Introduction.
It is pleasing to note for this website that around
3000 visits and 30,000 hits are made on
a monthly basis, and around 20,000 files are downloaded monthly to
mathematicians in around 100 countries, of which the U.S. accounts for 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 popular. This site is
unique in that it provides the only translation into English available of a
number of important works. Although I have endeavored to the best of my ability
to render the original Latin texts into their equivalent in modern English,
usually in the present tense as in modern mathematical usage, the texts are
presented with the understanding that they cannot be error-free, and reveal my
own idiosyncrasies to some extent. Usually I provide some notes to help you
along, especially at the start.
The site is produced, funded, and managed by myself, a retired person living in Adelaide, S. Australia, ( I originated in the N.E. of Scotland near the town of Ellon) ; I have a background in math/ physics (I have a Ph.D in atomic physics from Flinders University here in S.A., and a number of publications in various journals, such as Math. Gaz., Fibonacci Q., Am. J. Phys., Eur. J. Phys, etc., over the last 30 years) : my 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 : I have translated Euler's Mechanica , and his Tractus de Motu Corporum Rigidorum.....At present I am working on Euler's Foundations of Integral Calculus. Occasionally people write to me concerning things they are not happy about in the text, and their suggestions usually are put in place. If you feel that there is something wrong somewhere, or if you think that I can provide clarification on some point, please get in touch via e-mail. The amount of labour one spends 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. Occasionally, however, I just seem to have dozed off..... Finally, if you are a person involved in using the contents of this site in some way as class exercises, then I would like to hear from you, just so that I know what use is being made of the material contained here, I do hope that it is not being used to provide meaningless exercises for students. [See the links on the contents pages.]
We are now
three years old! Happy browsing! Aug. '09. I. B.
Latest
addition Feb. 6th, 2010, starting from the most recent : Almost
half of Euler's Integral Calculus has been
completed : at present Part I, Section I ( Ch. I – IX) & Part I, Section II
( Ch. I–VII), Part I, Section III, and Part II, Section I, Ch.1– Ch.VI has been translated; this book it is a goldmine
of Eulerian ideas on solving differential equations, and that is gradually being unfolded for you week
by week. Dr. E. Hirsch has now
translated Ch.I – Ch.IX of E842. Ch. IX is very interesting, as it shows how
close Euler was to understanding kinetic energy relations, where he uses the
word Effectiveness .
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 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. Also papers by Lexell and Euler tr. by J. Sten appear here, and Ch's 1, 2, 3, 4, 5 & 6 (parts of which are missing), 7, 8, & 9 of E842 by E. Hirsch. Link to the contents document by clicking here.
My translation of E015, Book I of Euler's Mechanica has now 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): Theoria Motus Corporum Solidorum seu Rigida. Link to the contents document by clicking here.
A
translation of Euler's Differential and Integral
Calculus has started. At present 1+(9+7+1) +6
chapters have been completed. Link to the
contents document by clicking here.
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. Feb. 6th,
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, especially
if you have any relevant comments or concerns.