A History of the Teaching of Elementary Geometry: With Reference to Present ... - Alva Walker Stamper - Google Knjige

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CONTENTS

THE TEACHING OF GEOMETRY BEFORE EUCLID

THE BEGINNING of GEOMETRY AMONG PRIMITIVE PEOPLE

Intuitive stage

Stage in which principles are

classify. Formation of rules.

Influences that helped to develop their geometry

PAGE

The pyramids. Rope Stretchers. Astronomy

Esthetic influence. Mural decorations

Utilitarian influence. The overflow of the Nile

Records.-The manuscript of Ahmes; inscriptions on the

THE GREEKS BEFORE EUCLID

The development of the subject-matter of elementary geometry

Thales and his school

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

Development of the geometry of areas.

contributions. Nothing known of methods of

proof. Geometry becomes an abstract science

The development of geometry at Athens

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

Books written on geometry. Euclid not the first.

Nature of the contributions. The "Eudemian

Summary." The founding of solid geometry by

Lack of harmony between the historic sequence

and that given later by Euclid

Educational features of the Greek geometry

In the Ionian and Pythagorean schools

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The Socratic method. The old Greek education.

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

Four-fold division of the mathematical sciences

Restriction as to the use of instruments

The notion of locus. The method of exhaus-

tion. Reductio ad absurdum. Reduction.

Analysis. The diorismus, or discussion

Summary of the general characteristics of the Greek geometry 25-26

THE WORK OF EUCLID AND HIS INFLUENCE ON THE

SUBSEQUENT TEACHING OF GEOMETRY

THE ELEMENTS OF EUCLID.

The contributions by the earlier Greeks

Euclid's sequence of subject-matter. Points of de-

parture from the Euclidean system

Summary of the three chief characteristics of the "Elements"

THE LATER INFLUENCE OF EUCLID

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THE TEACHING OF GEOMETRY FROM EUCLID TO THE

RISE OF THE CHRISTIAN SCHOOLS

His writings. Contributions to solid geometry.

of π. Use of methods already laid down. Founda-

tions of the integral calculus. Geometric and me-

chanical proofs. A recognition of the unity of the

mathematical subjects

Apollonius of Perga

His study of the conic sections. Relation to later

teaching of elementary geometry

At Alexandria after Apollonius

Applications of geometry to astronomy and surveying.

Those who carried on this work. The beginnings of

Extension of spherical geometry by Menelaus. Also

earlier by Theodosius

The commentators, Heron, Pappus, Theon,

The writings of Hypsicles, Geminus, Demascius of
Demascus

Ptolemy and his interest in geometry

Some phases of treatment of subject-matter in the

practical writings mentioned that have an educa-

tional significance

The geometric nomenclature and symbolism of

Heron. His treatment of the mensuration of

heights and distances

Brahmagupta. His differentiation of "gross” answers

Aryabhatta's brevity of proof.

from exact answers.

The use of verse

Translators and preservers of Euclid and of Greek

learning in general

Land surveying. The Codex Arcerianus

Influence of the Alexandrian school

Little influence of Euclid. Quintilian's estimate of

logical geometry

Summary showing the later influence on teaching

THE TEACHING OF GEOMETRY FROM THE RISE OF THE

CHRISTIAN SCHOOLS TO THE YEAR 1525

THE CHRISTIAN SCHOOLS OF THE MIDDLE AGES

The works of Capella, Boethius, Isidore of Seville, Cassi-

odorus, and their use in the schools

The teaching of geometry in the medieval schools before

The influence of Gerbert. His geometry

BOOKS ON PRACTICAL GEOMETRY BEFORE THE RISE OF THE

BOOKS THAT INFLUENCED THE UNIVERSITY

Leonardo of Pisa.

Robertus Anglicus. Sacrobosco. Bradwardine.

Regiomontanus. Educational significance of their

Savasorda. Jordanus Nemorarius.

THE UNIVERSITIES OF THE Middle AGES

Geometry taught before the introduction of Euclid

The teaching of Euclid.

At Paris, Oxford, Prague, Vienna, Heidelberg, Cologne,

Leipzig, Bologna, and Pisa. Character of the

THE TEACHING OF GEOMETRY FROM THE YEAR 1525 TO

THE PRESENT TIME

SOME EARLY PRINTED Books on GEOMETRY

Paciuolo. Fineus. Instruments employed in field work.

Belli. Gargiolli. Gloriosus. The

Bartoli. Cataneo.

influence of Albrecht Dürer. Geometry of a single

opening of the compasses

Tendencies in the above works that have a bearing on

The early universities

Place of geometry in the curriculum. Interest in Euclid

Geometry in the secondary schools of the sixteenth century 61-63

Geometry in the secondary schools of the seventeenth century 63-65

The influence of Comenius. The geometries of

Schröter and Gruvius

Geometry in the secondary schools of the eighteenth century 65–71

Importance of mathematics and science. The texts of

Wolf, Kästner, and Sturm, and their influence. The

Geometry in the secondary schools of the nineteenth century 71-72

Reorganization of the Gymnasia of Prussia. Admis-

sion to universities. General nature of the teaching

of geometry and mathematics in general

General resumé from the sixteenth century, showing the

development of the teaching of geometry from the standpoint

of the curriculum and of method. Tendencies most

General survey from the sixteenth century to the middle of the

Early books that influenced teaching

Ramus. Errard. Mercator. Arnauld.

Le Clerc. The interest in the teaching of geometry

up to the time of the'expulsion of the Jesuits

The eighteenth century

General survey.

Use of texts in class work. Books

of Rivard, Clairaut, and La Caille. Features with

educational significance. The military schools and

texts used in them

Legendre and his influence

The teaching of geometry in France since Legendre

Founding of the government schools. The lycées.

Suggestions on teaching by Lacroix. By Busset

In the universities

The thirteenth century. The fifteenth century. First

English translation of Euclid. Professorships of

mathematics at Oxford and Cambridge. Euclid's

'Elements" edited by Barrow, Whiston, Simson,

Gregory. In later times by Playfair and Todhunter.

The traditions Euclidean

Transition of geometry into the secondary schools

Before the creation of the Gymnasia

The beginning practical. Influence of Peter the Great

in establishing special schools where mathematics

was taught. Methods employed in these

Founding of the Gymnasia

Aim to develop pure science. Introduction of text-

books in geometry. The ecclesiastical schools.

Attempts to break away from the dogmatic method.

Gymnasia begin to send students to the university.

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