The greate invention of algebra: Thomas Harriot's treatise on equations

335 Pages·2003·2.003 MB·English

by  Stedall J.

TheGreateInventionofAlgebra
Doeyounotherestartle,toseeeverydaysomeofyourinventionstakenfromyou;
forIrememberlongsinceyoutoldmeasmuch(asKeplerhasjustpublished)that
themotionsoftheplanetswerenotperfectcircles. Soyoutaughtmethecurious
waytoobserveweightinWater,andwithinawhileafterGhetaldicomesoutwithit
inprint.AlittlebeforeVietapreventedyouoftheGharlandforthegreateInvention
ofAlgebra.AlthesewereyourdeuesandmanieothersthatIcouldmention;andyet
toogreatreservednessehathrob’dyouoftheseglories...Onlieletthisremember
you,thatitispossiblebytomuchprocrastinationtobepreventedinthehonorof
someofyourrarestinventionsandspeculations.
WilliamLowertoThomasHarriot,6February1610
The Greate Invention
of Algebra
T H O M A S H A R R I O T’S
T R E A T I S E O N E Q U A T I O N S
Jacqueline A. Stedall
CliffordNortonStudentintheHistoryofScience,
TheQueen’sCollege,Oxford,
and
OpenUniversity
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Stedall,Jacqueline.
Thegreateinventionofalgebra:ThomasHarriot’streatiseonequations/JacquelineA.Stedall.
Includesbibliographicalreferencesandindex.
1.Equations 2.Algebra–England–History–17thcentury 3.Harriot,Thomas,
1560-1621–Influence I.Harriot,Thomas,1560-1621 II.Title.
QA211.S772003 512.9’4–dc21 2002042558
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Dedication
ForRobertFox,JohnNorth
andPeterNeumann
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Acknowledgements
I
amindebtedtoanumberoflibrariansandarchivistswhohavehelped
me to locate and use the manuscripts of which this edition is based,
firstandforemosttoColinHarrisandhisstaffattheBodleianLibrary,
Oxford, whohavesooftenandsoreadilyprovidedmewiththehefty
boxescontainingthephotocopiesoftheHarriotandCavendishpapers.Iam
also grateful to Alison McCann of the West Sussex Record Office for her
assistancewiththePetworthpapersandtoLordEgremontforhispermission
to copy and use them. Sarah Wickham of Lambeth Palace Library helped
with great efficiency with the Torporley manuscripts, and the archivists of
theNorthamptonshireRecordOfficewiththeIshampapers.
I would like to give special thanks also to Muriel Seltman who first
introducedmetoHarriot’smanuscripts,andwhohasgivenmemuchwarm
support, and to Stephen Clucas who helped me in researching details of
Harriot’slifeandacquaintances.
While preparing this edition I have held the Clifford Norton Studentship
in the History of Science at The Queen’s College, Oxford, and have been
a member of the Centre for the History of the Mathematical Sciences at
the Open University. I have dedicated this book to three people who have
takenaparticularinterestinthisprojectandwhohavegivenmeunstinting
encouragementandsupport.
TheQueen’sCollege,Oxford J.A.S.
April2002
vii
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Contents
Illustrations xi
INTRODUCTION
I. TheTreatiseonequations 3
Harriot,TorporleyandViète 3
Harriot’snotation 7
TheOperationsofarithmeticinletters 8
TheTreatiseonequations 11
II. Harriot’salgebraafter1621 17
ThePraxis 20
TheCorrector 22
TheSummary 24
III. Harriot’sreputationandinfluence 26
TREATISEONEQUATIONS
Operationsofarithmeticinletters 39
Treatiseonequations
Section(a):Onsolvingequationsinnumbers 45
Section(b):Onsolvingequationsinnumbers 65
Section(c):Onsolvingequationsinnumbers 87
Section(d):Onthegenerationofcanonicalequations 125
Section(e):Onsolvingequationsbyreduction 175
Section(f):Onsolvingequationsbyreduction 239
ix