
PB
PA
PC
PA
PE
PF
PE
PD
PF
PD
PA>PB>PC
PD<PE<PF
Given two groups of three magnitudes, if the first magnitude is to the second as the fifth is to the sixth, the second is to the third as the fourth is to the fifth, and the first magnitude is greater than or equal to the third, then the fourth magnitude is also greater than or equal to the sixth.
(AB, CD, and EF; GH, IJ, and KL)
()
AB
CD
IJ
KL
()
CD
EF
GH
IJ
(AB≥EF)
(GH≥KL)
Given two groups of three magnitudes, if the first magnitude is to the second as the fourth is to the fifth, the second is to the third as the fifth is to the sixth, and the first magnitude is greater than or equal to the third, then the fourth magnitude is also greater than or equal to the sixth.
(AB, CD, and EF; GH, IJ, and KL)
()
AB
CD
GH
IJ
()
CD
EF
IJ
KL
(AB≥EF)
(GH≥KL)
If a first magnitude has to a second the same ratio as a third to a fourth, then any equimultiples of the first and third also have the same ratio to any equimultiples of the second and fourth respectively.
()
AB
CD
EF
GH
(IJ2AB, KL2EF)
(MN3CD, OP3GH)
()
IJ
MN
KL
OP
Given two groups of three magnitudes, if the first magnitude is to the second as the fourth is to the fifth and the second is to the third as the fifth is to the sixth, then the first magnitude is to the third as the fourth to the sixth.
(AB, CD, and EF; GH, IJ, and KL)
()
AB
CD
GH
IJ
()
CD
EF
IJ
KL
()
AB
EF
GH
KL
In[]:=
TakeSmallestBy[EntityList[EntityClass["GeometricScene","EuclidsElements"]],ByteCount[#["Statement"]]&,35]
Out[]=
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
In[]:=
EntityValue[%,"Statement"]
Out[]=
{,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,}
To bisect a given angle.
To bisect a given line segment.
To trisect a given line segment.
To find the center of a given circle.
To inscribe a circle in a given square.
To inscribe a square in a given circle.
To inscribe a circle in a regular pentagon.
To construct a square on a given line segment.
To describe a square about a given circle.
To inscribe a circle in a given triangle.
To circumscribe a circle about a given square.
To construct a square equal to a given polygon.
To circumscribe a circle about a given triangle.
To cut a given line segment in the golden ratio.
To describe a regular pentagon about a given circle.
To inscribe an regular hexagon in a given circle.
To inscribe a regular pentagon in a given circle.
To divide a given line similarly to a given divided line.
Two circles cannot be tangent to each other at two points.
To construct an equilateral triangle on a given line segment.
To draw a line through a given point parallel to a given line.
To circumscribe a circle about a given regular pentagon.
If two circles have more than two points in common, they must coincide.
Polygons which are similar to the same polygon, are similar to one another.
To construct a polygon similar to one given polygon and equal to another.
To inscribe inside a given circle a triangle similar to a given triangle.
To describe about a given circle a triangle similar to a given triangle.
From a given point to draw a line segment equal to a given line segment.
To draw a line perpendicular to a given infinite line from a given point not on it.
From a given point outside of a given circle to draw a line tangent to the circle.
The sum of the opposite angles of a quadrilateral inscribed in a circle is two right angles.
To cut off from the longer of two given unequal line segments a part equal to the shorter.
To construct a parallelogram equal to a given triangle, with one angle equal to a given angle.
To construct an angle equal to a given angle on a given line segment and at a point on it.
To cut off from a given circle a segment which contains an angle equal to a given angle.
Commonality of maximum length paths......