Printed Books

RATDOLT: 1482

A huge number of printed editions of Euclid have been produced over the last 500 or so years. The first printed edition was made in May 25, 1482, by the printer Erhard Ratdolt of Venice.  This edition was in Latin and based on the 13th century medieval manuscript produced by Campanus. It is now believed that the Campanus edition was derived from the so-called Adelard II manuscripts as well as other sources, one of which might have been the Greek-Latin translation that was done in Palermo in the 12th century. The Adelard II manuscripts are now believed to have been written by Robert of Chester (1) who used earlier Arabic editions of Euclid as well as a number of Latin editions  (also derived from Arabic copies) including editions by Adelard of Bath (Adelard I), Hermann of Carinthia and possibly others such as Boethius (a very early Greek to Latin translation form the 5th century).

ZAMBERTI (1505), GRYNEAUS (1533)

The introduction of the printing press in the 15th century changed how knowledge was disseminated and resulted in a deluge of books on all topics being printed and sold.  By 1600, Euclid had been translated and printed into most European languages, including a new Greek translation to Latin by Zamberti, 1505. The Greek codex used by Zamberti is unfortunately not known (Riccardi, 1828) but appears to be a Theon-based text.  In 1533, Gryneaus published the first printed Greek edition, apparently based on two Greek manuscripts (Venetus Marcianus 301 and Paris gr. 2343) as well as Zamberti’s Latin edition (Heath, 1925, page 101). The Codex Marciana 301 is most likely located in the Library of Saint Mark, Venice (Italian: Biblioteca Marciana). 

COMMANDINO: 1572

In 1572, Commandino published his Latin version of Euclid which was based on a different set of Greek manuscripts. At least one of these was based on the printed Greek manuscript by Grynaeus in 1533. The precise manuscripts Commandino used, however, is unknown, though it is suggested that he didn’t use the Greek texts held in the Vatican (Davide Pietrini, 2020). Nevertheless, it was Commandino’s edition that ultimately supplanted the original Campanus edition.

BILLINGSLEY: 1570

In the English speaking world, the first English translation of Euclid was by Billingsley in 1570 in London, with the title: “The elements of geometrie of the most auncient philosopher Evclide of Megara”. Other than differences in spelling from today, you may also notice that Euclid is referred to as Euclid of Magara. Unfortunately this was the wrong Euclid. Euclid of Megara was a philosopher who lived around 400 BC. This was  frequent source of confusion during the Renaissance. Billingsley’s copy was translated from the Greek edition by Gryneaus, as well as using information from the Campanus and Zamberti editions. One highly innovative aspect of Billingsley’s book was the use of pop up models in Book XI on solid geometry, which gave readers a better understanding of the proofs.

CLAVIUS: 1574

The final edition worth mentioning from this period is the edition by Clavius in 1574. As Clavius states himself, this wasn’t a new translation, but rather a consolidation of existing editions and commentaries.  It was by far the longest and most complete edition of the Elements ever produced, and collected almost everything that had been published in the previous centuries. It is also famous for being a copy of Euclid, which was translated into Chinese.  There is some variability in the sources on how many editions were printed and their content. 

The Clavius edition does not seem to be a literal copy of Euclid and provides more explanations for some of the steps. I provide an example of Book II, Proposition 4 from Clavius.

Christopher Clavius published his first edition of Euclid's Elements in 1574. He later issued three more revised editions. The total known editions by Clavius are:

"Euclidis Elementorum Libri XV" (Rome 1574, 1589, 1591, 1603, 1605; Frankfort 1612). After his death also these were republished in 1617, 1627, 1654, 1663, 1717, at Cologne, Frankfort, and Amsterdam, and were even translated into Chinese."

The above was taken verbatim from the catholic encyclopedia:  https://www.newadvent.org/cathen/04009a.htm

The list oddly misses the 1607 Frankfurt edition, but this could be an error, and they really meant 1607. I have no other record of a 1605 copy. The 1589 is a two-volume printing. The relationship between the two-volume edition and the single-volume edition is obscure.  However, the 1574 edition appears to be a single volume with 750 pages. The large size of the book probably prompted the release of a two-volume edition in 1589. Volume 1 and 2 can be found here: Volume 1, Volume 2. After that, it isn't entirely clear as to the number of volumes, although I know a volume 2 from 1654 exists. The 1607 edition might also be a two-volume set. 

The 1591 edition returned to a single volume but with now even more pages at 1166 pages. 

Another source from Sphere (see also references here) , a research group at the University of Paris Cité, has the following list: 

1574, 1589, 1591, 1603, 1607, 1607 (twice), 1611-12.

Heath (2nd edition) lists the following editions: 1574, 1589, 1591, 1603, 1607, and 1612.

The last edition, while Clavius was alive, is 1612 since that is the year he passed away at the age of 73.

However, there are posthumous editions such as the 1627 edition and most definitely the 1654 edition, as I have a copy, see also some comments here. 

Copies were also printed in the 18th century, such as this one in 1738. I am sure there are likely to be others.

ROBERT SIMSON: 1756

From the 17th century onwards, many more editions were produced. most notable were editions published by Isaac Barrow (1655),  John Keill (1708),  and Robert Simson (1756). It was Robert Simons' edition that was to become the standard English version of Euclid for many years afterwards and was copied multiple times.  

PLAYFAIR (1860), TODHUNTER (1862), CASEY  (1886)

Towards the end of the 19th century saw the publication of Euclid by John Playfair, the long series of editions by TodHunter for schools in 1862 and further editions by John Casey (1886).  These are just a few names, many more editions were published in this period. 

OLIVER BYRNE: 1847

One particularly interesting edition was by Oliver Byrne who published a truly unique revision using color and pictures to describe the various theorems. 

PEYRARD (1808), HEIBERG (1888), HEATH (1908)

Two other very important editions should also be mentioned. In 1808 Peyrard discovered by a completely new text of Euclid from the Vatican, one that predated Theon's copy from which all copies up to then had been based.  Between 1882 and 1888 Heiberg published the definitive edition of Euclid based on Peyrard's discovery and other sources. Heiberg published his edition in Greek, which though more authentic, was less accessible to many. It was Thomas Heath who finally published in 1908 the definitive edition of Euclid in English based on Heiberg's work. A second edition of Heath's edition came out in 1925 and can still be purchased today.

Key English 19th Century Editions of Euclid.

The 19th century saw a proliferation of editions that were made available to satisfy the need for High Schools and Universities in the UK, Canada and other countries (Except the US, which had largely switched to Legendre's edition of Geometry).

Key editions in this era were by Playfair, Potts (Higher education), Casey, Mackay and Todhunter (High Schools). There were many other editions published both in English and other languages, and each has its own particular interest.

 Todhunter was a prolific writer of mathematical textbooks, and his edition of Euclid became the standard text in English High Schools for many years.  Todhunter's edition was also available in a very compact pocket book edition, which was a popular size in the late 19th century. I wonder if this size became popular because of the growth in the railway. One could perhaps imagine the early commuters reading a few propositions each day in the railway carriage as they traveled to work (I suspect Thomas Heath did just this).

Mackay's book has the feel of a modern layout; Casey's edition is well known because it was essentially a rewrite of the original text.  The order of the books and propositions was unaltered, but the language was changed to make it more modern (by 19th century standards).

Playfair's edition, though published in 1795, was repeatedly published throughout the 19th century. 

Editions of Euclid continued to be published well into the 20th century. School editions were popular, such as Hall and Stevens, which was published first in 1886 but continued to be published up to 1908. 

By this time, even the English had realized that perhaps it was time to switch from Euclid to other repackaged books on geometry.  Although the order and mix of particular theorems changed, many of the proofs in modern textbooks on geometry are the same as those found in Euclid. It is remarkable that the proofs we find in the D'Orville Byzantium manuscript from 888 AD, the 5th-century commentaries by Proclus, or the 1st-century commentaries by Heron of Alexandria contain proofs still found in modern books on geometry printed today in 2026 AD. 

EDITIONS CURRENTLY IN PRINT

It is surprising that Euclid is still being published today in new editions.  This is the list of editions currently in print:

Buy these three volumes by Thomas Heath, a monumental series that goes into great depth:

The Thirteen Books of Euclid's Elements, translation and commentaries by Heath, Thomas L. (1956) in three volumes. Dover Publications. ISBN 0-486-60088-2 (vol. 1), ISBN 0-486-60089-0 (vol. 2), ISBN 0-486-60090-4 (vol. 3)

I don't have this copy, but it looks like a reprint of the above in one volume:

The Elements: Books I–XIII – Complete and Unabridged (2006) Translated by Sir Thomas Heath, Barnes & Noble ISBN 0-7607-6312-7.

This is a popular  retypeset edition based on Heath, with clear text and figures:

Euclid's Elements – All thirteen books complete in one volume, based on Heath's translation, edited by Dana Densmore et al. (2002), Green Lion Press ISBN 1-888009-18-7.

If you want to see a Greek version alongside the English text:

Euclid's Elements in Greek: Vol. I: Books 1-4 by  Richard Fitzpatrick (2007), ISBN 978-1411626720

This is a rendering of Euclid in a modern guise, also available as a free PDF. It is partly based on John Casey's edition, which was the first modern (19th century) attempt to update Euclid:

Plane Geometry (Euclid's Elements Redux) Books I–VI, (2017)  based on John Casey's translation, edited by Daniel Callahan, ISBN 978-1977730039

Euclid's Elements with Exercises edited by Kathryn Goulding, (2017) ISBN 978-0692925942

Oliver Byrne's Elements of Euclid, Art Meets Science, 2022, ISBN 978-1528770439. This turns out to be a simple facsimile of the original book, and the printing quality is not very good.

Byrne's Euclid: The First Six Books of the Elements of Euclid,  2023,  ISBN 979-8386507879, Newell Jensen.  The author also provides a free electronic copy at his web page. 

Of the Oliver Byrne editions currently in print, this is the edition I would probably recommend:

Oliver Byrne: The First Six Books of the Elements of Euclid (Varia) (Multilingual Edition) ISBN-13‏‎ 978-3836577380 

Finally this is my own edition of Book I. It's in color so that all angles and lines are color-coded, and I have a history of the book in the first chapter:

Euclid's Elements: Book 1, A new rendering, 2023, ISBN 978-1732548640

Classical Editions Available from archive.org and Google.

• Preclarissimũ opus elemento, Campanus of Novara (1482)

•  Commentary by Ṭūsī, Naṣīr al-Dīn Muḥammad ibn Muḥammad, 1201-1274  (1485)

• The elements of geometrie of the most auncient philosopher Evclide of Megara, Billingsley (1570)

• Euclidis elementorvm libri XV, Commandino, Federico (1572)

• Euclidis elementorum libri XV : accessit XVI de solidorum regularium comparatione, Vol 1, Clavius (1574)

• Euclides Elements of geometry: the first VI books, Thomas Rudd (1651)

• Euclidis Elementorum libri XV  Isacc Barrow (1659) (Not a good copy)

• The Elements from the Latin translation of Commandine by John Keill (1723)

• The First Six Books of Euclid by John Playfair (1833)

• The Elements by Robert Simson (1838)

• Oliver Byrne (1847)

• Todhunter's Euclid (1869)

• Euclid's elements of geometry book I, Francis Young (1871)

• Euclid’s Elements of Geometry Robert Potts (1876)

• The First Six Books by John Casey (1885)

•  Euclid's Elements of geometry: books I. II. III. IV., VI and portions of books V. and XI., Layng, A. E. (1891)

• Euclid's elements of geometry, H. M. Taylor (1893)

• A text-book of Euclid's Elements, Stevens and Hall (1896)

• Euclid's elements: books I, II, III, McKay and Thompson, (1902)

• The Elements by Sir Thomas Heath (1908)

• The following site contains a huge number of manuscripts in addition to Euclid's Elements

http://www.wilbourhall.org/