Introduction.
It is pleasing to note that for this website, around
3000 visits and 30,000 hits are made on a monthly basis, and that around 20,000
files are downloaded monthly to mathematicians and students of mathematics in
around 100 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 not in order have been Euler's De Sono, and some chapters of the
Mechanica I & II , & his Theoria Motus..., parts of Huygens' Horologium
are very popular, Vieta's Sectiones Angulares, 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 into English available 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 some notes to help you along, especially at the start.
The site is
produced, funded, and managed by Dr. Ian Bruce, a retired person living in
Adelaide, S. Australia, 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. At present work is being done on Euler's
Foundations of Integral Calculus, volumes I and II and most of volume III of
which are now complete. Occasionally people send e-mails concerning things they
are not happy about in the text, and their suggestions may be put in place,
provided they are not just airing their own ignorance, so be careful! 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 three years old! Happy browsing! Aug. '09. I. B.
Latest
addition July 30th, 2010, starting from the most recent : : A
translation of E842 Ch.20 By Dr E. Hirsch in his translation of E842 on the
fundamentals of science – this chapter is concerned with equilibrium in fluids;
A translation of E736 by I.Bruce, concerning
infinite series; recently volumes of Euler's Integral
Calculus have been translated
i.e. the Institutiones Calculi Integralis, volumes
11 and 12 in the Opera Omnia Series I, corresponding to volumes I & II in
the original first edition, and devoted to functions of one variable
only; this work overall it is a goldmine of Eulerian ideas on solving
differential equations, and which is gradually being unfolded for you week by
week. Sections I- IV of volume III have now been completed, on first and second
order equations in two variables; there
remains 2 appendices to translate in order to finish Euler's integration
masterpiece. A start has been made on Euler's Calculus of Variations, appended
to Vol. III.
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, 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, and Ch's 1- 6 (parts of which are missing), 7- 20 of E842 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 Differential and Integral
Calculus is underway at present. Volumes I & II of the Integral
Calculus have been completed, as well as Sections I- IV of volume
III, & part of the Appendix. You can access these by clicking: Link to
volume I or Link to
volume II , or Link to volume III.
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.
An annotated translation of Section VIII of Book II of Newton's Principia on sound is presented. 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. July 30th,
2010 latest revision. Copyright
: I reserve the right to publish any translated work in book form. However, if
you are a student, teacher, or just someone with an interest, you 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, especially if you
have any relevant comments or concerns.