Not much is known about Ziegenbalg’s life.^{[3]} His father was the German Pietist preacher, missionary, and proto-Indologist Bartholomäus Ziegenbalg (1682 or 1683–1719).^{[4]} His mother was Maria Dorothea Ziegenbalg (née Salzmann) (b. 1696). At the call of King Frederick IV of Denmark–Norway (r. 1699–1730), Bartholomäus Ziegenbalg worked as a missionary in Tranquebar, a Danish colony on the Coromandel Coast (now Tharangambadi in Tamil Nadu, India), from 1706 to 1714. He married Maria Dorothea in Germany in 1715, and in 1716 returned to Tranquebar with her. After the death of Bartholomäus Ziegenbalg in 1719, Maria Dorothea married Oluf Lygaard (1691–1741), the Deputy Commandant of Tranquebar, in 1720. The family moved to Copenhagen in 1721.^{[5]}

E. G. Ziegenbalg was born in 1716. Several sources state that he was born on the ship during his parents’ journey to India,^{[6]} though Jeyaraj [2019, 116] holds that he was born after his parents’ arrival in Tranquebar. After his mother’s marriage to Oluf Lygaard in 1720, he moved with them to Copenhagen in 1721.

In the preface to his translation of the *Elements*, Ziegenbalg described his education: A two-year stipend from King Christian VI of Denmark–Norway (r. 1730–1746) allowed him to study theology at the university in Jena in Germany. After completing his studies in Jena in 1738, he felt that he lacked the necessary talent to be a pastor or hold an academic chair in theology. King Christian VI then allowed him to spend two years in England to study the mathematical sciences, a subject he was interested in and had studied previously at the universities in Tübingen (see below) and Jena. Ziegenbalg wrote that he worked diligently on mathematics while he was at the universities in Tübingen and Jena, during his two years in England, and for another three years after his return (to Denmark, presumably). As the culmination of these many years of studying mathematics, Ziegenbalg dedicated his translation of Euclid’s *Elements* to King Christian VI.

The records of the University of Tübingen [Bürk and Wille 1953, 98] show that Ziegenbalg was part of a group of pupils from the monastic school at Maulbronn Monastery in Baden-Württemberg, Germany, who matriculated on 26 October 1735. Ziegenbalg received a stipend (on the grounds that his father had passed away) to the Tübinger Stift. The Tübinger Stift, which has a close relationship to the University of Tübingen, is a “study house” offering room, board, and coursework to prospective pastors and teachers that is owned by the Evangelical-Lutheran Church in Württemberg. On 21 November 1735, Ziegenbalg was awarded a baccalaureate degree. He was dismissed from the Tübinger Stift in 1736. It is not clear why he was dismissed, but it was presumably because he was awarded a royal stipend from Denmark to study theology at the university in Jena.

It is possible that Ziegenbalg’s interest in mathematics was kindled by the lectures of Johann Conrad Creiling (1673–1752) at the University of Tübingen.^{[7]} According to the University of Tübingen’s *Ordo studiorum* (a list of courses offered at the university) for 1734, Creiling offered instruction in mathematics at the university.^{[8]} More specifically, Creiling offered to read parts of *Wolffi Epitomen* with interested students. *Wolffi Epitomen* must refer to Christian Wolff’s *Elementa matheseos universae* (1713–1715). As we will see in a later section, Ziegenbalg referred to the Danish translation of the German version of this text (Wolff published both a German and a Latin version).

Ziegenbalg matriculated at the University of Jena on 2 November 1736 [Köhler 1992, 284]. At Jena, he studied under the Lutheran theologian Johann Georg Walch (1693–1775). On 11 October 1738, Ziegenbalg defended a thesis written by Walch, entitled *Historia transsubstantiationis pontificiae* [Walchio and Ziegenbalg 1738]. Such a defense was not an unusual exercise for an advanced student of theology at the time. The thesis is dedicated to Johan Ludvig Holstein (1694–1763), a Danish aristocrat who served as prime minister of Denmark from 1735 to 1751 and in 1742 was one of the founders of the Royal Danish Academy of Sciences and Letters. Holstein had influence in the College of Missions, which controlled the Danish mission in Tranquebar. He was also, like Ziegenbalg’s father, a Pietist. It is possible that the funding for Ziegenbalg’s studies in Germany and England came from Holstein or from funds controlled by him.

It is unclear where in England Ziegenbalg studied mathematics. Hirsching [1794–1815, xvii:126] states that Ziegenbalg stayed in Oxford for seven years (a span considerably longer than the two years Ziegenbalg himself says he spent in England), but Jeyaraj [2019, 117] says he studied mathematics in London. The University of Oxford has no record that Ziegenbalg matriculated there [Foster 1888], though it is possible that he studied informally in Oxford with a tutor. Christensen [1895, 169] notes that Ziegenbalg visited schools for craftsmen in London, which means he must have spent time in that city.

As noted above, Ziegenbalg wrote in the preface to his translation of Euclid that he worked on mathematics in Germany, during his two years in England, and for another three years after his return to Denmark. Since the translation was published in 1744, Ziegenbalg must have returned to Denmark from England around 1741, which is consistent with the fact that he completed his studies in Jena in 1738. That Ziegenbalg was in Denmark in 1741 follows from a note in [Æreboe 1889, 34, fn. 1] that he applied to succeed his stepfather Oluf Lygaard, who passed away that year, as manager of stamped paper (*stempelpapirforvalter*). In Copenhagen, Ziegenbalg met with German Lutheran missionaries, who would stay in the city for a while before traveling to Tranquebar. The missionaries held Bartholomäus Ziegenbalg and his missionary methods in high regard and are said to have appreciated meeting his son [Jeyaraj 2019, 117].

In 1747, Joachim Frederik Ramus (1685 or 1686–1769),^{[9]} who was professor of mathematics at the University of Copenhagen and Ziegenbalg’s mentor, was given an exemption from lecturing. Ziegenbalg became Ramus’ substitute and delivered the mathematical lectures at the university. He was also appointed “designated professor” (*designeret professor*); that is, he was named as Ramus’ successor. But Ziegenbalg passed away before Ramus, and therefore he never held a professorship in mathematics at the University of Copenhagen.^{[10]} Ziegenbalg wrote two university programs (public announcements issued by the rector of the University of Copenhagen) in Latin in 1755 [Nielsen 1912, 220], one on the usefulness of geometry, entitled *De utilitate geometriæ*,^{[11]} and the other entitled *De præcipuis frigoris qualitatibus et effectibus* (*On the Special Qualities and Effects of Cold*).

Also in 1747, Ziegenbalg became a member of the Royal Danish Academy of Sciences and Letters. He published three treatises in the proceedings of the Academy [Nielsen 1912, 220]: *Observationer, som ere gjorte over Veyrliget og Vindene i Kiøbenhavn fra Dec. 1745 til Juni 1748, samt kort Afhandling om slige Observations Nytte* (*Observations, which are Made of the Weather and Winds in Copenhagen from December 1745 to June 1748, as well as a Brief Treatise on these Observations’ Usefulness*); *En Merkværdig Egenskab, funden hos Snegle* (*A Peculiar Characteristic Found in Snails*); and *Aarsagen til Iis* (*The Cause of Ice*).

Ziegenbalg passed away on 17 June 1758 at the age of 41 or 42. (Although according to Hirsching [1794–1815, xvii:126], the date was 17 June 1759.) Poggendorff [1863, ii:1408] writes that Ziegenbalg died in Copenhagen.

The Danish translation of Euclid was Ziegenbalg’s only written contribution to mathematics. The fact that his other publications were on different subjects than mathematics is peculiar, but also typical for a time when many scholars were polymaths. As a result, it is not possible to assess Ziegenbalg’s mathematical talent. Christensen [1895, 214] assumes that Ziegenbalg, who left theology to pursue his interest in mathematics, must have had some mathematical ability. But as Nielsen [1912, 264] notes, the only thing that can be said with certainty is that he was insignificant as a mathematical writer.

Ziegenbalg’s translation never appeared in a second edition or printing. Hans Christian Linderup, who taught mathematics at Metropolitanskolen (at the time a prestigious secondary school in Copenhagen), wrote that he decided to publish a new translation of the *Elements* because it was difficult for his students to find copies of Ziegenbalg’s translation [Linderup 1803, preface]. Linderup’s translation, the second translation of Euclid’s *Elements* into Danish, was published in 1803 (the translation covers Books 1–6, translated from the Greek text of [Gregory 1703]).

[3] The following account is drawn from Worm [1773, ii:643–644]; Hirsching [1794–1815, xvii:126]; Nyerup and Kraft [1820, 685]; Poggendorff [1863, ii:1408]; Christensen [1895, 214 and passim]; Nielsen [1912, 220 and passim]; and Jeyaraj [2019].

[4] See [Sweetman 2003, 104–126] for an account of Bartholomäus Ziegenbalg’s life, missionary work, and contributions to Indology. Sweetman [2003, 107] and Jeyaraj [2006, 1] give 1682 as the birthyear of Bartholomäus Ziegenbalg, whereas Nyerup and Kraft [1820, 685] give 1683.

[5] The years of Maria Dorothea’s birth, marriage to Bartholomäus Ziegenbalg, journey to India, marriage to Oluf Lygaard, and journey to Copenhagen are all recorded in an engraving from 1737 by Johann Jacob Haid, which is kept at the Royal Danish Library and available online at http://www5.kb.dk/images/billed/2010/okt/billeder/object396288/da (accessed 14 March 2023). Jeyaraj [2019, 101] states that Maria Dorothea was born in c. 1693. It is not clear when Maria Dorothea passed away. A note in [Æreboe 1889, 33–34, fn. 1] states that she was alive in 1741, when her second husband, Oluf Lygaard, passed away. Furthermore, a son of Lygaard and Maria Dorothea named Johannes Jacobus (Johan Jacob) Lygaard was born in Copenhagen in 1739, but attended school in Flensburg (then a city in the Duchy of Schleswig, a part of Denmark–Norway, but now in Germany) from 1750, see [Achelis 1966, 344]. Maria Dorothea must have relocated to Flensburg after the death of Oluf Lygaard in 1741. Jeyaraj [2019] gives an account of the life of Maria Dorothea Ziegenbalg. However, it is incorrectly stated in that account that Maria Dorothea passed away in 1722, and that Oluf Lygaard passed away before her within a year after the family’s arrival in Copenhagen ([Jeyaraj 2019, 116]).

[6] Worm [1773, ii:643], Nyerup and Kraft [1820, 685], Poggendorff [1863, 1408], and Christensen [1895, 214] state that Ziegenbalg was born on the ship.

[7] For information about Creiling, see [Betsch 2005].

[8] The *Ordo studiorum* for 1734 is available online at http://idb.ub.uni-tuebingen.de/opendigi/LXV19_fol_1734 (accessed on 29 August 2021). Unfortunately, the *Ordo studiorum* for 1735 and 1736 are not available, but the one for 1737 can be found online at http://idb.ub.uni-tuebingen.de/opendigi/LXV19_fol_1737 (accessed 29 August 2021).

[9] For information on Ramus, see for example [Nielsen 1912, 163–164 and passim].

[10] Glunk et al. [2021, 45] and Jeyaraj [2019, 117] incorrectly state that Ziegenbalg was professor of mathematics at the University of Copenhagen.

[11] The copy of *De utilitate geometriæ* in the Royal Danish Library is unfortunately lost (personal communication from the Royal Danish Library, 16 June 2021).