Petro Vileišio aritmetikos vadovėlio „Keturi svarbiausiejie veikalai aritmētikos“ terminai

154 D. Šilobritaitė | The Four Most Important Elements of Petro Vileišis' Arithmetic Textbook | veikalai aritmētikos terminai The Four Most Important Works of Peter Vileišis Arithmetic Terms DIANA ŠILoBRITAITĖ Lithuanian Language Institute esMInIAI žodzIAI: mathematical terms, origin of mathematical terms, formation of mathematical terms For the 160th anniversary of the birth of Petras Vileišis Petras Vileišis (1851–1926) was a Lithuanian public figure who contributed to the publication and distribution of the forbidden Lithuanian press. He wrote or translated a number of popular science books (about 100) and textbooks on arithmetic, physics, geometry and history. Vileišis was a tenacious fighter for the freedom of the Lithuanian press and contributed to the creation of terminology in various fields, including mathematics. In the preface to his Selected Writings it is written that “He did a great educational work – with 155Terminologija | 2011 | 18 provided compatriots with a universal folk bookstore and introduced the basics of national entrepreneurship. P. Vileišis was a patron of Lithuanian cultural activities, reviving Lithuanianness in Vilnius, turning Vilnius into the centre of Lithuanianness. He is also the creator, publisher and editor of the first Lithuanian daily newspaper Vilnius žinios” (Vileišis 2004: 11). In 1886, P. Vileišis (signed under the pseudonym Petras Nēris) published in Tilžė a small (50 pages) textbook of arithmetic, Keturi svarbiausi darbai aritmētikos (Four most important works of arithmetic). According to mathematician Peter Rumšas, while writing this textbook, P. Vileišis created original and interesting arithmetic terms (Rumšas 1978: 58). It is the second printed Lithuanian work on arithmetic. The first printed Lithuanian arithmetic problem Uźduotinas, tai ira Rankius uźduocziu Aritmetikos arba Rokundos mokslo was published in Tilžė in 1885. This was the task of the famous Lithuanian social figure of the late 19th and early 20th centuries, the “self-taught linguist doctor” (Sabaliauskas 1979: 177) Jonas Spudulis (1860–1920). The Vrublevskių Library of the Lithuanian Academy of Sciences holds a manuscript copy of this problem (Arithmetic problem from which priest Katelė taught, obtained from Šinkūnienė, a resident of Paliepis) (see Šilobritaitė 2009: 186–197). as in J. Spudulis’s problem, but also some arithmetic terms are explained, e.g. : The addition („sudėtimi“1) is called the Nagrinėjamame P. Vileišio vadovėlyje pateikiamos ne tik užduotys, way, by which from a number of numbers of the same variety, one number called the sum is obtained, which itself is as much in unity as was in all the numbers in the additions2 Vlš 10; The subtraction („atimtis“) is the operation, by which, knowing the sum of two numbers of the same variety and one of the other number Vlš 16. It is important to say that the textbook contains the definitions of mathematics and its two branches: Matēmatika is called the science whose measure is the measurement and comparison between itself by multiplicity Vlš 3; Aritmētika is called the science of numbers Vlš 4; Counting is called the science of computing and writing all kinds of numbers Vlš 4. his hard work and his courage he was able to make the world a better place.” About 150 terms were collected for the study. 1 The term in quotation marks has been defined by the author of the article. 2 Samples are provided in authentic form. 156 D. Šilobritaitė | The Four Most Important Elements of Petro Vileišis' Arithmetic Textbook | veikalai aritmētikos terminai 1. VIENAŽODŽIAI TERMINAI P. Vileišio vadovėlyje rasti 62 vienažodžiai terminai (42,2 % visų rastų terminų). Kilmės atžvilgiu jie skirstomi į lietuviškos kilmės, nelietuviškos kilmės ir hibridinius terminus. 1.1. Vienažodžių terminų kilmė 1.1.1. LIETUVIŠKOS KILMĖS TERMINAI Didžioji dalis (47 terminai, t. y. 75,8 % vadovėlyje rastų vienažodžių matematikos terminų) yra lietuviškos kilmės, pvz.: apskriedimas „apibrėžtis“ Vlš 10, derējimas: Tasvisasvienokgalimaparaszytipasigaunantminētomisrokůtinēmisiratsimenantantsziutrijuderējimu Vlš 7, dalis: Aiszku, jogskaitleisumetamipažymēti,budaminekuriomisdalimisjieszkomosios sumos,turbūtiirtospacziosveislēs,nēsdalisvisuometyratospaczios gymēs,kaipirlabas,priekuriojiprigul Vlš 10, daugumas: Daugumu vadinasikožnasdidumas,galimasbūtipadalytasįkeliatądaliu Vlš 3, didumas: Dēlnusklempimodidumonekuriodaugumoreikiajįpalygintisu kitutospacziosveislēsdaugumu,kuriodidumaspervisusyranutartasir kursvienybevadinasi Vlš 3, gymē: Skaitliuspaeinanůsusidējimovienybiu, arbajudaliu,irtaivienosirpacziosgymēs Vlš 4,įpatybē:Tasatsitikimas atsiremiaantsziuįpatybiu:1.Liekanapasididinaantnekuriodaugumo, padidinantdidesnįskaitliųanttopatiesdaugumo,iratliekantskaitliųmažesnį- beatmainos Vlš 18, lavinimas „pratimas“ Vlš 10,palyginimas „lyginimas“ Vlš 3,parodymas: Parodymuvadinaiszteisinimąnekuriosapreiksztosteisybēs Vlš 14, pasigavimas: pasigavimassumetimo; pasigavimas atitraukimo; pasigavimaspadauginimo Vlš 46, priegimtis: Kožnojerokundojeiszpradžiosyražinomapriegimtisjieszkomojolabo,reikia- tiktaijo skaitliųatrasti <...> Vlš 4, rēžis: Rēžiuvadinamekožnąsusidējimąvienybiu,deszimcziuirsuimtupaskuisekancziuju Vlš 7, rodyklē: Yranutarta raszytitiktaivienąiszlygiuvaisiausdirbēju,statantvirszumijotruputįį deszinępusęsmulkiąrokůtinę,rodyklevadinamą,kurirodoskaitliųlygiu dirbēju,arbažingįjieszkomosiosgalybēs Vlš 32, skyrius: Yraduskyrei vienybiu:vienybēveislinē,kaiptai:vienasžmogus,irvienybēmatēmatikinē Vlš 3, svarbumas: Draugesutůmikaipkurinorintiszsziurokůtiniupersikeliapervienąeilęįkairępusę,jiaptursvarbumądeszimtįkartudidesnį Vlš 7, teisybē: Parodymuvadinaiszteisinimąnekuriosapreiksztosteisybēs Vlš 14, veislē: Vienybētadayranutartasirneatsimainąsdaugumaspasi- 157Terminologija | 2011 | 18 gaunąs dēl mērīšanas daudzumu tos paczios veislās Vlš 3, žīngis: Isz teisybēs, dēl apturējimo galybēs nekurio žīngio důto skaitļas it is enough to multiply these numbers through it itself as many times as there are unity without one in the step galybēs Vlš 32, marked „sign“ Vlš 11. Most of the terms of Lithuanian origin in the source under consideration are no longer used in mathematics or have a different meaning. The term „operation P. Vileišis įvardijo matematikos sąvoką veiksmas „pagrindinė matematikos Vlš 14“ means: “The justification of no work is called another work, which is acquired due to the discovery that the good good through the first work is different from Vlš 14. By the way, the author of the first Lithuanian mathematical problem J. Spudulis named this concept the term weikmė. It is worth mentioning that all the names of the basic arithmetic operations presented in P. Vileišis’ textbook are not used now: addition “sudėtis” Vlš 4, subtraction “atimtis” Vlš 4, multiplication “daugyba” Vlš 4, division “dibyba” Vlš 4. In the aforementioned J. Spudulis's workbook, the names of the actions are named as addition, subtraction, multiplication, division. According to the mathematician Zigmantas Žemaitis, "in other languages, the name of the mathematical operation itself is usually indistinguishable from the name of its specific execution process, whereas logically they should be separated. Therefore, later it was accepted to call the actions addition, subtraction, multiplication, division, and to leave the used terms multiplication, division to mark the execution of the actions (e.g., multiplication of fractional numbers)” (Žemaitis 1966: 196). It should be mentioned that the usage list did not include Lithuanian terms naming numbers with which arithmetic operations are performed: likutis „difference“ Vlš 16, padalys „part“ Vlš 35, dilytojas „divisor“ Vlš 35, padalė „part“ Vlš 35, daugintinis „multiply“ Vlš 22, daugiklis „multiplier“ 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279. The term labas Vlš 5, which did not become the meaning of the result of arithmetic action: Labas deszimties deszimcziu tapė was called szimtu Vlš 5. According to what has been said, it is possible to throw sieks with sieks, pounds with pounds, etc., in order to stop the marked good; but it is not possible to throw rubles with ůlektě, tables with houses, etc., if we only do not seek the good without name Vlš 10–11. The term is not used in modern mathematics, nor in any other field of mathematics. 3 The two-word terms greater number "content" VlŠ 16, smaller number "subtraction" VlŠ 16, approximate number "demuo" VlŠ 11 have not been preserved. 158 D. Šilobritaitė | The Four Most Important Elements of Petro Vileišis' Arithmetic Textbook | veikalai aritmētikos terminai In mathematical terminology, the term isztejítés Vlš 14 is not used, which in the source under consideration means the verification of the execution of basic arithmetic operations (addition, subtraction, multiplication and division). Other arithmetic terms that have not survived, e.g.: darbbējas4: Numbers in the rank of two workers are equal to the sum of the rank of two workers, or that sum without one unit Vlš 32, galybē "degree": The end of no one's majority is called the result of the level of a number of workers Vlš 32, kertůtis "square" (the second degree of a number): The end of 2nd rank is called kertůcziu <...>. Vlš 32, joint "demon": Numbers greater and smaller are called two joints of residues Vlš 16, unity "unit": There are two divisions in unity: unity in breeding, as it is: one man, and unity in mathematics, as it is one goal Vlš 3. 1.1.2. TERMS OF NON-LITHUANIAN ORIGIN There were few terms of non-Lithuanian origin found in the textbook (13 terms, i.e. 21% of all monosyllabic terms found). Some of them are no longer used in mathematical terminology. These are borrowed from Slavic languages5: ližma "number" Vlš 6, mēris "measure" Vlš 3 and rokunda "counting" Vlš 4. The international terms arithmētika Vlš 4, klase Vlš 6, kubs Vlš 32, līnija Vlš 12, matēmatika Vlš 3, minus Vlš 16, numerācija Vlš 4, plus Vlš 11, summa Vlš 10 and teorēma Vlš 28 are still used today (differing only in spelling). 1.1.3. HYBRID TERMS Two hybrid terms (with Lithuanian suffixes added to the non-Lithuanian root of the term) were found in the source: mēravimas Vlš 3, rokůtinē6 Vlš 7. They make up 3.2% of all single-word terms found. According to P. Rumša, the term rokůtinē is the oldest term for the concept of “digit”. This term is found in J. Weis's Elementary and in the dictionaries of P. Ruigis, K. Milkas and F. G. H. Nesselmann (see Rumšas 1978: 54). Only in arithmetic textbooks published in 1915–1916 is the term digit found, which was recognized as better than others to express this concept (Rumšas 1979: 54). 4 Vileišis calls the multiplier "multiplier" and the plural "plural". 5 The origin of terms is determined by reference to LKŽe and E. Fraenkelis dictionaries. 6 The textbook also uses the variant of this term rakůtinė Vlš 32. 159Terminologija | 2011 | 18 1.2. Vienažodžių terminų daryba One-word mathematical terms used in P. Vileišis’ textbook are divided into primary and secondary. 1.2.1. PRELIMINARY WORDS We found only two mathematical terms with one word followed by the primary words (they make up only 4.1% of the found terms with one word)7: hello Vlš 5 and spůgas Vlš 22. The term spůgas P. Vileišis called the multiplication sign: Multiplication with two digits is marked by writing the multiplier after the decimal half of the multiplier and separating it with a cross (X), or spůgu(.) 1.2.2. SECONDARY WORDS The majority of mathematical terms found are derivatives8 (95.9 % of single-word terms found). They are divided into adverbial derivatives, limb derivatives and adverbial derivatives. 1.2.2.1. Preludes. The textbook of P. Vileišis mainly contains abstracts of verbs with suffixes -imas (-ymas): apskridimas Vlš 10, subtraction Vlš 4, division Vlš 4, addition Vlš 7, justification Vlš 14, education Vlš 10, measurement Vlš 3, multiplication Vlš 4, comparison Vlš 3, demonstration Vlš 14, acquisition Vlš 46, marking Vlš 3, counting Vlš 4, addition9 Vlš 3, subtraction Vlš 4. Slightly fewer suffix derivatives consist of terms made with other suffixes: -um: plural Vlš 3, major Vlš 3, long Vlš 15, important Vlš 7 (these terms are derived from nouns and are names of properties); -ybė: galybė Vlš 32, įpatybė Vlš 18, lygybė Vlš 11, teisybė Vlš 14, vienybė Vlš 3; -uotis: kertůtis Vlš 32; -tis: prigimtis Vlš 4; -tojas: divisor Vlš 35, multiplier Vlš 22. It should be noted that P. Vileišis uses the derivatives of the prefix -tojas not for persons but for numbers with which mathematical operations are performed. With other suffixes only one example was found: -alas: shop Vlš 14; -ana: remaining Vlš 16; -ėjas: worker Vlš 22; -yklė: rodyklė Vlš 32; -lė: veišli Vlš 3; -tinė: rokůtinē Vlš 7; -tinis: multiplier Vlš 22. 7 This figure does not include terms of non-Lithuanian origin. 8 In determining the methods and means of terminology, reference is made to the works of S. Ambraz (1993; 2000), St. Keinis (1999; 2005), P. Skardžys (1943) and V. Urbutis (2009). 9 By addition, P. Vileišis refers to addition and multiplication: due to addition of numbers, two methods are used: addition and multiplication Vlš 4. 160 D. Šilobritaitė | The Four Most Important Elements of Petro Vileišis' Arithmetic Textbook | veikalai aritmētikos terminai The derivative of the suffix -lius, skaitlys „number“ Vlš 3, which became common around the middle of the 19th century, although it is already found in 16th-century Lithuanian writings (Mažvydo Catechism, Wolfenbüttel Postilla, Wilento Gospels, Bretkūno Bible and Postilla) (Rumšas 1978: 52–54). It is important to note that the current term number is found in the early 19th-century elementaries, but was later abandoned. P. Skardžius writes in Lithuanian word formation that numeral is typical of the Žemaičiai and East Prussian Lithuanians, while the Altai usually used the term skaičius (Skardžius 1943: 170). In 1906, the term "numbers" was replaced by "numbers" in mathematics textbooks, but the term "digit" was used in the press of the time, although rarely. 1.2.2.2. Derivatives of extremities. In P. Vileišis’ textbook, derivatives of extremities were also found: -is (-ys): part Vlš 10, division Vlš 35, ridge Vlš 7, joint Vlš 11, leg Vlš 32; -ė: gymē Vlš 4, division Vlš 35, mark Vlš 11; -(i)us: section Vlš 3, fruit Vlš 22. All these derivatives of the endings are made from verbs. 1.2.2.3. Dūrnieki. In the textbook, only one punching table picture Vlš 50 is found: Surszumi padētas galda bildes aiztur savēpi augļus vienā rokůtinēs Vlš to mean “table” (see table 50. Šis terminas nefiksuojamas LKŽe, galima tik spėti, kad jis galėtų picture multiplication “multiplication table” Vlš 50 (see figure)). Figure table of multiplication 161Terminologija | 2011 | 18 2. COMPOSITED TERMS In the textbook of P. Vileišis the compound terms are divided into two-word and three-word. They make up 57.8% of all found terms. For the purposes of this Article, ambiguous terms shall be divided into combinations of a compatible and an incompatible mark in terms of their expression. The majority of them are terms with both elements of Lithuanian origin. Only a few two-word terms were found, one of which is of non-Lithuanian origin: apturējimas sumos Vlš 11, czelas skaičius Vlš 11, gulsczias kryžius Vlš 22, rokůtinė svarbi Vlš 7, skaičius czelas Vlš 5, status kryžius Vlš 11, vardas klasės Vlš, vienybē matēmatikinē Vlš 3. The combinations of the conjugation mark used in the textbook are two-fold. One group consists of terms whose combining notation goes before the main notation term element, the other group consists of terms whose notation goes after the main notation term element. Combinatory signs of these terms, preceding the indicative word, are represented in the textbook by adjectives (bevardē padalē Vlš 36, partial division Vlš 40, greater numbers Vlš 16, smaller numbers Vlš 16, primary numbers Vlš 5, poor singularity Vlš 26, universal significance Vlš 7) and by participants of the active or passive kind (apreikszta teisybē Vlš 14, atsakanti rokůtinē Vlš 8, alternating significance Vlš 7, unalterable significance Vlš 7, unalterable majority Vlš 3, decided majority Vlš 3). It is important to say that the textbook of P. Vileišis also uses nominative forms of indicative verbs (adjectives and participles): aukščiausiasis rėžis Vlš 8, jieszkomasis labas Vlš 12, jieszkomasis skaičius Vlš 16, jieszkomasis vaisius Vlš 24, norimasis labas Vlš 4, padůtasis skaičius Vlš 4, sumestieji skaičiui Vlš 20, leidžiamasis skaičius Vlš 11. A large group consists of two-word terms, the combining mark of which goes after the comma. The signs of these two-word terms are also represented by adjectives (divizija paprastasis Vlš 41, labas beznomens Vlš 11, padalē teisingas Vlš 41, skaičius benomens Vlš 4, skaičius dalinis Vlš 3, vaisius partilinis Vlš 27, vaisius visůtinas Vlš 27, vienybē veislinē Vlš 3) and by participants of the inactive kind (labas pažymėtas Vlš 10, skaičiavimas kalbėjo Vlš 5, skaičiavimas raszytas Vlš 6, skaičius mišrus Vlš 3, skaičius pažymėtas Vlš 4). Almost all non-compatible signs are represented by a singular or plural genitive. Most of these terms are now used in an unusual word order: augimas skaičiumi Vlš 4, iszguldymas rėžio Vlš 7, isztarimas 162 D. Šilobritaitė | Four most important numbers Vlš 9, subtraction Vlš 46, | veikalai aritmētikos terminai division Vlš 47, multiplication Vlš 46, addition Vlš 46, imposition of unity Vlš 4, joint division Vlš 35, division of unity Vlš 3, table multiplication Vlš 50, addition of unity Vlš 4, variety division Vlš 35, subtraction Vlš 16, division Vlš 35, equality Vlš 11, multiplication Vlš 22, addition Vlš 11, multiplication of powers Vlš 32. The two-word incompatible term with the prefix be – rokůtinē without importance "zero" Vlš 7. In the textbook there are also two-word terms of ordinary expression of incompatible sign, the sign of which goes before the sign word: skaitliu iszskirimas Vlš 4, skaičiu kilimas Vlš 4, skaičiu sumetimas Vlš 4, skaitliaus skyrei Vlš 3. 2.2. Three-word terms All elements of three-word arithmetic terms are of Lithuanian origin and almost all of them are made up with the term in unity (naming classes of units). The main point of these terms has the non-conjugating sign with its conjugating sign, which follows the main point: in the singular of the second row Vlš 5, in the singular of the asztunth row Vlš 6, in the singular of the tenth row Vlš 6, in the singular of the ninth row Vlš 6, in the singular of the twelfth row Vlš 6, in the singular of the fourth row Vlš 6, in the singular of the fifth row Vlš 6, in the singular of the first row Vlš 5, in the singular of the seventh row Vlš 6, in the singular of the sixth row Vlš 6, in the singular of the third row Vlš 5, in the singular of the eleventh row Vlš 6. Other three-word terms of the discussed expression are the nature of the desired good Vlš 4, the fruit of the journey of the worker Vlš 28. The terms second joint in Vlš 11 and primary joint in Vlš 11 are defined differently – with the alignment and non-alignment mark. In addition, it should be noted that the word order of these two terms is unusual. In the textbook, a three-word term has been found, the indicative word of which has two conjugable indicatives: du rūžai lygatstogei Vlš 11. 3. Synonyms There are few cases of synonymous expression in P. Vileišis’s textbook. Synonyms rašomi skliausteliuose, jungiami kableliu arba jungtuku arba. Binary synonym strings were found (minus (lowest) Vlš 16, unchanging or perpetual significance Vlš 7, poor unity or primary unity Vlš 5, nature, or variety Vlš 36, counting (numeration) Vlš 4, status cross, plus Vlš 11) and a ternaire synonym string (rokůtinē without significance, or zero (zero) Vlš 7).