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Hugh (of Saint-Victor) - Practical geometry

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title Practical Geometry Practica Geometriae Mediaeval Philosophical - photo 1

title:Practical Geometry : Practica Geometriae Mediaeval Philosophical Texts in Translation ; No. 29
author:Hugh.; Homann, Frederick A.
publisher:Marquette University Press
isbn10 | asin:0874622328
print isbn13:9780874622324
ebook isbn13:9780585147970
language:English
subjectGeometry--Early works to 1800.
publication date:1991
lcc:QA444.H8413 1991eb
ddc:516
subject:Geometry--Early works to 1800.
Mediaeval Philosophical Texts in Translation
No. 29
Roland J. Teske, S. J., Editor
Lee C. Rice, Associate Editor
Practical Geometry
[Practica Geometriae]
Attributed To Hugh of St. Victor
Translated from the Latin
With An Introduction, Notes and Appendices
by
Frederick A. Homann, S. J.
Marquette University Press
Milwaukee, Wisconsin
1991, Marquette University Press
Printed in the United States of America
ISBN 0-87462-232-8
Library of Congress Catalogue Number: 91-60158
Page i
To Alfred and Mimi
With Gratitude and Love
Page ii
Table of Contents
Preface
iii
Introduction
1
1. An Author and a Date
1
2. A Tradition of Practical Geometry
2
3. Chronology Table
6
4. The Agrimensores
7
5. Agrimensorial Geometry
8
6. The Plan of St. Gall
12
7. Gerbert's Geometry
15
8. Hugh of St. Victor
16
9. The Later Agrimensorial Tradition
17
10. A Topical Outline of Practica geometriae
10
11. Commentary on the Text
11
The Applied Geometry of Hugh of Saint Victor
31
Appendices
71
A. Two-Station Methods of Altimetry
73
B. A Mechanical Bathometer
77
C. A Text of Geometria Gerberti
79
D. The Method of Eratosthenes
81
E. An Erroneous Solar Altitude Argument
83
F. A Geometric Text from De arca Noe morali
85
Bibliography
87

Page iii
Preface
This volume presents a translation of Practica geometriae, a twelfth century Latin treatise attributed by Abb Roger Baron, its twentieth century editor, to Hugh of St. Victor. The translation is based on Baron's critical edition and is intended to provide accessible source reading in medieval Latin mathematics, education, and scholastic thought. A brief introduction considers the mathemat ical content, quality, and place of Practica geometriae in the history of mathematics without addressing textual problems.
The translation attempts to put the author's often labored, repetitive, and occasionally obscure medieval Latin into idiomatic English. It follows Baron's arrangement of the text into Prologue, Praenotanda, and three Chapters with his subdivisions of them into fifty-seven sections, identified, for example, as (#40). The author did not command a large technical Latin vocabulary; he knows but a few Greek terms from Euclid and Ptolemy. Indeed, he admits belatedly, in (#55), to using terms loosely. He uses the Arabic "alidada" once and replaces it with the medieval Latin "mediclinium." His circumlocutions have been translated by current (and classical) English technical terms, for example, "duo trianguli habentes eandem proportionem" is rendered "two similar triangles." The Roman numerals of the manuscripts have been replaced by Arabic ones in the translation.
The medieval manuscripts Baron used have illustrations of varying quality, and some none at all. The figures in Baron's text, themselves reproduced from an earlier edition of Curtze, have been redrawn, and others added, to interpret the translation. Figures modified, or added, are marked with an asterisk, e.g., Figure 19*. Illustrations from later sources have been supplied to suggest the persistence of the methods taught in Practica geometriae. To avoid distractions, numbered footnotes have not been used, but references for statements made in the introduction can be found, according to page number, in the notes.
Page 1
Introduction
1. An Author and a Date
In 1955 the Abb Roger Baron collated seven Latin manuscripts to establish a critical edition of a twelfth century treatise,
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