Vienažodžių matematikos terminų sinonimija matematikos vadovėliuose (1910–1940)

Synonymy of one-word mathematical terms in mathematics textbooks (1910–1940) DIANA ŠILOBRITAITĖ Institute of the Lithuanian Language 1. INTRODUCTORY REMARKS The first mathematical concepts emerged in the time of primitive communities in response to the practical needs of human activity. It is believed that the term mathematics began to be used in Greece in the 6th century BC. Mathematics then became an independent science. Lithuanian mathematicians and linguists began to organize and standardize Lithuanian terms only from the end of the 19th century, although arithmetic had been taught in Lithuanian parish schools since the end of the 15th century, and in 1539 arithmetic and geometry were among the seven liberal arts taught at the Reformation school founded by A. Kulvietis in Vilnius. The first mathematical works in Lithuania were published in Latin and later in Polish, for example: Jonas Rudamina Dusetiškis’s Famous Mathematical Theorems and Problems (Illustr iora theoremata et problemata mathematica ex opticis geometria astronomia sphaera elementari computo ecclesiastico 1633), Osvaldas Krygeris’s Practical Arithmetic (Arithmetica practica in usum studiosae juventutis Academiae et Universitatis Vilnensis Societatis Jesu 1635), Mykolas Kazimieras Belkovskis’s Theorecentrica, or Mathematical Considerations on Points and Centers (Theorecentrica sive mathematicae de punctis et centris considerationes 1644), and others (LTE VII 1981: 308–312). In the mid-19th century, attempts were made to publish the first Lithuanian school mathematics textbooks. They were prepared by J. Stanevičius (around 1830) and M. P. Marcinskis (around 1860), but were not published. 1.1. Standardization of Mathematical Terminology: Textbooks and Dictionaries The first Lithuanian arithmetic textbooks were published at the end of the 19th century: P. Matulionis and J. Spudulis (compiled by J. Gailutis), Užduotinas, tai ira Rankius užduocziu Aritmetikos arba Rakundos mokslo (1885); P. Nėris (P. Vileišis), Keturi svarbiausieji veikalai Aritmetikos (1886); and S. Gimžauskas, Pradžiamokslis 146 Diana Šilobritaitė │ Vienażodžių matematikos terminų sinonimija… Lietuviško spaudrasčio ir rankrašččio (1888), S. Skačkausko Aritmetika (1897). Minėtų vadovėlių matematikos terminiją aptarė aritmetikos terminijos istorijos tyrinėtojas P. Rumšas (Rumšas 1978: 52–60). At the beginning of the 20th century, the number of Lithuanian mathematics textbooks and problem books increased—as arithmetic began to be taught in the native language. The standardization of terminology is evident: “arithmetic operations, the numbers on which the operations are performed, the results of those operations, the terms of fractions, and so on, are all called by the same names” (Rumšas 1980: 73). Several editions (1906–1918) of P. Bendorius and P. Daugirdas’s Collection of Arithmetic Problems and Examples appeared, as did P. Mašiotas’s Arithmetic Problem Book (1906, 2 parts) and A. Vėgelė’s translation of S. Thoma’s A Brief Course in Arithmetic (1916). Articles worth mentioning include [A. Dambrauskas’s] A. Jakštas’s A Few Words on the Criterion of Mathematical Poeticity (Draugija 1907 1: 28–31), A. Bernštein’s (translated by B. Lesys) Some Secrets of Numbers (Viltis 1908 78: 4; 1908 81: 4), P. Mašiotas’s From the History of Numeration (Draugija 1908 9: 396–400), and [A. Dambrauskas’s] A. Jakštas’s review of The Gradual Learning of Arithmetic, or Rokunda (Draugija 1909 27: 272). The first mathematics terminology glossaries were published midway through the period under study: M. Šikšnys’s Glossary of Arithmetic and Algebra Terms (Vilnius, 1919) and Z. Žemaitis’s Collection of Geometry and Trigonometry Terms (Kaunas, 1920). These were among the first printed Lithuanian terminology glossaries. They laid the foundations for Lithuanian school mathematics terminology. The article examines one-word synonyms for mathematical terms collected from secondary-school mathematics textbooks published in the first half of the 20th century (up to 1940). The material was collected from 24 textbooks: V. Budrevičius’s Theory of Algebra (1919); A. Busilas’s Arithmetic (1921); A. Busilas’s Young Surveyor (1921); J. Damijonaitis’s Arithmetic Textbook (1910 (1911), 2 parts); A. Jakštas’s Plane Trigonometry (1919); J. Mašiotas’s Mathematics Textbook (Geometry. 1937–1938, 3 parts); J. Mašiotas’s Mathematics Textbook (Arithmetic and Algebra. 1939–1940, 3 parts); K. Klimavičius’s Geometry (1938–1940, 3 parts); Masing (translated by A. Smetona), Theory of Arithmetic (1922); M. Šikšnys’s Geometry (1923); M. Šikšnys’s Elementary Algebra (1923); M. Šikšnys’s Geometry (1938–1939, 3 parts); and M. Šikšnys’s Arithmetic and Algebra (1939, 3 parts). The textbooks from the period under analysis were of two kinds: theoretical (devoted solely to theory) and mixed (presenting both theory and practice). Problem books were also published, but their terminology was not collected, since it differs little from that used in textbooks. Terminologija | 2007 | 14 147 2. ONE-WORD SYNONYMS OF MATHEMATICAL TERMS Most one-word synonymous terms in mathematics textbooks from 1910–1940 are used by different authors. Fewer synonyms are found that are used by the same author. In terms of origin, synonym sets are of two types: mixed-origin (synonymy between Lithuanian and foreign-origin terms) and common-origin (synonymy among purely Lithuanian terms). 2.1. One-word synonyms of mathematical terms used by the same author Only one set of Lithuanian term synonyms was found in a textbook by the same author: apibrėžimas (nusakymas) MAT 1922 11. The terminology glossaries of Z. Žemaitis and M. Šikšnys give only the term apibrėžimas, coined by J. Jablonskis on the basis of the verb apibrėžti, “to provide a definition” (see Rumšas 1975: 8). Mixed-origin synonym sets are more common in textbooks by the same authors: dvinaris – binomas ŠAA I 1939 110; gretasienis – paralelepipedas BJM 1921 79; įžambinė – hipotenūzė BJM 1921 17, KG 1939 19, KG 1940 31, MG I 1937 52, MG II 1938 4, MG III 1938 3, ŠG 1923 25, ŠG I 1938 36, ŠG II 1938 55, ŠG III 1939 4; kubas – šeštainis MAT 1922 46. The Lithuanian terms gretasienis, proposed by Z. Žemaitis, and įžambinė have become established and are used in mathematical terminology. MTŽ 1994 dvinaris and binomas are still given as synonyms: binomas see dvinaris – dvinaris, binomas: diferencialinis, tiesinis, but they are distinguished in some compound names: dvinario kubas, dvinario kvadratas and binomo skleidinys, binomo formulė. The non-Lithuanian-origin term kubas is used for a rectangular parallelepiped whose faces are squares. The terms paralelepipedas (cf. Russian параллелепипед, English parallelepiped) and hipotenūzė (cf. Russian гипотенуза, English hypotenuse) have not become established in Lithuanian mathematical terminology and are not used. 2.2. One-word synonyms of mathematical terms used by different authors Lithuanian synonyms of terms used by different authors are lexical and derivational. J. Pikčilingis considers lexical synonyms to be words from the same part of speech that sound different but denote the same thing, quality, or action (Pikčilingis 1969: 4). 148 Diana Šilobritaitė │ Vienažodžių matematikos terminų sinonimija… Lexical synonyms are the most frequent in the mathematics textbooks under study. 2.2.1. SYNONYMS OF MATHEMATICAL TERMS OF DIFFERENT ORIGINS One-word synonyms of terms of different origins are used particularly frequently by different authors: diagonal BJM 1921 3, ŠG I 1938 34 – diagonal BJM 1921 3, ŠG 1923 24; sector (of a circle) BA 1921 4, KG 1938 19, MG I 1937 26, ŠG 1923 66, ŠG I 1938 16, ŠG III 1939 24 – sector ŠG 1923 66 / sector ŠG III 1939 24; protractor BJM 1921 9, JPT 1919 7, KG 1938 28, KG 1939 5, KG 1940 70, MAA I 1940 142, MG I 1937 36, ŠG I 1938 21 – protractor ŠG I 1938 21; circular segment KG 1938 21, MG I 1937 26, ŠG 1923 66, ŠG I 1938 16, ŠG III 1939 25 – segment ŠG 1923 66, ŠG III 1939 25; angle bisector KG 1938 46, KG 1940 87, MAA III 1940 66, ŠG 1923 15, ŠG I 1938 40 – angle bisector KG 1938 46, ŠG 1923 15; median (of a triangle) KG 1938 46, ŠG 1923 26 – median JPT 1919 104, KG 1938 46, ŠG 1923 26; compass BA 1921 3, BJM 1921 30, JPT 1919 46, KG 1938 13, KG 1940 104, MG I 1937 19, MG II 1938 124, MG III 1938 75, ŠG 1923 10, ŠG I 1938 10 – compass KG 1938 51, ŠG 1923 10; leg BJM 1921 17, KG 1938 44, KG 1939 12, KG 1940 17, MAA II 1939 117, MG I 1937 52, MG II 1938 4, MG III 1938 3, ŠG 1923 25 – cathetus BJM 1921 17, KG 1938 44, ŠG III 1923 25; chord BJM 1921 52, KG 1938 20, KG 1939 32, KG 1940 45, MG I 1937 26, MG II 1938 48, MG III 1938 55, ŠG 1923 66, ŠG I 1938 16, ŠG II 1938 18, ŠG III 1939 5 – chord BJM 1921 52, JPT 1919 61, ŠG 1923 66. In Z. Žemaitis's Collection of Geometry and Trigonometry Terms, all these terms are also listed as synonyms. In present-day mathematical terminology, angle bisector (Russian биссектриса), diagonal (Russian диагональ), protractor (Russian транспортир), compass (Russian циркуль), cathetus (Russian катет), chord (Russian хорда) are not used. The terms angle bisector, diagonal, protractor, compass, leg, chord have become established (MTŽ 1994). The following are considered synonyms: sector – segment of a circle, circular segment – segment, but the established terms are the Lithuanian ones sector of a circle, circular segment. The term median and median are distinguished in present-day mathematical terminology: median (of a triangle) – “a line segment joining a vertex of a triangle to the midpoint of the opposite side (in geometry)” DŽ₅, median – “the middle (central) value of a random variable (in probability theory and mathematical statistics)” TŽŽŽe 2002. Z. Žemaitis does not use the Lithuanian-origin terms cone, perpendicular; cf.: cone BJM 1921 89, KG 1938 5, MG I 1937 8 – conus BJM Terminologija | 2007 | 14 149 1921 89; perpendicular BJM 1921 3, KG 1938 32, KG 1939 12, KG 1940 31, MAA II 1939 34, MAA III 1940 66, MG I 1937 46, MG II 1938 5, MG III 1938 53, ŠAA II 1939 24, ŠG 1923 15, ŠG I 1938 45, ŠG II 1938 10, ŠG III 1939 3 – perpendicular ŠG 1923 15. They are not used in present-day mathematical terminology either. In Z. Žemaitis's Collection of Geometry and Trigonometry Terms, the following are also not considered synonyms: quadrilateral BJM 1921 19, MAT 1922 44 – square BA 1921 7, BJM 1921 19, KG 1938 84, KG 1939 19, KG 1940 7, MAA I 1940 22, MAA III 1940 4, MAT 1922 44, MG I 1937 109, MG II 1938 3, ŠG 1923 62, ŠAA I 1939 44, ŠAA II 1939 3, ŠAA III 1939 11, ŠEA 1923 14. The adjectives quadrilateral-shaped – square are listed as synonyms in Z. Žemaitis's collection. In M. Šikšnys's Glossary of Arithmetic and Algebra Terms, the term digit is not used; in textbooks from later years, numeral became established: numeral BA 1921 5, BAT 1919 6, BJM 1921 9, KG 1938 22, MAA I 1940 11, MAA III 1940 46, MAT 1922 9, ŠG 1923 12, ŠAA I 1939 6, ŠAA II 1939 101, ŠAA III 1939 13, ŠG I 1938 81, ŠG III 1939 6 – digit BAT 1919 5. In M. Šikšnys's glossary, the terms used in textbooks addend BAT 1919 31, MAT 1922 11 – sum BA 1921 10, BAT 1919 17, BJM 1921 4, DAV 1910 39, JPT 1919 40, KG 1938 14, KG 1940 20, MAA I 1940 41, MAA III 1940 12, MAT 1922 11, MG I 1937 20, MG II 1938 6, MG III 1938 23, ŠAA I 1939 10, ŠAA II 1939 5, ŠAA III 1939 4, ŠEA 1923 10, ŠG 1923 11, ŠG I 1938 11, ŠG II 1938 33, ŠG III 1939 4 – are considered synonyms. However, M. Šikšnys also lists sum, but uses only the term sum in his textbooks, and that is the term that became established in mathematics. A four-member synonym series most often consists of one international term and three Lithuanian terms: transversal JPT 1919 28 – cross-section BA 1921 50, BJM 1921 44 – diameter BA 1921 50, KG 1938 20, KG 1940 38, MAA II 1939 17, MG I 1937 26, MG III 1938 53, ŠG 1923 66, ŠG I 1938 16, ŠG II 1938 17, ŠG III 1939 5 – diameter BJM 1921 89, JPT 1919 18, KG 1938 20, ŠG 1923 66. The terms transversal, cross-section used by individual authors did not become established. Nor is diameter used (Russian диаметр); diameter became established. A five-member series consists of four Lithuanian terms and one term of non-Lithuanian origin: scale DAV 1910 20 – scale KG 1940 39, MAA I 1940 22, MG II 1938 119, MG III 1938 4, ŠAA 1939 48, ŠG II 1938 68 – scale indicator KG 1940 39 – scale BA 1921 46, BJM 1921 35 – measure BJM 1921 39. As can be seen, the most frequent term is scale, which was used in later 150 Diana Šilobritaitė │ Vienažodžių matematikos terminų sinonimija... vadovėliuose (1938, 1940). Tačiau juose dar randamas terminas dydrodis, kurio vėliau buvo atsisakyta. Z. Žemaitis ir J. Jablonskis masteliui įvardyti siūlė mastą (plačiau žr. Klimavičius 2005: 143–146). One instance was found in which a synonym series consists of hybrid one-word terms, e.g.: liniuote BJM 1921 12, KG 1938 7, KG 1940 70, MAA II 1939 60, MG I 1937 11, MG III 1938 90, ŠAA II 1939 32, ŠG 1923 7, ŠG I 1938 7, ŠG III 1939 67 – linijuoklas JPT 1919 46. As can be seen, the term linijuoklas is used by only one author. This term did not take hold – the term liniuote has survived to the present day and is used in mathematical terminology. 2.2.2. SAME-ORIGIN SYNONYMS OF MATHEMATICAL TERMS There are quite a few cases in which one of the synonyms is used by most mathematics textbook authors, while the other is used by only one: apskritimas BJM 1921 51, KG 1938 17, KG 1939 30, KG 1940 7, MAA II 1939 149, MG I 1937 11, MG II 1938 3, ŠG 1923 43, ŠG I 1938 15, ŠG II 1938 17, ŠG III 1939 3 – ratlankis ŠG 1923 43 (in Z. Žemaitis’s Geometrijos ir trigonometrijos terminų rinkinėlyje, apskritimas and skraja are synonymous); atkarpa BA 1921 4, BJM 1921 23, KG 1938 10, KG 1939 5, KG 1940 5, MAA I 1940 11, MAA II 1939 32, MG I 1937 17, MG III 1938 21, ŠAA I 1939 8, ŠAA II 1939 26, ŠEA 1923 27, ŠG I 1938 10 – atrėžas JPT 1919 28 (Z. Žemaitis’s collection contains only atkarpa); gavinys MAA I 1940 15, MAA II 1939 9, MAA III 1940 11, ŠAA I 1939 156, ŠAA III 1939 3 – išdava MAA I 1940 15 (Z. Žemaitis gives only gavinys); rutulys BJM 1921 76, KG 1938 5, MAA II 1939 24, MG I 1937 9 – kamuolys KG 1938 5 (in Z. Žemaitis’s terminology collection: rutulys); liekana BA 1921 9, BAT 1919 37, JPT 1919 30, DAV 1910 27, KG 1938 12, MAA I 1940 35, MAA III 1940 34, ŠAA I 1939 6, ŠAA II 1939 101, ŠAA III 1939 15 – išdalos MAT 1922 30 (M. Šikšnys and Z. Žemaitis include both terms in their glossaries); lygtis BAT 1919 87, MAA II 1939 6, MG III 1938 6, ŠAA II 1939 50, ŠAA III 1939 11, ŠG III 1939 26 – lyginys JPT 1919 9, MAT 1922 128 (in Z. Žemaitis’s collection these terms are not considered synonyms: lygtis (Russian уравнение) and lyginys (равенство (формула))); sąlyga BJM 1921 38, JPT 1919 9, KG 1938 64, MAT 1922 110 – sutartis MAT 1922 110; sandauga BA 1921 10, BAT 1919 17, BJM 1921 45, KG 1939 12, KG 1940 7, MAA I 1940 48, MAA II 1939 15, MAA III 1940 3, MAT 1922 21, MG I 1937 41, MG II 1938 11, MG III 1938 14, ŠG 1923 11, ŠAA I 1939 7, ŠAA II 1939 9, ŠAA III 1939 3 – padaugas JPT 1919 53 (in M. Šikšnys’s terminology glossary: sandauga); skaitiklis BA 1921 5, BAT Terminologija | 2007 | 14 151 1919 17, JPT 1919 22, KG 1940 71, MAA I 1940 34, ŠAA I 1939 8, ŠAA II 1939 107 – suskaitýtojas DAV 1910 25 (in M. Šikšnys’s terminology glossary: skaitiklis); skritulys BA 1921 3, BJM 1921 51, JPT 1919 13, KG 1938 7, KG 1939 37, MAA I 1940 22, MG I 1937 11, MG III 1938 53, ŠG 1923 66, ŠG I 1938 5, ŠG III 1939 22 – ratas ŠG 1923 66 (in Z. Žemaitis’s terminology collection: skritulys). Terms presented in the earliest glossaries of mathematical terminology are used by many mathematics textbook authors; only some authors later introduced their own terms without justification. Speaking about the term lygtis, Z. Žemaitis noted that it had not appeared in earlier Lithuanian writings. It is therefore unsurprising that the term lyginys was used to denote this concept, particularly in earlier textbooks. J. Jablonskis proposed using the term lygtis in the plural rather than the singular. In his view, “this concerns the necessary interaction of two parts, their equality and balance” (Žemaitis 1966: 198). However, mathematicians convinced J. Jablonskis that “it is important to have this concept expressed in the singular, so that it is clear that the matter concerns not several equations, but one equation” (Žemaitis 1966: 198). The member vardiklis of the three-term lexical synonym series is the most frequently used in mathematics textbooks from the period under analysis: vardiklis BAT 1919 17, JPT 1919 22, KG 1940 71, MAA I 1940 34, ŠAA I 1939 8, ŠAA II 1939 63 – pažymėtojas DAV 1910 25 – ženklininkas BA 1921 5. It is also included in M. Šikšnys’s Aritmetikos ir algebros terminų žodynėlyje. The term pažymėtojas is used in a textbook (by J. Damijonaitis) published before the appearance of M. Šikšnys’s glossary (in the textbook by P. Matulionis and J. Spudulis [edited by J. Gailutis], Užduotinas, tai ira Rankius užduocziu Aritmetikos arba Rakundos mokslo (1885), the term žymėtojas is used). Vardiklis is already used in a 1919 textbook (it is also included in M. Šikšnys’s Aritmetikos ir algebros terminų žodynėlyje), so it is unclear why the term ženklininkas was used to denote this concept in a 1921 textbook. According to J. Vaskelienė, derivational synonyms are formations that share the same root, have similar meanings, and belong to the same word-formation category (Vaskelienė 2000: 75). In the mathematics textbooks analyzed, two-member derivational synonym series are the most frequent. Often, terms in synonym series differ in their derivational suffixes, e.g.: daliklis BA 1921 13, BAT 1919 17, MAA I 1940 72, MAA II 1939 5, MAT 1922 29, ŠAA I 1939 6, ŠAA II 1939 7, ŠAA III 1939 6, ŠEA 1923 38 – dalytojas DAV 1910 27; daugyba BA 1921 21, BAT 1919 16, JPT 1919 86, 152 Diana Šilobritaitė | Vienaðodžių matematikos terminų sinonimija... MAA I 1940 41, MAA III 1940 13, MAT 1922 21, ŠAA I 1939 31, ŠAA II 1939 97, ŠAA III 1939 9, ŠEA 1923 7, ŠG 1923 11, ŠG I 1938 12 – multiplication BA 1921 29, DAV 1910 4, DAV 1911 8, JPT 1919 74, MAT 1922 24; law BJM 1921 33, KG 1938 8 – taught MAT 1922 47. The term “divisor” did not take root in mathematical terminology because it contradicts the rules of word formation: the suffix –tojas is generally used to form names of agents and, much less often, names for bearers of verbal properties. This term was used in the first mathematics textbooks—those by P. Matulionis and J. Spudulis (compiled by J. Gailutis) (1885), and P. Nėris (P. Vileišis) (1886). After M. Šikšnys’s Glossary of Arithmetic and Algebra Terms appeared, daliklis (divisor) came into consistent use. The terms daugyba and dauginimas (and, until the 20th century, padauginimas was also used) are still used in contemporary terminology. According to Z. Žemaitis, the term dauginimas should be used “to denote the performance of specific operations” (Žemaitis 1966: 196). This group can include synonym sets in which one member is a substantivized participle and the other a suffix-derived noun: dalijamasis BA 1921 52, BAT 1919 17 – dalinys BA 1921 29, BAT 1919 52, DAV 1910 27, JPT 1919 53, KG 1938 14, MAA I 1940 72, MAA II 1939 14, MAA III 1940 15, MAT 1922 29, ŠAA I 1939 33, ŠAA II 1939 7, ŠAA III 1939 9, ŠEA 1923 7, ŠG I 1938 12, ŠG III 1939 6 (these terms are also listed as synonyms in M. Šikšnys’s Glossary of Arithmetic and Algebra Terms); liečiamoji BJM 1921 53, JPT 1919 29, ŠG 1923 72, ŠG II 1938 17 – lietėja KG 1939 35, KG 1940 52, MG II 1938 51, ŠG II 1938 17. The latter terms were the subject of considerable debate. Z. Žemaitis noted that the term liečiamoji could be ambiguous (although he included it in his Collection of Geometry and Trigonometry Terms): “is it a line that touches something, or one that is touched by something?” J. Jablonskis proposed the term lietėja, “emphasizing its particular activity” (Žemaitis 1966: 198). In contemporary mathematical terminology, the term liestinė is used for a line that has only one point in common with a curve (MTŽ 1994). Another synonym set consists of a substantivized definite adjective and participle form: pasviroji BJM 1921 53, MG I 1937 42, ŠG I 1938 28, ŠG III 1939 40 – pasvirusioji KG 1938 32, ŠG 1923 15. The term pasviroji has survived to the present and is used in contemporary mathematical terminology to denote a line inclined to a line or plane (MTŽ 1994). The following are also regarded as derivational synonyms: stačiakampainis KG 1938 82, ŠG 1923 60 – stačiakampis BA 1921 7, BJM 1921 19, KG 1939 5, KG 1940 31, MAA I 1940 22, MAA III 1940 153, MG I 1937 105, MG II 1938 3, ŠG Terminologija | 2007 | 14 1 5 3 I 1938 85, ŠG II 1938 3. In contemporary mathematical terminology, stačiakampis is used; it had already appeared in Z. Žemaitis’s Collection of Geometry and Trigonometry Terms. Mathematics textbooks contain sets of three and four derivational synonyms: kertamoji BIM 1921 52, KG 1940 9, ŠG 1923 66, ŠG II 1938 17 – kertė MAT 1922 44 – kirtėja KG 1939 34, KG 1940 52, MG II 1938 50, ŠG I 1938 16, ŠG II 1938 17; sudėtis BA 1921 72, BAT 1919 12, MAA I 1940 41, MAA II 1939 28, MAA III 1940 12, MAT 1922 11, ŠAA I 1939 20, ŠAA II 1939 93, ŠEA 1923 7, ŠG I 1938 11 – sudėjimas MAT 1922 12 – sudėstymas DAV 1910 3, DAV 1911 3; dalyba BA 1921 13, KG 1938 14, MAA I 1940 41, MAA III 1940 15, MAT 1922 29, ŠAA I 1939 31, ŠAA III 1939 9, ŠEA 1923 7, ŠG I 1938 12, ŠG III 1939 6 – dalijimas BA 1921 27, BAT 1919 65, DAV 1910 4, DAV 1911 9, ŠAA I 1939 157 – dalymas JPT 1919 74 – dalinėjimas MAT 1922 64; daugiklis BJM 1921 82, JPT 1919 128, MAA I 1940 48, MAA II 1939 5, MAT 1922 21, MG I 1937 21, ŠEA 1923 11, ŠG I 1938 12, ŠG III 1939 23 – dauginamasis BA 1921 16, BAT 1919 17, MAA I 1940 48, MAA II 1939 21, MAA III 1940 3, ŠAA I 1939 7, ŠAA II 1939 3, ŠAA III 1939 4 – dauginys ŠAA I 1939 31 – daugmuo BA 1921 18, BAT 1919 41, MAA I 1940 48, MAT 1922 21, ŠEA 1923 36. As can be seen, the synonyms occur in textbooks by both the same and different authors. To name the quantity multiplied by another quantity, J. Jablonskis proposed the terms daugmuo (for the first number) and daugiklis (for the second number). P. Rumšas notes that “daugmuo and dalmuo are coinages formed with the same suffix, so it is unclear why daugmuo was supposed to mean the multiplicand, whereas dalmuo, by contrast, did not mean the dividend but the quotient” (Rumšas 1975: 7). Not all the terms in the synonym sets mentioned above became established or are used in mathematics. For example, kertamoji – kertė – kirtėja: kertamoji means “a machine for cutting grain”; kertė means “the corner of a room or object; a small plot, an edge”; and kirtėja is a noun denoting a person. Although mathematics uses the term kertančioji linija (MTŽ 1994), the term kirstinė. (secant) is used for a line that intersects a curve at least at two points. Sudėstymas is also not used in contemporary mathematical terminology (cf. the base word of this term, sudėstyti, “to arrange, to fold”). Dalijimas and dalinėjimas have different meanings. The term daugyba proposed by J. Jablonskis was a coinage—it has only one meaning, a mathematical one: daugyba, mathematics, “the operation of multiplication” (J. Jablonskis): Multiplication table, multiplication alphabet (Z. Žemaitis). Multiplication of segments writings 154 Diana Šilobritaitė │ Vien ažodžių matematikos terminų sinonimija… (LKŽe). Composition and division may have arisen through terminologization—cf. composition 2. “addition, growth, figure”: Such is my build, and the children have not grown thin Tauragnai. The girl has a beautiful build, she is very tall Pandėlys; 4. “main, connecting part”: The beam is the composition of the whole plough Šeduva (the same applies to other newer meanings—2. “the totality of constituent parts, their arrangement, structure”: One must always move gradually from one composition of feed to another writings; 3. “the totality of people making up a collective, organization, etc.”: The composition of a team, council, commission writings), although the word may have been unfamiliar when used narrowly as a term, so this development is more likely only conjectural; division 2. “dividing”: They came to divide it up, so we got some land Vilkaviškis (Daukšiai, Veiveriai), and more broadly dalybos 1. “division of an inheritance or property by apportionment, dividing,” 2. “division, distribution” (LKŽe). A case in which the synonym series consists of two derivational synonyms and one lexical synonym merits separate mention: atimtis BA 1921 72, BAT 1919 11, MAA I 1940 41, MAA II 1939 28, MAA III 1940 12, MAT 1922 14, ŠAA I 1939 20, ŠAA II 1939 93, ŠEA 1923 7, ŠG I 1938 12 – atimstymas DAV 1910 3, DAV 1911 11 – atskait ymas DAV 1911 3. Atimstymas and atskait ymas are used only by one of the authors of the earliest mathematics textbooks (J. Damijonaitis). Soon, the neologism atimtis became established in mathematical terminology (M. Šikšnys’s collection of terms also lists only this term), and it was used by most authors of mathematics textbooks from the period under study. 3. CONCLUSIONS A considerable number of synonyms for one-word mathematical terms are used in secondary-school mathematics textbooks from 1910–1940. In terms of origin, they fall into two types—mixed-origin (Lithuanian and foreign-origin term synonyms) and same-origin (purely Lithuanian term synonyms). Mixed-origin term synonyms make up the majority. Fewer same-origin term synonyms are used. Hybrid synonyms are not characteristic of the mathematical terminology of the period under discussion. Purely Lithuanian terms used by the same author as well as by different authors are most often cases of lexical synonymy. The sources examined contain somewhat fewer cases of derivational synonymy. After the publication of the first glossaries of mathematical terms (M. Šikšnys’s Glossary of Arithmetic and Algebra Terms, Z. Žemaitis’s Collection of Geometry and Trigonometry Terms), the number of synonyms declined. There are many cases in which some mathematics textbook authors did not take into account the terms provided in those Terminologija | 2007 | 14 155 glossaries. However, they did so without justification. In M. Šikšnys’s and Z. Žemaitis’s collections of terms, as in the textbooks examined, the synonymous terms are in most cases of mixed origin. In M. Šikšnys’s textbooks published after the glossary appeared, synonymous terms still occur, but more often only one term is selected; it is also used in present-day mathematical terminology. It is difficult to judge the subsequent use of Z. Žemaitis’s terms, since no school mathematics textbooks written by him appeared during the period under study. Analysis of synonymy among one-word mathematical terms in mathematics textbooks from the first half of 1910–1940 suggests that the textbook authors of that period established the terms of the first mathematical glossaries, reduced instances of synonymy—with a few exceptions—and more often rejected foreign terms. ŠALTINIAI BA 1921 – Busilas A. Aritmetika. Uždaviny nas ir teorija, Kaunas. BAT 1919 – Budrevičius V. Algebros teorija, Vilnius. BJM 1921 – Busilas A. Jaunas matininkas. Geometrija vidurinei mokyklai, Kaunas. DAV 1910 – Damijonaitis J. Aritmetikos vadovėlis 1, Varšuva. DAV 1911 – Damijonaitis J. Aritmetikos vadovėlis 2, Varšuva. JPT 1919 – Jakštas A. Plokštinė trigonometria. Pilnas sistematiškas kursas. Teorija ir uždaviniai, Kaunas. KG 1938 – Klimavičius K. Geometrija 1, Kaunas. KG 1939 – Klimavičius K. Geometrija 2, Kaunas. KG 1940 – Klimavičius K. Geometrija 3, Kaunas. MAA I 1940 – Mašiotas J. Matematikos vadovėlis 1: Aritmetika ir algebra. Teorija ir uždavinynas vidurinei mokyklai, Kaunas. MAA II 1939 – Mašiotas J. Matematikos vadovėlis 2: Aritmetika ir algebra. Teorija ir uždavinynas vidurinei mokyklai, Kaunas. MAA III 1940 – Mašiotas J. Matematikos vadovėlis 3: Aritmetika ir algebra. Teorija ir uždavinynas vidurinei mokyklai, Kaunas. MAT 1922 – Masingas Aritmetikos teorija (vertė A. Smetona), Kaunas, Vilnius. MG I 1937 – Mašiotas J. Matematikos vadovėlis 1: Geometrija. Teorija ir uždavinynas vidurinei mokyklai, Kaunas. MG II 1938 – Mašiotas J. Matematikos vadovėlis 2: Geometrija. Teorija ir uždavinynas vidurinei mokyklai, Kaunas. MG III 1938 – Mašiotas J. Matematikos vadovėlis 3: Geometrija. Teorija ir uždavinynas vidurinei mokyklai, Kaunas. ŠAA I 1939 – Šikšnys M. Aritmetika ir algebra 1, Kaunas. ŠAA II 1939 – Šikšnys M. Aritmetika ir algebra 2, Kaunas. ŠAA III 1939 – Šikšnys M. Aritmetika ir algebra 3, Kaunas. ŠĖA 1923 – Šikšnys M. Elementarinė algebra, Kaunas. ŠG 1923 – Šikšnys M. Geometrija, Kaunas. ŠG I 1938 – Šikšnys M. Geometrija 1, Kaunas. ŠG II 1938 – Šikšnys M. Geometrija 2, Kaunas. ŠG III 1939 – Šikšnys M. Geometrija 3, Kaunas. 156 Diana Šilobritaitė | Vien ažodžių matematikos terminų sinonimija… LITERATŪRA DŽ5 2005: Dabartinės lietuvių kalbos žodynas (elektroninis leidimas), Vilnius. Klimavičius J. 2005: Terminas prie termino. II. – Terminologija 12, 143–146. Knygos lietuvių kalba 1918–1940. Kontrolinis sąrašas. T. 1: Knygos A–Č, Vilnius, 1997. Knygos D–J, Vilnius, 1997. Knygos K, Vilnius, 1998. Knygos L–M, Vilnius, 1999. Knygos N–R, Vilnius, 2000. Knygos S–T, Vilnius, 2001. Knygos U–Ž, Vilnius, 2002. Lietuvos bibliografija 1, Vilnius, 2006. Lietuvos bibliografija 2, Vilnius, 2006. LKŽ: Lietuvių kalbos žodynas (elektroninis leidimas), Vilnius. LTE VII 1981: Lietuviškoji tarybinė enciklopedija 7, Vilnius. MTŽ 1994: Matematikos terminų žodynas. Sud. V. Bagdonavičius, P. Golokvoščius, R. Kašuba, J. Kubilius (vadovas) ir kt., Vilnius. Pikčilingis J. 1969: Leksinė ir gramatinė sinonimija, Kaunas. Rumšas P 1975: J. Jablonskio indėlis į lietuvių aritmetikos terminiją. – Kalbos kultūra 29, 3–16. Rumšas P. 1978: Lietuvių aritmetikos terminai XIX amžiuje. – Kalbotyra 29(1), 52–60. Rumšas P. 1980: Lietuvių aritmetikos terminai XX amžiaus pradžioje. – Kalbotyra 31(1), 69–78. Šikšnys M. 1919: Aritmetikos ir algebros terminų žodynėlis, Vilnius. TŽŽe 2002: Interleksis. Kompiuterinis tarptautinių žodžių žodynas (elektroninis leidimas). Ats. red. A. Kinderys, Vilnius. Vaskelienė J. 2000: Darybiniai sinonimai, Šiauliai. Žemaitis Z. 1920: Geometrijos ir trigonometrijos terminų rinkinėlis, Kaunas. Žemaitis Z. 1956: Iš atsiminimų apie J. Jablonskį. – Literatūra ir kalba 1, Vilnius. Žemaitis Z. 1966: Lietuviškos matematinės terminologijos istorijai. – Lietuvių kalbotyros klausimai 8, 195–202. SYNONYMY OF ONE-WORD TERMS OF MATHEMATICS IN TEXTBOOKS OF MATHEMATICS (1910–1940) The first Lithuanian textbooks of mathematics (Užduotinas, tai ira Rankius užduocziu Aritmetikos arba Rakundos mokslo (1885) by P. Matulionis and J. Spudulis, Keturi svarbiausiejie veikalai Aritmetikos (1886) by P. Nėris (P. Vileišis), Pradžiamokslis Lietuviszko spaudraszczo ir rankraszczo (1888) by S. Gimžauskas and Aritmetika (1897) by S. Skačkauskas) were published at the end of 19th century. Before that textbooks of mathematics in Lithuania were published in Latin, later in Polish. From the beginning of the 20th century publishing of Lithuanian textbooks and exercise books of mathematics became more intensive. At that time Aritmetikos uždavinių ir pavyzdžių rinkinys (1906–1918) by P. Bendorius and P. Daugirda, Aritmetikos uždavinynas (1906) by P. Mašiotas and other textbooks were published. This article deals with one-word synonymous terms of mathematics in textbooks of mathematics published in the first half of the 20th century. The material for the article was collected from the following textbooks: Algebros teorija (1919) by V. Budrevičius, Aritmetika (1921) by A. Busilas, Jaunas matininkas (1921) by A. Busilas, Aritmetikos vadovėlis (1910–1911) in two parts by J. Damijonaitis, Plokštinė trigonometrija (1919) by A. Jakštas, Matematikos vadovėlis (Aritmetika ir algebra) (1939–1940) in three parts by J. Mašiotas, Matematikos vadovėlis (Geometrija) (1937–1938) in three parts by J. Mašiotas, Geometrija (1938–1940) in three parts by Terminologija | 2007 | 14 157 K. Klimavičius, Aritmetikos teorija (translated by A. Smetona) (1922) by Masing, Geometrija (1923) by M. Šikšnys, Elementarinė algebra (1923) by M. Šikšnys, Geometrija (1938–1939) in three parts by M. Šikšnys, Aritmetika ir algebra (1939) in three parts by M. Šikšnys. The majority of one-word synonymous terms were being used by different authors. Synonyms used by the same author are less frequent. In respect of origin synonymous terms are of two types – of different origin (synonymy of Lithuanian and foreign terms) and of the same origin (synonymy of Lithuanian terms). In Masing’s textbook there was only one pair of Lithuanian synonyms – apibrėžimas (nusakymas) (definition). Synonyms of a different origin are more frequent in textbooks by the same author (dvinaris – binomas (binomial), gretasienis – paralelepipedas (parallelepiped)). Lithuanian synonyms used by different authors are separated into lexical and derivational synonyms. Lexical synonyms in the textbooks researched are most frequent. There are quite a few cases when one of the synonyms was being used by the majority of the authors of textbooks and another one – only by one of the authors (apskritimas – ratlankis (circle), šgaviny s – išdava (result)). Derivational synonyms are less common. In most cases such synonyms differ only in suffixes (daliklis – dalytojas (denominator)). Cases when one of the synonyms is a noun of a particular formation and another one is a substantivized adjective or participle are less frequent (liečiamoji – lietėja (tangent)). Synonymous one-word terms of different origin are used by different authors very frequently (įstrižainė – diagonale (diagonal), statinis – katetas (leg)). After the appearance of the first dictionaries of terms of mathematics (Aritmetikos ir algebros terminų žodynėlis (Concise dictionary of terms of arithmetic and algebra) by M. Šikšnys and Geometrijos ir trigonometrijos terminų rinkinėlis (Collection of terms geometry and trigonometry) by Z. Žemaitis) the number of synonyms reduced. There were some cases when the authors of textbooks of mathematics did not take into consideration terms used in the above-mentioned dictionaries, although this was unjustified. The analysis of synonymy of one-word terms of mathematics in textbooks published between 1910 and 1940 leads to the conclusion that the authors of textbooks of mathematics from this period embedded terms of the first dictionaries of mathematics, except in isolated cases, and reduced the synonymy by rejecting foreign terms in many cases. Abundant usage of synonymous terms in textbooks of mathematics from the beginning of the 20th century shows that terminology of mathematics was being intensively ordered at that time. The mentioned period is a very important time of the establishment of Lithuanian terminology of mathematics. Gauta 2007-10-15 Diana Šilobritaitė Lietuvių kalbos institutas P. Vileišio g. 5, LT-10308 Vilnius E. paštas [email protected] 158 Diana Šilobritaitė | Vienaðodžių matematikos terminų sinonimija…