Table Of ContentPLATE I
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ELIAS ALLEN (fl. l6o6, Ob. 1654)
The doyen of Stuart instrument-makers is here seen with some of his tools
on the wall behind him, and a universal dial and a circumferentor con
spicuous under his hand. The latter instrument, first designed by John
Godwyn, was very popular with surveyors.
THE
MATHEMATICAL
PRACTITIONERS
OF TUDOR & STUART
ENGLAND
BY
E. G. R. TAYLOR
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3 00201 0091289 0
CAMBRIDGE
for the Institute of Navigation
AT THE UNIVERSITY PRESS
I9S4
GE2103
Martino Publishing, P.O. Box373, Mansfield Centre CT06250
U.S.A.
ISBN 1-57 898-293-6
Copyright© 1954, 1967 Cambridge University Press .
Reprinted with permission.
All rights reserved. No new contribution to
this publication may be reproduced, stored
in a retrieval system, or transmitted, in any form or by
any means, electronic, mechanical, photocopying,
recording, or otherwise, without the prior permission of
Cambridge University Press
This work is a facsimile edition of
The Mathematical Practitioners of
Tudor & Stuart England
by E.G.R. Taylor
Published in Cambridge 1954
Printed in the United States of America
On 100% Acid-Free Paper
CONTENTS
List of Illustrations vii
Foreword page ix
Preface xi
Parti. NARRATIVE
Introduction
P-3
Chapter I 1485-1558 P-1
Mathematical practice abroad. John Cabot in Bristol. Nicholas Kratzer at court.
The first English practitioners. The influence of Cambridge scholars. Work of
Leonard Digges.
Chapter II 1558-1600 p. 26
William Cuningham’s survey of methods and instruments. Land survey and
cartography. Vernacular text-books of William Bourne. The work of John Dee
and Thomas Digges. Robert Norman and William Borough. The London
Mathematical Lecture. Thomas Hariot and Edward Wright.
Chapter III 1600-1630 p. 49
Influence of the Gresham Professors. Logarithms and trigonometry. Ralph
Handson’s text-book. The improvement of navigational tables and instruments.
John Tapp and the Seaman's Kalender. Gunter and Oughtred. The Line of
Numbers.
Chapter IN 1630-1650 p. 67
Instruments and equipment for Captain James’s voyage. Observations for varia
tion and longitude. Gellibrand and the secular variation. Richard Norwood’s
text-books. New measure of the degree. Samuel Foster and the quadrant.
George Atwell, surveyor and teacher. Dr Pell and the teaching of mathematics.
v
I
CONTENTS
Chapter V 1650-1662 p. 84
The Invisible College. John Williams at Oxford. The surveyors, Leybourne
and Wing. John Wybard. New Lunar Tables by Thomas Streete. Henry Bond
and the longitude. Mathematical book and instrument shops. Robert Hooke
at Oxford. Controversy on university teaching of new arts and sciences.
Chapter VI 1660-1675 p. 99
Practical mathematics at the Restoration. Early work of the Royal Society
on observations at sea and the longitude problem. London surveyors and
instrument-makers. Mathematical practice in Scotland. Robert Hooke’s devices
and inventions. John Seller and the English Pilot. A committee for the longi
tude. John Flamsteed, Astronomer Royal. French measure of the degree.
Chapter VII 1675-1695 p. 114
Christ’s Hospital Mathematical School. Samuel Pepys as Governor. Defects
of the current charts. Pepys and Halley. New surveys. The pendulum clock,
barometer and calculating machine. The French Connoissance des Temps.
Chapter NW\ 1695-1714 P-132
New attitude towards mathematical practice. The Use of the Globes. The Theory
of Earth. University lectures on natural philosophy. London lectures on applied
mathematics. The Lexicon Technician. Hauksbee’s ‘Course of Experiments’.
New mathematical schools.
Chapter IX 1714—1715 p. 148
The longitude problem. Varenius' Geographia Generalis. A commission for the
longitude. Candidates for the reward. Jeremy Thacker’s criticisms. The Orrery.
Edmund Stone’s review of English instruments. A contemporary instrument
maker’s stock-list.
Part IL PRACTITIONERS
The Practitioners, with Biographical Notes P- 165
Partin. WORKS
Works on the Mathematical Arts and Practices, with
Descriptive Notes p. 311
Bibliography of Secondary Works Consulted p. 432
Index P- 433
vi
LIST OF PLATES
I Elias Allen frontispiece
By courtesy of the Director of the Science Museum, London
II Thomas Gemini’s Astrolabe facing page 20
By courtesy of Henri Michel
III Charles Whitwell’s Compass of Variation 48
By courtesy of the Trustees of the British Museum
IV (a) Charles Whitwell’s Sun and Night Dial 49
By courtesy of the Trustees of the National Maritime
Museum, Greenwich
(b) Elias Alien’s Sun and Night Dial
By courtesy of the Director of the Science Museum, London
V Gunter’s Quadrant, made by Walter Hayes 64
By courtesy of the Director of the Science Museum, London
VI Gunter’s Sector 65
By courtesy of the Trustees of the British Museum
VII The Several Parts of a Survey 86
By courtesy of the Trustees of the British Museum
VIII William Leybourne 87
By courtesy of the Trustees of the British Museum
IX Levelling Instruments 98
By courtesy of the Trustees of the British Museum
X (a) Thomas Tuttell’s Ivory Cross-staff and Back-
staff 99
(6) Jacob Cunigham’s Telescope
Both by courtesy of the Director of the National Maritime
Museum, Greenwich
vii
J
LIST OF PLATES
XI Edmund Culpeper’s Universal Ring-dial facing page 110
By courtesy of the Director of the Science Museum, London
XII The Royal Observatory 130
By courtesy of the Director of the Science Museum, London
MAP
The Work Places of the London Practitioners
between pages 162-3
FACSIMILE
The Scheme of John Dee’s Mathematical Preface
to Euclid facing page 432
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FOREWORD
BY
THE ASTRONOMER ROYAL
T avigation up to and even beyond the sixteenth century
was almost entirely a practical art, in which success de-
-L M pended upon experience, sound common sense and good
seamanship. The navigator had for his use the compass, the log,
and some form of cross-staff; he had to allow as best he could
for the strength of the wind and the set of the tide or current,
and had to estimate his position by a crude method of dead
reckoning. Practically nothing was known about the variation
of the compass.
The education given in English schools was based almost
entirely on Latin grammar; little, if any, mathematics was
taught, while simple arithmetic, which was considered suitable
only for clerks, was entirely neglected. John Flamsteed, the first
Astronomer Royal, who because of ill health had to leave school
in 1660 at the age of fourteen, relates that after he had left his
father taught him ‘arithmetic, including the doctrine of fractions
and the golden rule of three’. John Newton remarked in 1677,
as Professor Taylor mentions, that he had never heard of any
grammar school in England in which mathematics was taught.
The first school in which mathematical instruction was
regularly given appears to have been Christ’s Hospital where, on
■I
the order of Charles II, a mathematical side was started, the :|
mathematics to be taught with a view to its practical application.
This order was prompted by his interest in the development of
the navy and mercantile marine, and by the realization that for
'I
improvements in methods of navigation, which were being made Hl
possible by theoretical advances, to be translated into practice
some knowledge of mathematics was essential for naval officers
and other shipmasters. Even so it proved to be singularly
difficult to find a competent mathematical master, so that I!
Flamsteed was for some while required to add to his already
ix
FOREWORD
onerous duties at the Observatory the instruction in mathe
matics and in the use of instruments of some of the boys from
the mathematical side of the school.
There was in fact for long a complete divorce between practice
and theory: the seamen were ignorant of mathematics and the
mathematicians had no practical experience. In consequence
no basis for technical progress was to be found. It was only
gradually that a demand for instruction in geometry and
astronomy arose to meet the need for improved techniques in
navigation, surveying, gunnery and horology. This need was
supplied in some measure, though inadequately, by the mathe
matical practitioners of London long before it began to be pro
vided by the universities. Many of these teachers were men with
practical experience but of no great education who worked in
close association with the instrument-makers; the text-books
they used were mostly derived from earlier books and showed
no originality of treatment. But there were exceptions; from
time to time new ideas were conceived and improvements in
instruments were made. There was progress, though it was slow.
Professor Taylor has given a fascinating account of these
mathematical practitioners and of the development of ideas,
methods and instruments from Tudor times to early in the
eighteenth century, which forms a valuable contribution to a
little-known epoch in the history of navigation and surveying.
The second part of the work contains a list of the practitioners,
with biographical notes and details of their work. The third part
consists of a list of the more important works on the mathe
matical arts and practices. These biographical and biblio
graphical notes will be invaluable for reference purposes. This
volume embodies a vast amount of historical research, and it is
fitting that its publication should be sponsored by the Institute
of Navigation, whose objects include the encouragement of
research and the promotion of knowledge in navigation and its
associated sciences.
H. SPENCER JONES
Herstmonceux, 1953
X
w
PREFACE
his book is a chronicle of lesser men—teachers, text-book
writers, technicians, craftsmen—but for whom great scien
tists would always remain sterile in their generation. In
the attached catalogue of Mathematical Practitioners a great
name does here and there appear, as when without loss of dignity
a Thomas Hariot shows the sailor how to manage his cross-staff,
or an Isaac Newton polishes his own speculums. But the
majority of those mentioned are important only as members of
a group, a group only very lately thought worth attention.
The book is arranged so as to meet the needs of two classes of
readers. Those with more general interests will find a narrative
unencumbered with footnotes, and may ignore the reference
numbers. The student of the history of science will find the detail
he is likely to want in the Biographies (Part II) and in the
annotated list of Contemporary Works (Part III). These works
are the main source material for the whole book, but a brief
bibliography of secondary sources has been added.
The author’s thanks are due to the Council of the Institute of
Navigation for sponsoring the work, and more particularly to
the Executive Secretary, and his staff, for arranging all the details i
of pubheation, and seeing the book through the press.
The author has also been indebted to the officers of the Oxford
Museum of the History of Science, the Science Museum, London,
the National Maritime Museum, Greenwich, and the Whipple
Museum at Cambridge for many answers to inquiries, as well
as to the Librarians and other officers of the Royal Society, the
Royal Geographical Society, and the British Museum for much
help. Acknowledgment is due also to M. Henri Michel,
Dr Derek Price, and Commander W. E. May, among others,
for permission to use published material.
E. G. R. T.
I
Ralph’s Ride, Bracknell, 1953 •i
xi
