Euclid Book 4

Proposition 1

Construction

Statement

Statement HTML

To place a chord in a given circle equal to a given line segment not greater than the diameter.

Construction steps

Construction Steps HTML

Let the circle through points A, B, and C centered at O be the given circle, AC the diameter, and DE be the given line segment with ⎪DE⎪ ≤ ⎪AC⎪.

Find F on AC such that ⎪AF⎪ = ⎪DE⎪.

Construct the circle through the point F centered at A and let its intersection with the original circle be G.

Join AG. Chord AG has been constructed equal to the given line segment DE.

Original statement

ϵἰς τὸν δοθέντα κύκλον τῇ δοθϵίσῃ ϵὐθϵίᾳ μὴ μϵίζονι οὔσῃ τῆς τοῦ κύκλου διαμέτρου ἴσην ϵὐθϵῖαν ἐναρμόσαι.

English translation

Into a given circle to fit a straight line equal to a given straight line which is not greater than the diameter of the circle.

Computable version

In[1]:=

GeometricSceneA.,B.,C.,O.,D.,E.,F.,G.,{},GeometricStepCircleThroughA.,B.,C.,O.,LineA.,O.,C.,Line[D.,E.],EuclideanDistance[D.,E.]≤EuclideanDistanceA.,C.,GeometricStepF.∈LineA.,C.,EuclideanDistance[A.,F.]EuclideanDistance[D.,E.],GeometricStepGeometricAssertionCircleThrough[F.,A.],CircleThroughA.,B.,C.,O.,"Concurrent",G.,GeometricStepLineA.,G.,EuclideanDistanceA.,G.EuclideanDistance[D.,E.]//RandomInstance

Out[]=

PlaneGeometry`GeometrySceneDrawerDump`makeGraph

icsFromRulesAbsoluteThickness[2],

EdgeForm

Thickness[Large],Line



GeometricPoint

A.,



GeometricPoint

C.,Circle



GeometricPoint

O.,



GeometricQuantity





Unspecified

radius,

{{C["GeometricPoint"][A.],

C["GeometricPoint"][B.],

C["GeometricPoint"][C.]}, {1, 1,

0}},Circle



GeometricPoint

A.,



GeometricQuantity





Unspecified

radius,

{{C["GeometricPoint"][F.], C["Geometri

cPoint"][C["Unspecified"]["ref",

"{3, 1, 1, 1, 0}", "1"]], C["Geo

metricPoint"][C["Unspecified"]["r

ef", "{3, 1, 1, 1, 0}", "2"]]},

{3, 1, 1, 1,

0}},AbsoluteThickness[2],

Line



GeometricPoint

A.,



GeometricPoint

G.,AbsoluteThickness[2],

,Line



GeometricPoint

D.,



GeometricPoint

E.,

AbsolutePointSize[17],

Point



GeometricPoint

D.,Inset D. ,



GeometricPoint

D.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

D.,

AbsolutePointSize[17],

Point



GeometricPoint

E.,Inset E. ,



GeometricPoint

E.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

E.,

AbsolutePointSize[17],

Point



GeometricPoint

A.,Inset A. ,



GeometricPoint

A.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

A.,

AbsolutePointSize[17],

Point



GeometricPoint

C.,Inset C. ,



GeometricPoint

C.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

C.,

AbsolutePointSize[17],

Point



GeometricPoint

F.,Inset F. ,



GeometricPoint

F.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

F.,

AbsolutePointSize[17],

Point



GeometricPoint

O.,Inset O. ,



GeometricPoint

O.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

O.,

AbsolutePointSize[17],

Point



GeometricPoint

G.,Inset G. ,



GeometricPoint

G.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

G.,

AbsolutePointSize[17],

Point



GeometricPoint

B.,Inset B. ,



GeometricPoint

B.,AbsolutePointSize[17],

Opacity[0],

Point



GeometricPoint

B.,{}



GeometricPoint

A.{4.59574,

-2.70406},



GeometricPoint

B.{3.5469,

-4.24024},



GeometricPoint

C.{-3.99844,

0.9114},



GeometricPoint

D.{-2.29716,

-2.28942},



GeometricPoint

E.{2.81701,

1.24679},



GeometricPoint

F.{-1.13544,

-0.293028},



GeometricPoint

G.{-1.02284,

-5.36696},



GeometricPoint

O.{0.298653,

-0.89633},



GeometricQuantity





Unspecified

radius,

{{C["GeometricPoint"][A.],

C["GeometricPoint"][B.],

C["GeometricPoint"][C.]}, {1, 1, 0}}

4.66185,



GeometricQuantity





Unspecified

radius,

{{C["GeometricPoint"][A.],

C["GeometricPoint"][B.],

C["GeometricPoint"][C.]}, {3, 1, 1, 2,

0}}4.66185,



GeometricQuantity





Unspecified

radius,

{{C["GeometricPoint"][F.], C["GeometricP

oint"][C["Unspecified"]["ref", "{3,

1, 1, 1, 0}", "1"]], C["Geometric

Point"][C["Unspecified"]["ref", "{3,

1, 1, 1, 0}", "2"]]}, {3, 1, 1, 1,

0}}6.21767

Last updated on: 2022-03-04.

A collection of classical geometry in computable formats along with code and diagrams.

Computable Euclid

Euclid Book 4

Proposition 1

Construction

Statement

Statement HTML

Construction steps

Construction Steps HTML

Original statement

ϵἰς τὸν δοθέντα κύκλον τῇ δοθϵίσῃ ϵὐθϵίᾳ μὴ μϵίζονι οὔσῃ τῆς τοῦ κύκλου διαμέτρου ἴσην ϵὐθϵῖαν ἐναρμόσαι.

English translation

Into a given circle to fit a straight line equal to a given straight line which is not greater than the diameter of the circle.

Computable version

Additional instances

Dependency graphs

Classes