Introduction.
It is pleasing to note that for this website, around
3500 visits and 30,000 hits are made on a monthly basis, and that around 25,000
files are downloaded monthly to mathematicians and students of mathematics in
around 120 countries, of which the U.S. accounts for approximately half, on a
regular basis. There is, of course, some seasonal variation depending on
semester demand. The most popular files
downloaded recently not in order have been Euler's Integration Ch.I, and some
chapters of the Mechanica I & II , parts of Huygens' Horologium are very
popular, some early Euler papers, esp. E025, and various parts of Gregorius and
James Gregory's Optica Promota, and there is of course a constant demand for
material on logarithms, and Harriot's book salvaged from his posthumous notes
is of interest to browsers. Lately Jim Hanson's work on Napier's Bones and
Promptuary have been very popular. This site is unique in that it provides the
only translation available into English of a number of important works. Texts
are presented with the understanding that they cannot be error-free, and reveal
the translator's idiosyncrasies to some extent. Usually there are some notes to
help you along, especially at the start.
This site is
produced, funded, and managed by Dr. Ian Bruce, an independent researcher whose
aim is to provide the modern mathematical reader with a snapshot of that
wonderful period, from roughly the year 1600 to 1750 or so, when modern
analytical methods came into being, and an understanding of the physical world
was produced hand-in-hand with this development. The work is an ongoing process
: translations of Euler's Mechanica , and his Tractus de Motu Corporum
Rigidorum.....are given, as well as his integral and differential calculus
textbooks. At present work on Newton's Principia is under way, and Book I is
almost completed; this includes notes by the Jesuit brothers Leseur & Janquier
from their annotated edition, and by myself, as well as ideas from the books by
Chandrasekhar, Brougham & Rouse, etc . The
traditional translates of the Principia do not give extensive notes, if
any at all. Some of Newton's methods are
obscure, and it has pleased me to be able to unravel some of these. The
Principia never was, and never will be, an 'easy read'; however, Newton was a
man from the new age of mathematical science initiated by Kepler and Galilio,
opening a hidden door via calculus, and who ushered in almost single handedly
the world of mathematical analysis of physical phenomena: Newton's view of the
world, controversial at the time because of the idea of action at a
distance, is still the one largely that
we accept.
Occasionally people send
e-mails concerning things they are not happy about in the text, and their suggestions
may be put in place, if they have a point. If you feel that there is something
wrong somewhere, or if you think that further clarification on some point can
be provided, please get in touch via the
e-mail hyperlink. The amount of labour spent on a given translation suffers
from the law of diminishing returns, i.e. more and more has to be done in
revision to extract fewer and fewer errors. The site is now 5 years old!
Happy browsing! IAN BRUCE. September 2011.
Latest
additions Jan. 16th, 2012: Starting from
the most recent, a translation of the 3rd edition of Newton's
Principia continues with notes added according to Leseur & Janquier from
the 'Jesuit edition', and from the work by Brougham & Routh, especially in
Book II, as well as from other commentators, especially Chandrasekhar; all the
diagrams have been redrawn :at present all the Sections I–XIV of Book I have
been translated, and all the Sections I–IX of Book II are presented here; and half
of Book III as far as Prop. XXXV, which includes a lot of lunar theory ; together with the prefaces for the three
editions by Newton, the Editor's preface to the second edition by Roger Cotes,
and the Definitions and Axioms. Prior to
that, some of Euler's work on the theory of numbers has been presented :
E134, E026 & E054 together [they
deal mainly with Fermat's Little Theorem] with a letter in translation sent by
Fermat to Wallis in 1658, which is interesting, as it shows how Fermat regarded
his excursions into the properties of numbers, and Euler's later reaction to
his methods. Euler's Institutiones Calculi
Differentialis, The Foundations of Differential Calculus, has now been
translated in full; the three volumes of
Euler's Institutiones Calculi Integralis, on the Foundations of
Integral Calculus have been translated
also, corresponding in total to volumes 10,
11, 12 and 13 in the Opera Omnia Series I of Euler's works. This is the first
time a complete translation of these works on the calculus, which laid the
foundations for the future development of mathematical analysis at the close of
the 18th Century, has
appeared in English and may still be of interest to historians of mathematics.
However, do not expect a light read, as there is in excess of 2000 pages!
Mirifici Logarithmorum Canon Descriptio..... (1614), by John Napier. This seminal work by Napier
introduced the mathematical world to the wonders of logarithms, and all in a
small book of tables. Most of the book, apart from the actual tables, is a
manual for solving plane and spherical triangles using logarithms. Included are
some interesting identities due to Napier. Jim Hanson's work on Napier's
Promptuary and Bones is in place here, with a few other items in the Napier
index Link to the contents document by clicking
here.
Mirifici Logarithmorum Canon Constructio... (1617); A posthumous work by John Napier. This book along with the above, started a revolution in computing by logarithms. The book is a 'must read' for any serious student of mathematics, young or old. Link to the contents document by clicking here.
Arithmetica Logarithmica, (1624), Henry Briggs. The theory and practise of base 10 logarithms is presented for the first time by Briggs. Link to the contents document by clicking here.
Trigonometria Britannica, (1631), Henry Briggs. The methods used for producing a set of tables for the sine, tangent, and secant together with their logarithms is presented here. No Latin text provided. Link to the contents document by clicking here.
Angulares Sectiones, (1617), Francisco Vieta. Edited and presented by Alexander Anderson. Vieta's fundamental work on working out the relations between the sine of an angle and the sine of multiples of the angle is set out in a labourous manner. No Latin text provided. Link to the document by clicking here. It is 25 pages long!
Artis Analyticae Praxis, (1631), 'from the posthumous notes of the philosopher and mathematician Thomas Harriot' , (edited by Walter Warner and others, though no name appears as the author), ' the whole described with care and diligence.' The almost trivial manner in which symbolic algebra was introduced into the mathematical scheme of things is still a cause for some wonder; it had of course been around in a more intuitive form for a long time prior to this publication. Link to the contents document by clicking here.
Optica Promota, (1663), James Gregory. Herein the theory of the first reflecting telescope and a whole theory for elliptic and hyperbolic lenses and mirrors is presented from a geometrical viewpoint. Link to the contents document by clicking here.
Opus Geometricum quadraturae circuli, Gregorius a St. Vincentio, (1647) (Books I & II only at present). A great march via geometric progressions expressed geometrically is undertaken by Gregorius as he examines the idea of a limit, refuting Zeno's Paradox; moving on eventually to discovering the logarithmic property of the hyperbola, before stumbling on the squaring of the circle. This is a long term project! Link to the contents document by clicking here.
Some Euler Papers solving problems relating to isochronous and brachistochrone curves are presented in E001 and E003; a dissertation on sound in E002; Euler's essay on the location and height of masts on ships E004; while reciprocal trajectories are considered in E005 (1729); E006 relates to an application of an isochronous curve; E007 is an essay on air-related phenomena; E008 figures out catenaries and other heavy plane curves; E009 is concerned with the shortest distance between two points on a convex surface; E010 introduces the exponential function as an integrating tool for reducing the order of differential equations; E011 is out of sequence, concerns transformations of differential equations; Ricatti's 1724 paper on second order differential equations is inserted here; E012 & E013 are concerned with tautochrones without & with resistance; E014 is an astronomical calculation; all due to Leonard Euler. E019, E020, E025, E026 & E054 & E134 & Fermat letter to Wallis, E031, E041, E044, and E045 are present also, some of which are referred to in the Mechanica; E736. Also papers by Lexell and Euler tr. by J. Sten appear here incl. E407 recently, and translations of E842 & E81 by E. Hirsch. Link to the contents document by clicking here.
My translation of E015, Book I of Euler's Mechanica has been completed. This was Euler's first major work running to some 500 pages in the original, and included many of his innovative ideas on analysis. This is a complete translation of one of Euler's most important books. Link to the contents document by clicking here.
My translation of E016, Book 2 of Euler's Mechanica has also been completed; this is an even longer text than the above. Both texts give a wonderful insight into Euler's methods, which define the modern approach to analytical mechanics, in spite of a lack of a proper understanding at the time of the conservation laws on which mechanics is grounded. Link to the contents document by clicking here.
The translation of Euler's next major contribution to mechanics is now complete (E289); this contains the first definition of the moment of inertia of a body, and also develops the mathematics of adding infinitesimal velocities about principal axes: Theoria Motus Corporum Solidorum seu Rigida. Link to the contents document by clicking here.
A
translation of Euler's Foundations of Integral Calculus
is now complete. You can access these by clicking: Link to
volume I or Link to
volume II , or Link to volume III.
A
translation of Euler's Foundations of Differential
Calculus is now complete. You can access these by clicking: Link to DifferentialCalculus .
An early translation of Euler's Letters to a German Princess E343, is presented here in mostly subject bundles. These 233 little essays give a rare insight into Euler's mind, and to the state of physics in the 1760's. Link to the contents vol.1 document by clicking here.
Link to the contents vol.2 document by
clicking here.
Progress has been made in a new translation of Newton's Principia; this translation includes resetting of all the original type, new diagrams, and additional notes from several sources: at present the prefaces, including the extended one of Cotes, the Definitions, Axioms, and all the Sections 1–14 of Book I are available, together with all the Sections 1–9 of Book II; an earlier annotated translation of Section VIII of Book II of Newton's Principia on sound is now complete and included in the main flow of the text, which helps in understanding Euler's work De Sono. A start has been made on Book III, with the System of the World as far as Prop. XXXV. Link to the contents document by clicking here.
An annotated translation of Johan. Bernoulli's Vibrations of Chords is presented. Link to the contents document by clicking here.
An annotated translation of Christian Huygens' Pendulum Clock is presented. Link to the contents document by clicking here.
An annotated translation of Brook Taylor's Methodus Incrementorum Directa & Inversa is presented. Link to the contents document by clicking here.
The Lunes of Hippocratus are extended by Wallenius in a much neglected paper presented 'pro gradu' in 1766 at the Royal Academy of Abo (Turku, in Finland); the student defending the paper was Daniel Wijnquist; a full geometrical derivation of each lune is given, followed by a trigonometric analysis. I wish to thank Johan Sten for drawing my attention to this work, and for his help in tracking down an odd reference. Link to the document by clicking here.
Ian Bruce. Jan.16th ,
2012, latest revision.
Copyright : I reserve the right to publish any translated work in book form.
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can copy part or all of the work for legitimate personal or educational uses.
Please feel free to contact me if you wish by clicking on my name here,
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