The Thirteen

Books of Euclid's

ElementsBooks III-IX

Vol. 2

Books of Euclid's

ElementsBooks III-IX

Vol. 2

Many editors have held that this should not have been included among definitions. Some, e.g. Tartaglia, would call it a postulate; others, e.g. Borelli and Playfair, would call it an axiom; others again, as Billingsley and Clavius, while admitting it as a definition, add explanations based on the mode of constructing a circle; Simson and Pﬂeiderer hold that it is a t/zeorem. I think however that Euclid would have maintained that it is a definition in the proper sense of the term and certainly it satisfies Aristotle's requirement that a definitional statement (optonxbs Aéyos) should not only state the fact (76 511) but should indicate the cause as well (de anima 11. 2, 413 a The equality of circles with equal radii can of course be proved by superposition, but, as we have seen, Euclid avoided this method wherever he could, and there is nothing technically wrong in saying By equal circles I mean circles with equal radii. No ﬂaw is thereby introduced into the system of the Elements; for the definition could only be objected to if it could be proved that the equality predicated of the two circles in the definition was not the same thing as the equality predicated of other equal figures in the Elements on the basis of the congruence-axiom, and, needless to say, this cannot be proved because it is not true. The existence of equal circles (in the sense of the definition) follows from the existence of equal straight lines and 1. Post. 3.

PIBN | 10058930 |

ISBN | 978-1-330-23172-2 |

ISBN (Hardcover) | 978-0-260-39871-0 |

Language | English |

Category | Geometry |

Pages | 440 |

Words | 149693 |

Vocabulary | 1810 |

The

Foundations

of Geometry

Foundations

of Geometry

A Treatise on

Elementary

GeometryWith Appendices Containing

Elementary

GeometryWith Appendices Containing

The Thirteen

Books of Euclid’s

ElementsTranslated From the Text of Heiberg,

With Introduction and Commentary;

Introduction and Books I, II

Vol. 1

Books of Euclid’s

ElementsTranslated From the Text of Heiberg,

With Introduction and Commentary;

Introduction and Books I, II

Vol. 1

Elementary

Geometry

Plane

Geometry

Plane

The Elements

of Geometry

Elements

of Geometry

Elements

Pelicotetics or the

Science of Quantity,

an Elementary Treatise

on Algebra and Its

Groundwork, Arithmetic

Science of Quantity,

an Elementary Treatise

on Algebra and Its

Groundwork, Arithmetic

Diophantus

of AlexandriaA Study in the History

of Greek Algebra

of AlexandriaA Study in the History

of Greek Algebra

The Thirteen

Books of Euclid's

ElementsTranslated From the Text of Heiberg,

With Introduction and Commentary;

Books X-XIII and Appendix

Vol. 3

Books of Euclid's

ElementsTranslated From the Text of Heiberg,

With Introduction and Commentary;

Books X-XIII and Appendix

Vol. 3

A Treatise on

the Circle and

the Sphere

the Circle and

the Sphere

Shop

Mathematics

Mathematics

Introduction

to QuaternionsWith Numerous Examples

to QuaternionsWith Numerous Examples

A History

of Greek

MathematicsFrom Aristarchus to Diophantus

Vol. 2

of Greek

MathematicsFrom Aristarchus to Diophantus

Vol. 2

Archimedes

A History

of Greek

MathematicsFrom Thales to Euclid

Vol. 1

of Greek

MathematicsFrom Thales to Euclid

Vol. 1

The Works of

ArchimedesEdited in Modern Notation,

With Introductory Chapters

ArchimedesEdited in Modern Notation,

With Introductory Chapters

Elements of

GeometryPlane and Solid

GeometryPlane and Solid

Selections

Illustrating the

History of Greek

MathematicsFrom Thales to Euclid

Vol. 1 of 2

Illustrating the

History of Greek

MathematicsFrom Thales to Euclid

Vol. 1 of 2

A Short History

of Greek

Mathematics

of Greek

Mathematics

Handbook of

Mathematics

for Engineers and

Engineering Schools

Mathematics

for Engineers and

Engineering Schools

Proceedings of

the Edinburgh

Mathematical

Society, 1887

Vol. 5

the Edinburgh

Mathematical

Society, 1887

Vol. 5

Euclid’s Elements

of GeometryBooks I. II. III. IV. Vi. And Portions of Books

V. And XI., With Notes, Examples, Exercises,

Appendices and a Collection of Examination Papers

of GeometryBooks I. II. III. IV. Vi. And Portions of Books

V. And XI., With Notes, Examples, Exercises,

Appendices and a Collection of Examination Papers

The Thirteen

Books of Euclid's

ElementsBooks III-IX

Vol. 2

Books of Euclid's

ElementsBooks III-IX

Vol. 2

Geometry and

TrigonometryGeometry, Plane Trigonometry,

Natural Trigonometric Functions,

Logarithmic Trigonometric Functions

TrigonometryGeometry, Plane Trigonometry,

Natural Trigonometric Functions,

Logarithmic Trigonometric Functions

The Axioms

of Projective

Geometry

of Projective

Geometry

The Mathematical

Principles of

Natural PhilosophyTo Which Are Added, Newton's System

of the World; A Short Comment

on and Defence of the Principia

Vol. 1 of 3

Principles of

Natural PhilosophyTo Which Are Added, Newton's System

of the World; A Short Comment

on and Defence of the Principia

Vol. 1 of 3

The Fourth

Dimension

Dimension

Elements of

Geometry

Geometry

Spherical

TrigonometryFor Colleges and Secondary Schools

TrigonometryFor Colleges and Secondary Schools

Plane Geometry

Suggestive

Method

Suggestive

Method

Plane and

Spherical

Trigonometry

Vol. 3

Spherical

Trigonometry

Vol. 3

Space-Time-Matter

A Treatise on

Trigonometry, and

on Trigonometrical

Tables and

Logarithms

Trigonometry, and

on Trigonometrical

Tables and

Logarithms

Indian

Mathematics

Mathematics

Projective

Geometry

Vol. 1

Geometry

Vol. 1

Plane

Geometry

Geometry

Elements of

Geometry

Geometry

Mathematical

TreatiseContaining I, the Theory of Analytical

Functions, II, Spherical Trigonometry,

With Practical and Nautical Astornomy

TreatiseContaining I, the Theory of Analytical

Functions, II, Spherical Trigonometry,

With Practical and Nautical Astornomy

The Pythagorean

TriangleOr the Science of Numbers

TriangleOr the Science of Numbers

Projective

Geometry

Vol. 2

Geometry

Vol. 2

Elements of

Geometry

Geometry

Geometry the Elements of Euclid

and Legendre Simplified and

Arranged to Exclude From

Geomtrical Reasoning the Reductio

Ad Absurdum; With the Elements of

Plane and Spherical Trigonometry,

and Exercises in Elementary

Geometry and Trigonometry

and Legendre Simplified and

Arranged to Exclude From

Geomtrical Reasoning the Reductio

Ad Absurdum; With the Elements of

Plane and Spherical Trigonometry,

and Exercises in Elementary

Geometry and Trigonometry

The Method of

Fluxions and

Infinite SeriesWith Its Application to the

Geometry of Curve-Lines

Fluxions and

Infinite SeriesWith Its Application to the

Geometry of Curve-Lines

Non-Euclidean

GeometryA Critical and Historical

Study of Its Development

GeometryA Critical and Historical

Study of Its Development

Solid

Geometry

Geometry

A Course of

MathematicsFor the Use of Academies,

as Well as Private Tuition

Vol. 1 of 2

MathematicsFor the Use of Academies,

as Well as Private Tuition

Vol. 1 of 2