Hellenic Open University, GREECE maria1979@her.forthnet.gr
Abstract
The subject of this paper is the transmission of European mathematical knowledge to Greece in the 18th and early 19th century, i.e. during the final decades before the Greek Revolution, mainly through mathematics textbooks. This event is illustrative of the dissemination of scientific information in the wider area of Europe. . In an age (the pre-revolutionary period), when there was an endeavour to advance Greek education and stimulate spiritual awakening, Greek scholars realised that the most important thing was not only or even mainly the production of original work, but the transmission of knowledge, in the form of translations or compilations, from Europe, where scientific and philosophical knowledge had long been developed to a high degree. And this was exactly what they did.
Of the 28 mathematics textbooks which circulated in printed form during the 18th and the first decades of the 19th century, 11 are translations of Western European works, such as those of Tacquet, Metzburg, Euler and others, while the rest are compilations, as is expressly stated in the title or preface of most. Apart from these, however, several other works which remained in manuscript form are also the result of compilation or translation efforts.
To begin, I would like to note that all the people mentioned in this paper are among the most important scholars of the Greek nation under Ottoman rule in the 18th and early 19th centuries.
The fall of the Byzantine Empire was followed by about two and a half centuries whose main feature was sterile scholasticism. Sciences became a marginal part of the curriculum1, as Ottoman rule discouraged the diffusion of
1 For more details, see M. Terdimou 2006.
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contemporary theory and the Patriarchate remained staunchly faithful to theology and grammar as the only appropriate sources of education. During these centuries, Greek mathematical education was ensured by Byzantine reckoning manuals, Emmanuel Glyzonios‘s2 Arithmetic (20 editions from 1568 [Venice] to 1823), and simple mathematical textbooks. Twelve anonymous Arithmetic manuscripts have been recorded up to and including the 17th century, with twelve anonymous manuscripts containing elements of Euclidean Geometry and two with excerpts from works by Euclid, Proclus, Psellos and Nicomachos Gerasinos (Karas 1992).
Of course, this situation arose from and was sustained by the particular circumstances of Hellenism, circumstances which not only did not stimulate interest in modern scientific thinking but even caused the isolation of the Greek nation from Europe. Thus, at the beginning of the 18th century, with rare exceptions (Sougdouris, Papavassileiou, Notaras), scholars had almost no scientific education.
In the late 17th century the Ottoman Empire, in its attempt to adjust to the new political climate developing in Europe, awarded privileges to the enslaved Greeks, who were eventually able to control trade and diplomacy to a great extent, especially following the Treaty of Küçük Kaynarca (1774), which contributed to the development of trade. The creation of the commercial class, the development of the Phanariot class and their rise to the rule of the Danube Hegemonies, resulted in the creation of novel views and a new intellectual awareness among the Greeks. More and more social classes realised that, from then on, society would improve only through knowledge arising from a systematic education and remediation of the sciences, and not through an empirical relationship with matters, which was no longer considered sufficient. The number of scholars studying in the West increased substantially.
During the first decades of the 18th century, the main places of study were the Italian universities, especially those of Padua and Pisa. During the last decades prior to the Greek Revolution of 1821, Greek scholars showed a preference for French and German or German-speaking universities (Vienna, Halle, Göttingen), particularly Vienna, where there was a significant Greek community and which was to become the most important publishing centre for Greek textbooks in the 18th century. It should be noted that during this period, there was a prevalent view that Germany boasted ―first-class physicists and mathematicians‖, and that nowhere in the world were the natural sciences so solidly taught as at German universities (Karas 1993, pp 37-39).
After completing their studies, many scholars returned home, bringing with them the new scientific knowledge with which they had come in contact with. In other words, the return of sciences to the Greek intellectual world was a transference of knowledge from Europe, where the major scientific achievements of the 16th and 17th centuries had laid the foundations of modern mathematics and natural sciences. The channels of scientific thought traversing the Old World were gradually reaching the Greeks, in a typical example of the transmission of scientific knowledge in the wider European area.
From the first decades of the 18th century, efforts began for the foundation of schools and libraries, and the translation or writing and publication of mathematics textbooks to serve primarily educational needs.
Education was now organised, as it had not been earlier, and the rising commercial class was the most important social body for the cultivation of letters. Educators were no longer sought after in ecclesiastical circles alone, and the proposed education system began to specialise.
The number of mathematical works published, particularly from the latter half of the 18th century onwards, is impressive, especially compared to that of previous centuries. Approximately 30 titles were published, not counting commercial literature and equivalence tables. These are works of Arithmetic, Geometry and Algebra; some contain both Arithmetic and Algebra, while some even include Calculus.
On closer examination of these books, it is immediately apparent that 11 are translations of Western European texts, while the rest are compilations, as expressly stated in the title or preface of most of them3. Apart from these, however, several other works which remained in manuscript form are also the result of compilation or translation.
This observation, of course, is neither surprising nor impressive, but only to be expected: at a time when efforts were being made to improve education and awaken the intellect, scholars realised that what was most important was not only, or even mainly, the production of original works, but the transmission of knowledge, in the form of compilations or translations, from Europe, where scientific and philosophical knowledge were already developed. They knew that modern European thought, combined with their ancestral heritage, could reform the intellectual climate that had held sway over the enslaved Greek nation for centuries. They also knew that education is the strongest means of acquiring a national conscience, and therefore the best motivating force for people trying to gain their freedom. The following fragment from the Greek review Kalliopi (Vienna, 1819-1821) is characteristic of this mentality: We steal ideas from philosophers and clothes from the erudite
2 Emmanuel Glyzonios or Glyzounis (1530-1596), from the island of Chios, studied medicine and letters in Italy. His Arithmetic was the master-key which covered the public‘s daily needs.
3 Most contemporary works are ―paraphrases, epitomes, compilations or simply translations of Western European works, from every branch of theoretical and scientific knowledge‖: Henderson (1977), p.17.
to dress our nation. For this reason we came to Europe ... to steal from the original sources, from the best sources of what we do not have (Karas2003, p. 653).
The aim of translation is common to all: to benefit the Greek Race: ―to benefit the Race I translated this book from the German into our own language, without taking the effort into account‖( Kavras 1800, p. vii), says Zisis Kavras, while Psalidas states: ―I wanted to translate the book ―Mathematicae‖ of the Professor of Mathematics, seeing the use and benefit of mathematics to the public...‖ (Psalidas 1794, ―To Anaginoskonti‖), words used to justify their attempts to translate mathematical works. Koumas even promotes Psalidas‘s translation, writing, ―But Psalidas by the Mathematical Elements of Metzburg, which he translated and taught, greatly benefited his countrymen‖(Koumas 1832, p. 575).
In our opinion, this does not diminish the scholars‘ contribution and work in the slightest. The choice of subject for translation, if not made by chance, presupposes knowledge, consideration and a particular familiarity with the subject. The selection criteria, however, differ from person to person and period to period.
One of the first mathematical textbooks to be taught in contemporary schools, the Introduction to Mathematics (1695) by Papa-Vassilios, is a translation ―from the tongue of the Latins‖. The same is true of the first printed mathematical book, published in 1749, the Mathematical Way by Anthracites, who had studied in Italy. Unfortunately neither of the original texts translated has yet been identified. Nor do we know the original of Glyzonios‘ s Logariastike (1568), the work reprinted most often for almost three centuries, although it is almost certainly some practical Italian Arithmetic.
The term Geometry at this time mainly referred to Euclidean geometry. A work of Geometry widely used by scholars was that of Αndrea Tacquet (Netherlands, 1612-1660)4, Elementa geometriae planae et solidae, et selecta ex Archimede theoremata (Antwerp 1654), a work essentially constructed from
Euclid
‘s Elements with material fromArchimedes
. Itwas translated into Greek, English and Italian (Gillispie vol. XIII, p. 235.). Many editions of Elementa geometriae were produced over the next 150 years: (1665, 1683, 1701 Antwep), (1761, Padova) and the revised editions by William Whiston (1703, Cambrige), (1725, Antwerp), (1727, London (English version)), (1745, Rome), (1762, Venice).
It was first translated into Greek by Eugenios Voulgaris (Elements of Geometry) in 1753-59 (Koumas 1832, p. 562), but did not circulate in printed form until 1805. Voulgaris used the Cambrige‘s latin edition revised by the protestant William Whiston, of 1703.
Voulgaris makes several interventions to Tacquet‘s text, both criticising Tacquet for omitting sentences from the Elements, and interposing many more proofs than the Euclidean ones in the original.
Approximately ten geometry manuscripts by Voulgaris have been recorded to date, all drawn from lessons he gave at the schools where he taught.
Iosipos Moisiodax also translated the same text, but his version remained in manuscript form (Moisiodax 1780, p.
43), under the title ―Paraphrase and variation of Andrea Tacqet‘s Elementa…‖5.
N. Theotokis used Tacquet‘s textbook to write the first volume (Geometry-Arithmetic) of his three-volume Elements of Mathematics (1798). As for Benjamin of Lesbos, it is notable that Tacquet is the only European mathematician mentioned in the whole of his Geometry (Benjamin of Lesbos 1820, p. 59). From the study of the textbooks it also emerges that Benjamin was greatly influenced by Tacquet, probably via Voulgaris‘ translation.
The question that arises is why this particular text was so favourably received by Greek scholars. Iosipos Moisiodax justifies his decision to translate the textbook as follows: ―I once translated the Elements of Andrea Tacquet and even his Trigonometry, both because that great man precisely follows Euclid, and because he is in this more accurate than any other of the moderns‖ (Moisiodax 1780, p. 43).
From another reliable source, European this time, we are informed that ―this book of Tacquet‘ s was the most popular of all his works, and although it was no more than a paraphrase of works by Euclid and Archimedes, it was distinguished by the distinctness and clarity of the text. All his writings, in any case, played an important role in teaching, for whole generations of students were taught basic Mathematics from them‖ (Gillispie vol. XIII, pp. 235-236). This shows that the scholars mentioned did not choose this particular work by chance.
Another French mathematician whose mathematical textbook was translated into Greek, and moreover was the first Algebraic printed text, was Nicolas-Louis de Lacaille (1713-1762), professor of Mathematics at the Collège Mazarin, whose main work in Mathematics was Leçons élémentaires de Mathématiques (1741)6.
4 Andrea Tacquet (1612-1660) studied mathematics, logic, physics and theology at Louvain. He wrote many good elementary texts designed as mathematics textbooks for Jesuit colleges. Elementa geometriae (1654) was his most popular teaching work.
5 Library of Roman Academy, Bucurest, MS 1513.
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Thirty five years after the latin edition of 1762 (Vienna) Spyridon Asanis and Ionas Sparmiotes translated the first part of the work (pp. 1-133). It was published in Venice in 1797, under the title Elements of Arithmetic and Algebra. The translators possibly used this latin edition of the work.
Regarding the above translation, Koumas notes that ―Asanis enhanced it with much useful information on analysis and thus the first Algebraic text appeared through the medium of the press to the Race‖ (Koumas.1832, p. 575). In other words, this book is the first text purely concerned with algebra to circulate in Greek. From 1797 onwards, the appearance of this first complete algebraic textbook in Modern Greek education contributed, among other things, to the gradual creation of a dynamic in the area of algebraic education, something reflected in the burst of publishing in the field of Algebra from this point on.
The second part of Lacaille‘s work translated by Asanis and comprising Geometry, remained in manuscript form7. The third part was translated by Asanis and Koumas, and printed in Venice in 1803 under the title Analytical Treatise of Conic Sections. The translators also used the latin edition (1762) of the work.
Moisiodax translated this textbook as well (Moisiodax 1780 p. 44-45) but his translation has not survived. He describes the book as follows: ―The most illustrious de Lacaille in two minuscule volumes discusses everything to do with either analytical or synthetic Mathematics, beginning as an introduction with Arithmetic....‖ (Moisiodax 1780, p. 44-45). Thus, Moisiodax regards it as a work suitable for teaching, something confirmed by the large number of reprints in the West.
Moisiodax used Lacaille‘s text in teaching Mathematics at the School of Iasio.
Another favourable opinion of the book is contained in an 1818 issue of Logios Hermes, where it is described as follows: ―This book, albeit in a single volume, contains the most essential and basic elements of almost all pure mathematics...‖8.
The work of Leonard Euler (1707-1783) could certainly not be absent from the translational interests of Greek scholars. An extract from the work Eléments dřAlgèbre, par M. Leonard Euler traduits de lřallemand… (Lyon, 1774), a French translation of the Vollstandige Anleitung zur Algebra (St Petersburg 1770), was translated by Ionas Spermiotes9.
According to information from Logios Hermes10, the original of the textbook translated from the German by Zisis Kavras, the Elements of Arithmetic and Algebra (Jena 1800) was also by Euler. We believe that this really is a translation of the above work, which, according to Dirk Struik, ―was the template for many later Algebra texts‖ (Struik p. 198) We do not know why Kavras‘ name is not mentioned either in the preface or on the title page; there is just the note ―Translated from the German by a fellow countryman who loves his race, for his fellow countrymen‖. The absence of Euler‘s name is no surprise, as contemporary authors did not feel it necessary to acknowledge their sources in any form. Stefanos Dougas also recommends this text by Kavras as the most suitable for beginners.
―Asanis decided to write a textbook on differential and integral calculus, and he translated this great and erudite text by Euler‖ (Gedeon 1976, p. 181). This mention by Manuel Gedeon is the only information we have on the translation in question, which, if it was ever written, has not yet been found.
Athanasios Psalidas and Michael Christaris chose to translate a textbook by G. I. Metzburg. ―I wanted to translate the book ‗Mathematicae‘ by the Professor of Mathematics, who taught here at the Academy [of Vienna] for more than twenty years, because this treatise is intelligible, methodical and succinct...‖ (Psalidas 1794, pp. xiv, xv.), stressed Psalidas in the preface to his Arithmetic, the first volume of his work (Vienna 1794). It contains many alterations to the original text, as he says himself. The original, entitled Gl. Georg Ignat L.B. de Metzburg, Mathematicae in unsum Tironum Conscriptae. Tom. I.
ed. IV, Vienna 1793, was the Latin translation from the German. This transmission of mathematical knowledge was rooted in the learning environment offered in Vienna, where Psalidas had studied from 1787 to 1795.
The second volume was to remain in manuscript form (Karas 1992 p.153). A full translation of the work was presented by Michael Christaris, entitled Elements of Arithmetic and Algebra (Padua 1804). The translator preferred the German edition of Metzburg‘s textbook, Des Freyhernn von Metzburg... Arithmetik und Algebra (Vienna 1788). Christaris does not give a specific reason for choosing this particular work. His choice was probably not based on his own informed opinion of the book, as he was a doctor rather than a mathematician. We should not overlook the fact that Metzburg was roughly contemporary with Psalidas and Christaris, and that Greek scholars generally tended to translate new texts
6 Nicolas-Louis de Lacaille (1713-1762) mathematician and astronomer. His mathematical work Leçons élémentaires de Mathématiques (1741) was frequently reprinted (1764, 1768, 1770 and 1778), revised by Abbé Joseph-François Marie and translated into Latin, Spanish, Italian and English. Nielsen (1935), p. 221.
7 Library of Milies, MS 6.
8 Logios Hermes, 15 August 1818, pp. 420-424.
9 Olympiotissa Library, MS 43.
10 Logios Hermes, 20 October 1811, p. 355.
appearing in Europe for the first time. The ultimate aim, as we have said, was the transference of modern knowledge. This aside, however, Metzburg taught at the Academy of Vienna for 24 years (Psalidas 1794, p. iv), meaning that his work had already been tried and tested as a teaching textbook.
Christian Wolff (1679-1754) is better known as a philosopher than a mathematician. The Latin translation of his mathematical work (Halle 1717) (Gillispie vol ΧΗV, p. 483) Elementa matheseos universae (Halle 1730), comprising two volumes, Elementa arithmeticae and Elementa geometricae, was quite widely used by Greek scholars.
Nikolaos Zerzoulis translated the whole of Wolff‘s textbook, as his surviving manuscripts attest. Wolff‘s work also certainly aided Theotokis in writing his Arithmetic.
Dimitrios Govdelas makes several references to Wolff in his book on algebra (Govdelas 1806, pp. 8, 422, 441, 510), and drew on the German scientist‘s work for his own textbooks (Camariano-Cioran 1974, p. 232).
The work Cursus mathematicus (Halle 1758-1767), by Segner (1704-1777)11 was also chosen by Voulgaris as a suitable subject for translation, which was printed in 1767. Voulgaris justifies his choice in the preface, saying that ―The German Academies, which are among the most celebrated in Europe, approved the Man‘s works as absolutely accurate‖.
The Geometry of Octavian Camett was translated by Dimitrios Razis because, as he says, ―Camett set the Euclidean elements in a new order and applied a more comprehensible method‖ (Razis 1787, p. 12) and was published in Venice (1787).
Spyridon Asanis and Ionas Sparmiotes chose to translate Grandi‘ s (1671-1742)12 Conic Sections (Florence 1750) in order to reinstate ancient mathematical learning, as always in the service of the Greek Race. The original text is the Sectionum Conicarum Synopsis clar. viri D.Guidonis Grandi et Schenatibus aucta Ad. Octaviano Cametti.
The work Les éléments dř Euclide de M. Ozanam... démontrés dřune manière nouvelle et facile par M. Audriene by Jacques Ozanam (1640-1717) was used, among others, by Nikiforos Theotokis in his Geometry. Ozanam was only a minor mathematician, but he wrote books many of which became very popular and were often reprinted (Gillispie vol. X, pp. 263-265).
In his chapter on ―Conic Sections‖, Theotokis drew on Josepho Orlando‘s Sectionum conicorum tractatus (Naples 1744) (Karas 1992 p. 94).
In a manuscript by the same scholar entitled ―Elements of Arithmetic and Geographic Science...‖, one section consists of ―The Interpretation of the Logarithmic book by Gafendi, translated from the German into the Greek tongue‖ (Karas 1992, p. 96), which, however, is not included in the printed edition.
Alexis Clairaut was one of the French mathematicians linked to the philosophers of the Enlightenment. Αn extract from his work Eléments de la Géométrie. De la mesure des figures et des solides was used by Ioannis Phournaios in his Geometry, as he notes in one of his manuscripts: ―Additions to Clairaut‘s Geometry. On the transformation of shapes‖13.
Alexis Clairaut was one of the French mathematicians linked to the philosophers of the Enlightenment. Αn extract from his work Eléments de la Géométrie. De la mesure des figures et des solides was used by Ioannis Phournaios in his Geometry, as he notes in one of his manuscripts: ―Additions to Clairaut‘s Geometry. On the transformation of shapes‖13.