More than two millennia after Elements was written by the Greek mathematician Euclid, it made its appearance in Tamil. It was translated by a Christian Missionary named Henry Bower and published by the Church Mission Press in Palayamkottai in 1861. A couple of months ago, we shared the first book in this translation on the IMSc website.
The original Elements consists of thirteen books covering geometry, number theory, and logical deduction. It systematically presents definitions, postulates, and propositions, providing rigorous proofs for theorems. Its influence on our way of thinking did not stop just with science and mathematics, but has impacted language, religion and art.
Many years ago, my interest in popular science and maths led me to Thomas Heath’s English translation of Elements. However, I didn’t engage with the text enough to appreciate its historical importance, and my interest faded over time. This was until last year, when the book came into my field of view again. I was incessantly looking for the right Tamil words for scientific and mathematical terms while translating Vigyan Pratibha educational material for school students along with Uthra Dorairajan from DG Vaishnav College, Chennai. Somewhere along the way, I remembered Euclid’s Elements and started wondering if it had been translated into Tamil. An online search didn’t yield many results, usual archival sources returned empty and I couldn’t find anything in libraries or bookstores. But I was fortunate to be at IMSc, a great place to mine information about this seminal work that has inspired mathematical thought and spawned many translations.
Euclid's proof of the Pythagorean theorem involves constructing squares on each side of a right triangle and then proving that the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides. Artist Crockett Johnson’s painting (header image) was inspired from this proof, and is among the first in his series of geometric paintings.
The history and journey of Elements has been recorded beautifully in Benjamin Wardhaugh’s book 'Encounters with Euclid: How an Ancient Greek Geometry Text Shaped the World’. When Euclid’s Elements first came into print in the 16th century, the German printer Erhard Ratdolt was forced to adopt new printing techniques to accommodate its many geometric figures. In the 17th century, Baruch Spinoza, an influential Dutch philosopher, used Euclid’s style of reasoning to write his book ‘Ethics Demonstrated in Geometrical Order’. Instead of points, lines and angles, Spinoza dealt with God, mind, emotions, human bondage and freedom. Abraham Lincoln was deeply influenced by Elements and is said to have studied its first six volumes. In Steven Spielberg’s biographical film, we see Daniel Day-Lewis as Lincoln charismatically justifying equality through the self-evident and common notions of Euclid (Things equal to the same thing are also equal to one another - Common Notion 1, Book One). More recently, the American cartoonist and illustrator Crockett Johnson, found inspiration in Elements among other books to create over a hundred geometric paintings in an amalgamation of art and science.
Elements has been translated numerous times, driving movements that influenced mathematical thought and generated new ideas across the world. In the 8th and 9th centuries, it was among the classic texts in various languages that were translated in the intellectual epicenter of Baghdad. There have been multiple translations of the books into Arabic.The polymath Omar Khayyam even explained the difficulties in its postulates. In a relay of recitation and translation, a Latin version was generated from Arabic via Spanish in 12th century England. In a similar change of hands across languages, Xu Guangqi and Matteo Ricci worked on the Chinese translation of Elements in 17th century China. In his diaries, Ricci points to challenges in translation arising from differences in grammar between the east and west, and highlights the importance of the text as a crash course in logic. In 18th century India, Jagannatha Samrat translated the text into Sanskrit and there are said to be versions of it in Urdu, Marathi, Hindi, Oriya among other Indian languages.
In search of a translation in Tamil, I spoke to several maths researchers at IMSc who guessed that there must be one but didn’t know for sure. I found a concrete lead when R Ramanujam, a former faculty in Computer Science, said that Elements was indeed translated into Tamil in the nineteenth century. With this information, I approached our librarian Maruthu Pandiyan and asked for help in locating a copy. He contacted many physical libraries in Chennai and Tamil Nadu to no avail, and found only a mention in the Jaffna library. He eventually located a digital copy in the British Library. I was really excited to have found the translation from 160 years ago that seems to have been lost from our collective memory. I started putting up the text on the IMSc website and took about four months to complete the task. The Tamil vocabulary used wasn’t very different from today with the exception of some words and spellings.
We have found and shared only the first book in Euclid’s treatise, but I hope that we can find the rest of them. Elements is an expression of our mathematical thought and is invaluable to read in one’s native language, like the translations of literary and religious texts that we make our own. With modern tools at our disposal, it is much easier to translate seminal scientific and mathematical texts into various languages and is a mission worth our time. We may have far surpassed the mathematics described in the Elements, but it is an important chapter in the history of mathematics, which holds insights about the path of reasoning and generation of new scientific ideas.
Henry Bower's translation of the first book of Euclid's Elements into Tamil.
