Projective

Geometry

Vol. 2

Geometry

Vol. 2

The present volume is an attempt to carry out the program out lined in the preface to Volume I. Unfortunately, Professor Young was obliged by the pressure of other duties to cease his collabora tion at an early stage of the composition of this volume. Much of the work on the first chapters had already been done when this hap pened, but the form of exposition has been changed so much since then that although Professor Young deserves credit for constructive work, he cannot fairly be held responsible for mistakes or oversights.

Professor Young has kindly read the proof sheets of this volume, as have also Professors A. B. Coble and A. A. Bennett. Most of the drawings were made by Dr. J. W. Alexander. I offer my thanks to all of these gentlemen and also to Messrs. Ginn and Company, who have shown their usual courtesy and efficiency while converting the manuscript into a book.

The second volume has been arranged so that one may pass on a first reading from the end of Chapter VII, Volume I, to the beginning of Volume II. The later chapters of Volume I may well be read in connection with the part of Volume II from Chapter V onward.

I shall pass by the opportunity to discuss any of the pedagogical questions which have been raised in connection with the first vol ume and which may easily be foreseen for the second. It is to be expected that there will continue to be a general agreement among those who have not made the experiment, that an abstract method of treatment of geometry is unsuited to beginning students.

In this book, however, we are committed to the abstract point of view. We have in mind two principles for the classification of any theorem of geometry: (a) the axiomatic basis, or bases, from which it can be derived, or, in other words, the class of spaces in which it can be valid; and (b) the group to which it belongs in a given space.

PIBN | 10025400 |

ISBN | 978-1-330-31849-2 |

ISBN (Hardcover) | 978-0-484-60774-2 |

Language | English |

Category | Geometry |

Pages | 523 |

Words | 175140 |

Vocabulary | 1811 |

The Works of

ArchimedesEdited in Modern Notation,

With Introductory Chapters

ArchimedesEdited in Modern Notation,

With Introductory Chapters

An Introduction

to Projective

Geometry

to Projective

Geometry

Mathematical

Questions, With

Their SolutionsFrom the "Educational Time"; With Many

Papers and Solutions Not Published in the

"Educational Time"; From January to June, 1869

Vol. 11

Questions, With

Their SolutionsFrom the "Educational Time"; With Many

Papers and Solutions Not Published in the

"Educational Time"; From January to June, 1869

Vol. 11

Annals of

Mathematics,

1901

Vol. 3

Mathematics,

1901

Vol. 3

Non-Euclidean

GeometryA Critical and Historical

Study of Its Development

GeometryA Critical and Historical

Study of Its Development

The Elements of

Non-Euclidean

Geometry

Non-Euclidean

Geometry

A History

of Greek

MathematicsFrom Thales to Euclid

Vol. 1

of Greek

MathematicsFrom Thales to Euclid

Vol. 1

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

Introduction

to QuaternionsWith Numerous Examples

to QuaternionsWith Numerous Examples

The Elements

of Analytic

Geometry

of Analytic

Geometry

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

Higher

GeometryAn Introduction to Advanced

Methods in Analytic Geometry

GeometryAn Introduction to Advanced

Methods in Analytic Geometry

Archimedes

The Axioms

of Projective

Geometry

of Projective

Geometry

Projective

Geometry

Vol. 1

Geometry

Vol. 1

Spherical

TrigonometryFor Colleges and Secondary Schools

TrigonometryFor Colleges and Secondary Schools

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

An Introduction

to the Theory

of Automorphic

Functions

to the Theory

of Automorphic

Functions

Principles

of Geometry

Vol. 2

of Geometry

Vol. 2

Geometry and

TrigonometryGeometry, Plane Trigonometry,

Natural Trigonometric Functions,

Logarithmic Trigonometric Functions

TrigonometryGeometry, Plane Trigonometry,

Natural Trigonometric Functions,

Logarithmic Trigonometric Functions

Mathematical

Questions

and Solutions

Vol. 12

Questions

and Solutions

Vol. 12

The

Foundations

of Geometry

Foundations

of Geometry

Transactions of

the American

Mathematical

Society

Vol. 24

the American

Mathematical

Society

Vol. 24

A Treatise on

the Circle and

the Sphere

the Circle and

the Sphere

Projective

Geometry

Vol. 2

Geometry

Vol. 2

The Fourth

Dimension

Dimension

Projective

Geometry

Geometry

The Axioms of

Descriptive

Geometry

Descriptive

Geometry

Introduction

to Analytic

Geometry

to Analytic

Geometry

The Thirteen

Books of Euclid's

ElementsBooks III-IX

Vol. 2

Books of Euclid's

ElementsBooks III-IX

Vol. 2

Mathematical

Papers

Vol. 1

Papers

Vol. 1

An Elementary

Treatise on

Modern Pure

Geometry

Treatise on

Modern Pure

Geometry

Hyperbolic

Functions

Functions

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;

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

The

Messenger of

Mathematics

Vol. 34

Messenger of

Mathematics

Vol. 34

Vector

AnalysisAn Introduction to Vector-Methods and Their

Various Applications to Physics and Mathematics

AnalysisAn Introduction to Vector-Methods and Their

Various Applications to Physics and Mathematics

The Quarterly

Journal of Pure

and Applied

Mathematics, 1904

Vol. 35

Journal of Pure

and Applied

Mathematics, 1904

Vol. 35

Lectures on

MathematicsDelivered From Aug. 28 to Sept. 9, 1893 Before Members of the

Congress of Mathematics Held in Connection With the World's

Fair in Chicago at Northwestern University, Evanston, Ill

MathematicsDelivered From Aug. 28 to Sept. 9, 1893 Before Members of the

Congress of Mathematics Held in Connection With the World's

Fair in Chicago at Northwestern University, Evanston, Ill

A History

of Greek

MathematicsFrom Aristarchus to Diophantus

Vol. 2

of Greek

MathematicsFrom Aristarchus to Diophantus

Vol. 2

An

Introduction

to Mathematics

Introduction

to Mathematics

Mathematical

Questions, With

Their SolutionsFrom the "Educational Times," With Many

Papers and Solutions Not Published in the

"Educational Times"; From July to December 1866

Vol. 6

Questions, With

Their SolutionsFrom the "Educational Times," With Many

Papers and Solutions Not Published in the

"Educational Times"; From July to December 1866

Vol. 6

Elements of

Quaternions

Vol. 1

Quaternions

Vol. 1

A Short History

of Greek

Mathematics

of Greek

Mathematics

Mathematical

Questions

and Solutions

Vol. 10

Questions

and Solutions

Vol. 10

Solid

Geometry

Geometry

GeometryApplied to the Mensuration of Lines,

Surfaces, Solids, Heights and Distances

Surfaces, Solids, Heights and Distances

Proceedings of

the Edinburgh

Mathematical

Society, 1891

Vol. 9

the Edinburgh

Mathematical

Society, 1891

Vol. 9