Slike strani
PDF
ePub
[merged small][ocr errors]

PREFACE

While much has been written on the history of mathematics, comparatively little attention has been given to the history of its teaching. Günther's “Geschichte des mathematischen Unterrichts im Deutschen Mittelalter bis zum Jahre 1525” and Suter's “Die Mathematik auf den Universitäten des Mittelalters" are the only prominent works that emphasize the teaching side. Among the works that treat the general history of mathematics, those of Cantor, Hankel, Gow, and Allman have been of great assistance. Much information has also been gained from miscellaneous articles, standard works on the history of education, and early texts, the latter constituting, for the most part, the original sources for this study.

The material that has been utilized in the first three chapters is to be found chiefly in the standard histories of mathematics, but wherever possible the original sources have been consulted. Originality is claimed only for the selection and arrangement of this portion of the subject-matter and for the conclusions drawn. The material for the next three chapters has been gleaned very largely from the original sources.

The author is under great obligation to Professor David Eugene Smith of Teachers College, Columbia University, under whose direction this dissertation has been prepared, for helpful counsel and criticism, and for rendering much of this work possible through his valuable collection of early printed books.

ALVA WALKER STAMPER.

New York, June, 1906.

CONTENTS

.

.

PAGE

THE TEACHING OF GEOMETRY BEFORE EUCLID

THE BEGINNING OF GEOMETRY AMONG PRIMITIVE PEOPLE .

1-4

Intuitive stage

2–3

Stage in which principles are recognized. Ability to

classify. Formation of rules. Practical use

3-4

Logical stage

Application with logic as a basis

4

THE EGYPTIANS

4-10

Influences that helped to develop their geometry

4-7
The pyramids. Rope Stretchers. Astronomy
Æsthetic influence. Mural decorations

Utilitarian influence. The overflow of the Nile

Records.—The manuscript of Ahmes; inscriptions on the

Temple at Edfu

7-9

Summary

9-10

THE GREEKS BEFORE EUCLID

10-26

The development of the subject matter of elementary geometry 10-16

Thales and his school

10-11

The first propositions given to geometry. The

practical not neglected. First problems of

construction. Development of a deductive

geometry of lines

Pythagoras and his school

11-13

Development of the geometry of areas. Further

contributions. Nothing known of methods of

proof. Geometry becomes an abstract science
The development of geometry at Athens

13–16

Interest in geometry. The Sophists. The schools

of Plato and Aristotle. The Three Problems of

Antiquity and their relation to the development

of the subject-matter of geometry

13

Books written on geometry. Euclid not the first.

Nature of the contributions. The “Eudemian

Summary.” The founding of solid geometry by

Eudoxus

13-16

Lack of harmony between the historic sequence

and that given later by Euclid

16

Educational features of the Greek geometry

16-26

In the Ionian and Pythagorean schools

16-17
At Athens

17-25

The Socratic method. The old Greek’education.

Plato's disposition of geometry in the curriculum 17-18

Four-fold division of the mathematical sciences . 18-19

Restriction as to the use of instruments

19-20

[ocr errors][merged small]

36-37

Interest in Euclid .

37-38

The commentators, Heron, Pappus, Theon,

Proclus

« PrejšnjaNaprej »