22 How was Greek science imported into other languages?

§1 This chapter widens the view and compares several major traditional languages of science and their ways of expressing Greek scientific thought. The focus will be on Latin, Sanskrit, and Arabic, but some scattered comments about Chinese are added as well. Greek translations into Latin happened in several stages and in at least four key periods, as was shown above (chap. 6 §2 with fig. 7). As the Arabic language has a rather different structure than Greek and Latin (and Indo-European in general), it may come as a surprise how quickly the Arabs were able to assimilate Greek science and learning, subsequently producing significant advances in many fields. The adoption began during the reign of Caliph Hārūn al-Rašīd (r. 786–809) and continued under his son al-Maʾmūn (r. 813– 833). It was facilitated by Syriac precursor translations and by translators already used to dealing with scientific Greek. During this relatively short period, Arabic became a more or less standardised language of science and produced adepts who founded schools and traditions that were often to last for half a millennium. Indeed, the ‘revolution’ in Latin science in the twelfth century – which was considered above (chap. 11) – took some of its texts to translate from such Arabic sources. Sanskrit has a rather similar structure to Greek, and could have quite effortlessly been used to translate scientific Greek; it largely relies on compounds to render technical terminology, as will be seen. Greek science does not seem to have been much translated into Sanskrit in Antiquity, yet there was definitely contact that led among other things to a flourishing of mathematics around the fifth century AD (with authors such as Āryabhaṭa) in India, and later on, through Arabic mediation, in many other fields. Already in the time immediately after Alexander the Great, there were quite close relations between the two peoples. King Aśoka (ca. 304–232) had Greek subjects in Kandahar, for he had edicts in-

scribed in Greek (Schlumberger 1964). The case of Chinese is different again; direct contact between Graeco-Latin science and China seems to start as late as the Jesuit mission in China in the later sixteenth century, and then ran through the Latin medium. 7 The much older indirect access to Graeco-Roman ways of thinking through the Silk Road and through contact with Buddhist India (itself in contact with Greek culture) is hard to gauge. At any rate, it does not seem to have been lasting; for instance, the Chinese only learned that the Earth is spherical from the Jesuits. 8 More general questions of the relation of cultural spheres, language, and science will be taken up below (chap. 24). 9 §2 In order to argue from concrete data, two influential Greek texts were chosen and their translations into these languages studied: the strongly formalised scientific language of geometry in Euclid's Elementa, and the less mathematical and more descriptive but logically structured kind of Greek in Aristotle's lectures (namely the Poetica, a work that scientifically studies parts of ancient Greek culture) are used as source material. These two works can stand for a 'hard' science and a human science text respectively, and will illustrate some differences between them. Both works were translated into all the languages with which we are concerned. In a first part, the translations of these two texts are briefly described in order to provide a background; then some peculiarities of the language of each of them are considered; finally, their way of translating is studied by looking at statistical values on the one hand and at some representative sentences and how they were rendered on the other.
Euclid's Elementa was an immensely successful book; it remained the standard geometry schoolbook for over two millennia. 10 It was studied, commented, and also translated many times. Figure 48 shows some of the translations into the languages studied here. In Antiquity the book quickly replaced all older manuals on geometry, which are now completely lost. The same fate might easily have happened to Euclid's original text as well, for Theon of Alexandria reworked it slightly around AD 360, correcting inconsistencies. 11 His revised text was the only one known until a single manuscript containing the older text was found in the 7 Jami & Delahaye (1993) study this cultural contact. 8 See Cullen (2001) on previous cosmological theories in China. 9 For help in mastering of the Arabic material, I am indebted to Benjamin Gleede and Emanuele Rovati. The Chinese was kindly checked by Wolfgang Behr. 10 This was still the case in the nineteenth century; cf. for instance Robert Potts's school translation of 1845. 11 A recent summary of geometry in Antiquity and the Early Middle Ages by Barbara Ferré can be found in her edition of Martianus Capella, Les noces, vol. 6, pp. ix-xxiv. nineteenth century. 12 It is the basis of Heiberg's editio maior, which, incidentally, also contains a fresh Latin translation. The complicated situation of the early surviving Latin translationsthat is, those from the twelfth centurywas disentangled in many publications by Busard, who also edited them. 13 Only one of them was made directly from the Greek, the anonymous 'Sicilian translation' (already used above in the text sample in chap. 20); the others went through Arabic. The first known translation, apparently by Boethius, was lost early. 14 Besides quotations in other works, some fragments of books XI-XIII have survived on a palimpsest. 15 The few extant pre-twelfth-century Latin writers who wrote about geometry often just used the Greek terminology, as Martianus Capella does in his 12 Città del Vaticano, BAV,Vat. gr. 190, from the early ninth century. 13 For the disentanglement of the three 'Adelard' versions, see Clagett (1953); Burnett (1997b). On Adelard in general, see Burnett (1987). 14 But at least partial translations of the Elementa may have existed before Boethius, as indicated by the accurate knowledge of Martianus Capella (but he may have translated ad hoc from the Greek) of some parts of them (see Stahl 1971: 128-129 Observations on the Greek of the two texts §4 The first thing even a casual observer notes in the language of the Elementa is its uniform and formal organisation. Except for the definitions and axioms at the beginning of every new subject, the theorems always follow the same form: πρότασις (the formulation), ἔκθεσις (the 'setting out', a more detailed exposition introducing the letter nomenclature for the geometric objects in question), διορισμός (the 'definition' of how to reach the solution), κατασκευή (the geometric construction), ἀπόδειξις (the proof that the construction was correct, often by reductio ad absurdum), and συμπέρασμα (the 'conclusion', a restatement of the theorem, ending in the famous ὅπερ ἔδει δεῖξαι, our 'Q.E.D.'). 27 Besides these six steps, there is a diagram whichcontrary to modern maths books (where such diagrams only illustrate the problem and are not essential for the mathematical content)often contains information that is not explicitly stated in the text, typically the relative position of the points to which letters are assigned. An example sentence, which will be studied in translation below, is Euclid, Elementa I, prop. 47 πρότασις (the Pythagorean Theorem): Ἐν τοῖς ὀρθογωνίοις τριγώνοις τὸ ἀπὸ τῆς τὴν ὀρθὴν γωνίαν ὑποτεινούσης πλευρᾶς τετράγωνον ἴσον ἐστὶ τοῖς ἀπὸ τῶν τὴν ὀρθὴν γωνίαν περιεχουσῶν πλευρῶν τετραγώνοις. 'In any right-angled triangle the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.' The language itself is also very uniform. 28 Acerbi (2021: 1) has described this language in detail, including statistical material and concluding that it is a Kunstsprache 'exhibiting a limited lexicon and highly regimented syntactic features, which in some cases may well be termed "extreme"'. The technical nominal lexicon is small and is in a one-to-one correspondence with the geometric objects covered (list in Acerbi 2021: 35-36). For other PoS, there is more variation, especially some unexpected synonyms -διπλάσιος, διπλασίων, διπλοῦς ('double'; 36)but the number of lemmata and distinct words is very small compared to other Greek texts, as we shall see. Concrete geometric objects are designated by algebraic letter-names such as 'AB', each letter standing for one point. Thus, in Euclid we find a very specialised type of language: the vocabulary is small, synonyms are avoided, unambiguity is sought; but, of course, it is a rather specialised vocabulary with many words for things that do not exist outside geometry. Words for such new geometric objects could be coined easily in the Greek language, which is very fond of compoundslike Sanskrit but in contrast to Latin and Arabic. A few examples show that (i) some terms could be taken from everyday language more or less as is (e. g. σημεῖον, 'point'; γραμμή, 'line'; ἐπιφάνεια, 'surface'; γωνία, 'corner'; κύκλος, 'circle'; ἴσος, 'equal'; ἄνισος, 'unequal') or in a more technical but still recognisable way (κάθετος, 'let down (of a plumb line) → perpendicular'; ἀμβλύς, 'blunt → obtuse (angle)'; ὀξύς, 'pointy → acute (angle)'; μονάς, 'solitary, by oneself → (mathematical) unit'). Some (ii) are hardly still recognisable, such as ῥόμβος ('rhombus'), normally a sound-producing cult instrument similar to the Australian bull-roarer of rhomboid shape, or ἀντιπάσχω ('to be reciprocally proportional', literally 'to suffer in turn'). Many others (iii) are just compounds of everyday words that are immediately understandable for a Greek-speaker (e. g. εὐθύγραμμος, 'rectilinear'; ἡμικύκλιον, 'semicircle'; ἰσόπλευρον, 'equilateral'; ἀσύμπτωτα, 'which never meet'; ἰσογώνιον, 'equiangular'; διάμετρος, 'diameter').
(iv) Compounds may, of course, also contain parts that may not be familiar to the non-geometrician, such as δωδεκάεδρον ('dodecahedron'), where ἕδρα means 'face of a geometric figure' (usually it means 'seat', and a non-geometer would hardly know what a 'twelve-seater' is).
The syntax is equally monotonous, as the few numbers in table 25 suggest: among these values, conditional clauses (εἰ, ἐάν, ἐπεί) are very common, as is parataxis using καί ('and'), γάρ ('for'), or very frequently ἄρα ('thus'). Infinitives and participles are much rarer than usual in Greek. Of the linguistic phenomena typical for Greek scientific writing (as will be seen below in Aristotle), absolute and participial constructions are rare, but the article is used a lot more than in other Greek. Indeed, the feminine article without any noun except a formula (e. g. ἡ ΑΒ) signifies a 'line' (ἡ γραμμή) through A and B, its neuter τὸ Α a 'point' (τὸ σημεῖον), and its masculine ὁ ΑΒΓ a 'circle' (ὁ κύκλος). There are also more such short designations: τὸ ἀπὸ ΑΒ for the square (τὁ τετράγωνον) 'on' AB, ἡ ὑπὸ ΑΒΓ for the angle (ἡ γωνία) 'under' the three points. 29 But this latter feature is, of course, not essential for geometry; it just shortens the text by saying ἡ ΑΒ ('AB') instead of ἡ γραμμή, ΑΒ ('a line, called AB') 30 each time. 31 Such letter symbols make up a full 16% of all words in the Elementa. Together with the article they make up more than a third of all words in the Elementa. Acerbi (2021: 86) points out: The article that precedes the letters has two functions. The first is distinguishing between objects designated by identical strings of letters, because the gender of the article is the same as that of the noun modified by the string of letters: ὁ ΑΒΓ is a circle but τὸ ΑΒΓ is a trianglefor instance inscribed in circle ὁ ΑΒΓ […]. The second function is to produce a linguistic item suited to be a noun, which must have a declension: the case of the noun can only be deduced from the case of the article. This latter function is found below to be a crucial feature of Greek scientific language in general (chap. 24 §6). None of the studied translations was able to reproduce this special feature of Greek geometry as none of these languages disposes of an article and three genders. The two works in translation §5 In order to study the translatability of these two kinds of scientific Greek, a look is taken first at representative sentences in the translations, then at a list of technical terms and how the translators dealt with them, and finally some figures about the translations are considered. In the case of Euclid, most translations rewrite the text more than translating it: they add comments, make little changes to the proofs, even correcting minor mistakes here and there. Some add long commentaries, such as Clavius, Ḥaǧǧāǧ, and Ps-Ṭūsī; on the other hand, the Sicilian 36 e. g. Elementa I, prop. 16, ed. Heiberg, vol. 1, p. 42: Παντὸς τριγώνου μιᾶς τῶν πλευρῶν προσεκβληθείσης ἡ ἐκτὸς γωνία ἑκατέρας τῶν ἐντὸς καὶ ἀπεναντίον γωνιῶν μείζων ἐστίν ('For any triangleone of its sides having been producedthe exterior angle is larger than the interior and opposite angles' Heiberg translates similarly into modern academic Latin. Ḥaǧǧāǧ (p. 172) works with participles (underlined), especially often of kāna ('to be') and also relative clauses (italics). A verbum de verbo English translation is given. The Arabic dual is employed. Samrāṭ (vol. 1, p. ६१) works with compounds and can formulate very concisely indeed in Sanskrit: The two works in translation (tatra samakoṇatribhujasya) karṇavargo (bhujadvayasya vargayogena) tulyo bhavati. '(Therefore ⸤of right-angled-triangle⸥) ⸤square of hypotenuse⸥ (⸤of the two-sides⸥ ⸤by square-adding⸥) equal becomes.' Everything contained in one word is marked here by lower half-brackets. The Chinese translation puts this (in simplified characters, followed by pīnyīn transliteration): 凡三边直角形、对直角边上所作直角方形与馀两边上所作两直角方形并、等。 fán sānbiān zhíjiǎo xíng: duì zhíjiǎo biān shàng suǒ zuò zhíjiǎo fāngxíng yǔ yú liǎng biān shàng suǒ zuò liǎng zhíjiǎo fāngxíng bìng, děng. 'For any three-sided shape with a right angle [the following applies]: A square shape made above the side facing the right angle and the two square shapes made above the sides of the other two angles combined [are] equal.' Apparently, Arabic and Sanskrit use opposing strategies: while Sanskrit uses compounds, Arabic resorts to clauses. Chinese uses neither; it states all that is needed paratactically. The Latin syntax can remain much closer to the Greek than the other languages considered here, but like Arabic it tends to use more relative clauses.
The following table (table 26) lists the translations of some of the geometric vocabulary; relatively straightforward examples are given first, then less easily translatable ones. For Sanskrit, the constituent parts of compounds are marked by dashes. Literal translations are added for interesting cases.   43 This word 'originally meant a cord of reeds used by the sacrificial priest to measure the side of the square altar' (Rekhaganita, vol. 2, appendix 2, p. 12). It is totally unrelated to its opposite, mūladarāśiḥ (ῥητός, rationalis).
Clearly, many of these terms had to be newly invented by the translators. An example for which all other languages needed lengthy descriptions is παραλληλόγραμμον; others, such as πρῶτος ἀριθμός, were easy to imitate (only English uses Latin 'prime', not the expected 'first number'). The Sicilian translator often just transliterates difficult Greek terms (occasionally including verbs such as παραβάλλειν; I.44), 44 Robert does the same for Arabic (elmunharifa for 'trapezium'), as does Adelard with mutekefie ('being reciprocally proportional') or alkaida for basis. The later Latin translations tend to use much less direct loans. Arabic, Sanskrit, and Chinese do not usually take direct loans at all, 45 Samrāṭ's kendraṁ (κέντρον) is an exception. The more complex notions are rendered by compounds in Sanskrit and constructus clauses in Arabic, 46 which clearly feels much less at home with these formulations than Sanskrit, with its compounds, does. For instance, Samrāṭ writes the descriptive and very clear, although rather long compound viṣama-koṇa-sama-catur-bujaṃ ('not-same-angle-same-four-sider') for 'trapezium'. In Chinese such concepts are formed by combinations of characters, in this case wúfǎ sìbiānxíng ('no-law-four-edge-form'), which, however, is less precise. Now, some statistical data about the translations. 47 Which combinations of characters should count as one semantic unit ('word') is often unclear in Chinese; preferably, one just counts characters. 48 The first number includes names for geometric objects, such as AB, as 'words'. 49 Not counting proper names. The numbers were automatically calculated in Corpus Corporum using word-lists mostly from Perseus. In ambiguous cases, the first lemma was chosen and some It is to be remembered that Gerard translated from Arabic and that the Sicilian translation is a verbum de verbo translation of the Greek: it reaches amazing brevitas. Chineseboth the language and its scriptfunctions completely differently. This makes comparison difficult, but the Chinese translation seems to be very short as well, although the number of unique characters is higher than that of the lemmata in the Greek or in the Anonymus Siculus. Further interpretation is provided in the next section and contrasted with Aristotle.
Aristotle §6 For Aristotle's Poetica, the statistical data is provided first (in order to keep the two tables close together), then we consider a representative sentence and the translations of some technical terms. 50 The Arabic translator Abū Bišr (p. 220) expands this rather condensed statement considerably: w-ʾaṣnāfu-hā ṯalāṯatun: (i) wa-ḏālika ʾima ʾan yakūna yušbihu bi-ʾašyāʾi ʾaẖari wa-l-ḥikayatu bi-hā, (ii) wa-ʾima ʾan takūna ʿalā ʿaksi hāḏā: wa-huwa ʾan takūna ʾašyāʾu ʾaẖaru tušbihu wataḥākī, (iii) wa-ʾima ʾan taǧrā ʿalā ʾahwālin muẖatalifatin lā ʿalā ǧihatin wāhidatin bi-ʿayni-hā. The translation of scientific descriptions of matters rooted in a particular culture cannot work without a rather deep knowledge of the culture in questionin contrast to geometry, which travels much more seamlessly. The uncommon vocabulary in the Poetica consists mostly of names of genres and poets. Abū Bišr, an Aristotelian logician, is not interested in the performance of these Greek forms of art at all. Nath provides a list of his transliterations of those terms unfamiliar within Sanskrit, but taken to be familiar to his readers in their international (i. e. English) form, for example dithurambaḥ or platān, for 'dithyramb' and 'Plato' respectively, which are well formed and can be easily declined in Sanskrit. 56 Rigolino (2013: 146) concludes about the Arabs: In the other three languages, such a procedure was clearly impossible, as the languages are unrelated (or at least do not share the Begriffsgemeinschaft, as in the case of Sanskrit) and work rather differently syntactically. In Arabic, translators had to reformulate many things; compounds in particularas seen in the list for Euclidwere often turned into constructus clauses. Besides, it was noted that the Arabic translators had a tendency to be rather prolix, for instance to say things twice with slight variation. In Sanskrit things are again very different: this language is so fond of compounding that the number of words tends to become less in translating (though not the number of characters). Samrāṭ even makes compounds of geometric objects and speaks of, for instance, the 'A-B-line'. Nath makes compounds of lists. 60 Sanskrit is famous for its special scientific language, 58 The same is apparently true for Chinese, whose writing system gives it a natural tendency to brevity. 59 More on this technique in chap. 10 §5 above and Roelli (2014a). In early Church texts, this was very different; although there was a wide spectrum from verbatim to very free translations, the verbum de verbo type is hardly ever encountered (Gleede 2016: 356). 60 Such as mahākāvyā-tragādī-kāmādī-stutikāvyāni for Ἐποποιία δὴ καὶ ἡ τῆς τραγῳδίας ποίησις, ἔτι δὲ κωμῳδία καὶ ἡ διθυραμβοποιητική (1.2, p. 238).

Conclusions
which goes so far as to give cases specialised scientific functions in the sentence. 61 For instance, causes are indicated by a bare ablative. A normal speaker or reader of the language who is unaware of these special rules will be unable to understand anything in such a text. A similar heavily nominal style can be observed in German, but it resorts more to compounding and, unlike Sanskrit, does not go so far as re-engineering its syntax. 62 It can be concluded that Euclid is much easier to translate than Aristotle due to several factors. Not only is Euclid's content more easily accessible to non-Greeks than the Greek art forms studied by Aristotle's Poetica; it would also seem that a highly formalised language using a small and well-delineated vocabulary and simple syntax also helps a lot in this respect. However, Euclid's highly formalised language can even be formalised and compressed much further, as is indeed done in modern mathematics. Thus, these two statements amount to the same thing: Ἐὰν ὦσιν ὁσοιδηποτοῦν ἀριθμοὶ ἑξῆς ἀνάλογον, ἀφαιρεθῶσι δὲ ἀπό τε τοῦ δευτέρου καὶ τοῦ ἐσχάτου ἴσοι τῷ πρώτῳ, ἔσται ὡς ἡ τοῦ δευτέρου ὑπεροχὴ πρὸς τὸν πρῶτον, οὕτως ἡ τοῦ ἐσχάτου ὑπεροχὴ πρὸς τοὺς πρὸ ἑαυτοῦ πάντας. (Elementa IX,prop. 35,ed. Heiberg,vol. 2, X nÀ1 i¼0 ar i ¼ a r n À 1 r À 1 On the other hand, in the human sciences, texts are still written in a much less formalised language today, although it is definitely also a highly specialised kind of language with many foreign words (especially Greek and Latin ones) and often still a complicated and non-repetitive syntax which is used to mimic in language complex structures from the field studied. A German example: ably without wanting to and without even noticing itit made this persistent tradition of lively further development fade.' In translating such texts, one faces two problems, one concerning vocabulary and one of syntax and nuances. Normenentfaltung may be renderable by 'unfolding of norms', but other nuances can in no way be preserved in the English: consider zählebig turning into a mere 'persistent' without the connotation of 'life', or the closeness of erkennen and anerkennen. The same is true for the musical connotations of Verklingen. The first problem can thus be solved relatively easily by taking over the foreign words missing in the target language and hoping that readers will understand them, or alternatively by forming calques (as I did in the example). The next chapter will give further examples of each approach. The second problem is much more tricky, as has been seen in the examples from Aristotle's Poetica in this chapter. What we see here may be a difference between natural and human sciences: that the former are much more easily formalised. On the whole, it would seem that different languages had to master different problems in order to express Greek science. Science can be seen as a web of strictly defined scientific entities. The entities need names when translating into a language not yet familiar with the science in question, but the web must also be recreated. The former task is relatively straightforward and can be accomplished by loaning or calquing (as the tables above have shown). The latter option is, in general, to be preferred, as loaned words tend to remain foreign material in the target language that is not well integrated into its semantic web. Think of the famous Russian бутерброд, which does not have to contain butter at all. 64 Indeed, in our examples, later translations have tended to use the calquing more profusely than the former. The web of these new concepts takes time to become established in the target language. Often, this web's internal organisation also has to be changed; for instance, Latin could not use the article to denote lines, points, or circles the way Euclid did in Greek. The next chapter considers the debt of modern vernacular scientific terminology to scientific Greek and Latin.