Terminology of the First Mathematics Glossaries

DIANA ŠILOBRITAITĖ

Institute of the Lithuanian Language

The first half of the 20th century was an important period for the standardization and systematization of mathematical terminology. This was a period when a considerable number of Lithuanian mathematics textbooks and problem books (both original and translated) for secondary schools appeared (for more details, see Šilobritaitė 2007: 146–158).

Mathematics teachers at Lithuanian gymnasiums in Voronezh—Marcelinas Šikšnys, Zigmas Žemaitis, and Pranas Mašiotas (who attended consultations on mathematical terminology only occasionally)—saw the diversity of terms in mathematics textbooks and resolved to review all the terms then available from the ground up and create those that were missing (for more, see Žemaitis 1966: 195). There was much work to be done, since the authors of the first mathematics textbooks, which appeared at the end of the 19th century, “had to create Lithuanian mathematical terms themselves, usually by translating them word for word from other languages” (Rumšas 1979: 52). Consequently, when Lithuanian was permitted as the language of instruction in schools and ever more mathematics textbooks and problem books began to be published, terminological confusion was unavoidable: the terms used by the authors of some textbooks differed considerably from those used by other authors.

Jonas Jablonskis, a standardizer of the Lithuanian language, readily agreed to help the mathematicians: when a term was proposed, he “would first ask them to describe the essence and principal properties of the concept to be expressed by that term, and only then would he either agree with the mathematicians’ opinion or explain why the chosen term was unacceptable” (Rumšas 1974: 11). The results of creating and organizing mathematical terminology were Marcelinas Šikšnys’s Glossary of Arithmetic and Algebra Terms (1919) and Zigmas Žemaitis’s Collection of Geometry and Trigonometry Terms (1920). These were the first printed Lithuanian terminology glossaries, published in “Kaunas, the temporary capital of the restored Lithuanian state” (Klimavičius 2003: 11). The aim of this article is to discuss noun and noun-phrase terms in the first glossaries of mathematical terminology. The glossaries’ headwords that are adjectives, participles, verbs, and so on are not examined in this article.

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1. MARCELINAS ŠIKŠNYS’S GLOSSARY OF ARITHMETIC AND ALGEBRA TERMS

Marcelinas Šikšnys (1874–1970) buvo žymus XX a. matematikos mokytojas (dirbo ir lietuvių kalbos mokytoju (žr. Šikšnys 1962: 81)), kūręs lietuvišką matematikos terminiją. Matematikos mokslus M. Šikšnys baigė Maskvos universitete. Dirbo mokytoju Rygoje, Voronežė, Vilniuje. Jo parašyti aritmetikos, algebros ir geometrijos vadovėliai buvo leidžiami keletą dešimtmečių. Lietuvių terminologijai svarbus šio matematiko parengtas Aritmetikos ir algebros terminų žodynėlis, išleistas Lietuvių mokslo draugijos 1919 metais. M. Šikšnys jau buvo parengęs Matematikos terminų projektą (1918), kuriame pateikė ne tik aritmetikos ir algebros, bet ir geometrijos bei trigonometrijos terminų.

The Glossary of Arithmetic and Algebra Terms is small in format and scope (47 pages). It consists of two parts: the first (pp. 3–25) presents Lithuanian–Russian terms in alphabetical order, and the second (pp. 26–47) Russian–Lithuanian terms.

In the Lithuanian section of the Glossary of Arithmetic and Algebra Terms, M. Šikšnys lists about 250 headwords (221 in the Russian section), of which more than 150 are expressed by nouns. M. Šikšnys does not provide the grammatical forms of the terms, but in a few cases indicates the singular genitive: aukštis, –čio1, brūkšnis, –io, ilgis, –io, lygtys, –čių. The glossary already attempts to mark the stress of terms (the pitch accent is marked incorrectly): bėgalė, daugiãnaris, dvinãris, vienanãris.

Almost all the headwords are single words, but compound terms also occur: kompleksinis skaičius, mišras skaičius, nedalus skaičius, netikra trupmena.

When listing mathematical (and also other fields’) terms, M. Šikšnys often explains their meaning: minusas (subtraction sign “–”); paviršiai – поверхность; paviršiai yra dviejų matavimų (matlinkių) dydis (the singular form paviršius is now used for “boundary separating a geometric solid from external space”; in Z. Žemaitis’s Collection of Geometry and Trigonometry Terms the singular form paviršius: šonų paviršius⟧ is given); saikas (a measure of the volume of dry goods and liquids); skaidymas (of a number) – разложение; skaičiaus skaidymas nedaliaisiais daugikliais; skaidinys – разложение, результатъ разложения; паверте skaičių nedalųjų daugiklių sandauga гаuname то skaičiaus skaidinį. The meaning of the term pliusas is explained only in Russian: pliusas – плюсъ (знакъ сложения).

¹ Terms are presented as they are in the glossaries.

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In certain terminology entries, compound terms are sometimes given alongside single-word terms: report – учеть: bill report, mathematical and commercial; formation – составление: formation of equations – составление уравнений; equations, -čių – уравнение: the unknown and known (free) terms of equations; root of an equation, solving an equation, equilateral (equal-sided) equations, and so on.

There are cases in which M. Šikšnys gives only the Lithuanian term and its Russian equivalent, without any explanation: axiom – аксиома; subtraction – отнимание, отнятие; quotient – частное; multiplicand – множеимое; taking – отнимание, вычитание; area – площадь; number – число, etc.

The adjectives and participles given as headwords in the glossary are in the indefinite form, but the definite form is also used in compound terms: free: the free (known) term of an equation; similar: collecting (combining) similar terms of a polynomial; whole (number): a whole number and a fraction. Sometimes an infinitive is given: to measure: measurable and immeasurable quantities.

1.1. Terms of Lithuanian origin

The Lithuanian-origin mathematical terms given in M. Šikšnys’s Glossary form the basis of present-day elementary mathematical terminology. Most of the terms have remained unchanged and become established: generalization, definition (in the textbook translated by A. Smetona in 1922, the term description is also used alongside it), minuend, subtraction, infinity, dash, division, part, dividing, divisor, quotient, polynomial, multiplication, multiplier, multiplying, product, term, combination, increase, quantity, joining, union, raising, degree, remainder, equality, measure, measurement, mixture, indeterminacy, inequality, base, surfaces, example, area, value, expression, limit, index, product, ratio, number, decomposition, partition, numerator, digit, difference, parentheses, reduction, solution, enlargement, addition, root, rule, identity, checking, extraction, fraction, content, volume, problem set, problem, multiplier, operation, translation, unit, sign. Lithuanian terms from the Glossary in economics and finance, physics, and technology are still in use today: report (economics), alloy (technology), exchange (economics), interest (finance), borrower (finance), lender (finance), heaviness (physics), weight (physics).

Nevertheless, not all the terms given in the Glossary are used in contemporary mathematics. For example, davinys (also included in Z. Žemaitis’s Collection of Geometry and Trigonometry Terms): data of a problem, numerical (number) data. The Lithuanian Dictionary davinys is deemed unsuitable for denoting the concept “what

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is given and relied upon in drawing conclusions”; the term now used is duomuo. Daoinį was also used by M. Šikšnys in his 1923 Geometry textbook.

The term event given in the Glossary (Russian результат), meaning “a number obtained by adding several numbers,” is also no longer used. It has now been replaced by the international term result, which M. Šikšnys, an advocate of Lithuanian terminology, does not include. Event is now used only in probability theory: asymptotic, random, certain, elementary, etc., event (MTŽ 1994).

Other terms no longer used in a mathematical sense include: designation (now notation, name, title); class (in a number): units, thousands, millions, etc. (now class); section (now column, which in the Glossary was given with a different meaning: column – грань: when extracting the square root, we divide the digits of the number into columns <…>); shortening: shorten a fraction by six (now simplification).

In some cases the form of a term has changed slightly, for example: formation (now composition: equation formation MTŽ 1994); comparison (now comparison); finding (now finding).

For an equality containing unknowns, M. Šikšnys proposed the plural term equations, -čių, which was initially adopted because, as M. Šikšnys put it, “equations consist of two parts, and in a similar case our language usually uses the plural” (Šikšnys 1962: 86). J. Jablonskis had also agreed with this. However, mathematicians later convinced him that “it is important to have that concept expressed in the singular, so that it is clear that what is meant is not several equations, but one equation” (Žemaitis 1966: 198).

1.1.1. TERMS OF LITHUANIAN ORIGIN: SYNONYMS

Synonymous terms are often presented without any references, in separate term entries—the Russian term corresponding to several Lithuanian ones indicates their synonymy. Of such synonymous pairs, only one of the terms became established. There were lavinimas (Russian упражнение) and pratimas (Russian навык, упражнение); in the Russian part of the Glossary they are presented differently: упражнение – lavinimas, pratimas, and the latter term became established (in his Geometrijos ir trigonometrijos terminų rankinėlyje, Z. Žemaitis proposed as many as three terms for designating this concept: pratinimas, pratimas, prasmas). The entries for Tolumo and nuotolio in the Russian section likewise show that they are synonymous: расстояние – nuotolis, tolum as (atstumas). Tolumo. Z. Žemaitis considered atstumą synonymous with Tolumo: tolum as – расстояние; from city A to city B is c versts in distance. The 1994 MTŽ gives only atstumas (Russian расстояние, English distance).

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Synonymous terms are sometimes given with the cross-reference see (sometimes see). In such cases, the Russian equivalent is given under the term to which the reference points: pažymys, see “žymė” and žymė (pažymys) – признак: dalingumo žymės; tikrumas, see “tikslumas” and tikslumas – точность: padalyti, ištraukti šaknis vieneto, dešimtosios dalies, šimtosios dalies ir tt. tikslumo (tikrumo); skaičiuotė, see “skaičiavimas” and skaičiavimas (skaičiuotė) – счисление: skaičiavimas žodžiu ir raštu; sudėjimas – see dėjimas ir dėjimas – складывание: daugiaženklių skaičių dėjimo (sudėjimo) taisyklė. Today, only one of the aforementioned synonyms is used: požymis (a modified form of the term) and sudėjimas. Skaičiavimas and skaičiuotė, tikrumas and tikslumas have persisted in mathematical terminology, but they are not considered synonyms: skaičiavimas: apytikslis, artutinis, asociacinis, etc., and skaičiuotė: arabų, dešimtainė, dvejetainė, etc.; tikrumas (Russian достоверность, English certainty, truth, reliability) and tikslumas (Russian точность, English accuracy, exactness, precision): absoliutusis, santykinis, etc. (MTŽ 1994). Z. Žemaitis noted that Dėjimo was unsuitable: this term “does not necessarily mean the combining of two numbers <⋯>; likewise, ‘dėjimas’ can mean adding and putting aside, putting on and taking off, putting in and taking out <⋯>” (Žemaitis 1917). The Russian equivalents show that M. Šikšnys apparently considered the terms atėmimas (Russian отнимание, отнятие) and ėmimas (Russian отнимание, вычитание) synonymous. Neither became established in mathematics—in all cases, the term atimtis is used, and this term is also included in the Glossary. In the synonym series pakeitimas (keitimas), the term given in parentheses (keitimas) is also listed as a headword, but pakeitimo is not given alongside it. That these terms are synonyms is shown by the compound term given in the entry for keitimas: keitimas: (pa)keitimo kelias. These terms are no longer considered synonyms (as shown by their subordinate designations): keitimo būdas, keitimo metodas, keitimo operacija and pakeitimo aksioma, pakeitimo koeficientas, whereas in subordinate designations keitimo taisyklė and pakeitimo taisyklė are synonymous (cf. taisyklė: (pa)keitimo) (MTŽ 1994).

There is a case in which a synonym appears only in parentheses and is not listed as a headword: dalinys (dalijamasis), but in the entry for the term dalyba the terms are presented in the reverse order: dalyba – деление (матем. дѣйствіе); dalijamasis (dalinys). In the project for a mathematical-terms dictionary, M. Šikšnys proposed only dalinį (Šikšnys 1918: 322). Z. Žemaitis likewise proposed dalinį with the meaning “quotient”: “Now ‘the multiplied number’ and ‘dalinis’ or ‘product’ and ‘quotient’. These two numbers are the results of multiplication and division. To express this meaning, Lithuanian most often uses suffixes; for example, pirkinys, malinys, though used in the sense of the thing bought or ground, also means the thing that is the result of buying or grinding. On this basis we have named the aforementioned two numbers …”

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…dauginiu ir daliniu” (Žemaitis 1917). In the 1950s, it was proposed that the term dalijamasis be used as the principal term, while dalinys was considered inadvisable (Rumšas 1975: 60). This assessment of the terms is also reflected in DŽ₂, but DŽ₃ already treats dalinys 2. mat. as normative, meaning “dividend.” This is the term used in mathematical terminology.

The terms gretinys (Russian размещение) and perstata (Russian перестановка), which M. Šikšnys regarded as secondary (given in parentheses and not listed as headwords), also became established. Their synonyms gretinimas and perstatinėjimas are no longer used in mathematics.

Not one of the terms in this synonym series became established in mathematics: tiekybė (tie kis) – Russian количество. The term now used to designate this concept is kiekis (MTŽ 1994).

For the remainder in division, M. Šikšnys proposed two separate terms: išdalos (division) and liekana (subtraction, division, root extraction). J. Jablonskis agreed: We also call the remainder in division išdalos (LKŽₑ). In time, only liekana became established. This term is found already in the earliest mathematics textbooks (for more detail, see Rumšas 1979: 52).

Sometimes synonymous terms in the Glossary are separated by a semicolon: dalumas, dalin-gumas (dalumas became established), dalinėjimas, dalinėjimo kelias (the term used in mathematics for this concept is nuoseklusis dalijimas), kitėjimas, kitimas (only kitimas became established).

M. Šikšnys had already attempted to distinguish terms formed with endings from those formed with suffixes (the distinction is not always shown in the Russian part of the Glossary); these are clearly distinguished in present-day mathematical terminology. The terms are presented one way in the Lithuanian section and another in the Russian section. In the Lithuanian section: aukštis (Russian вышина) and aukštumas (Russian высота, вышина), ilgis (Russian длина (величина)) and ilgumas (Russian длина (значение величины)), platumas (Russian ширина) and plotis (Russian ширина (въ смыслѣ величина)), storis (Russian толщина (величина)) and storumas (Russian толщина (значение величины)); in the Russian section: вышина – aukštis, -čio (aukštumas); длина – ilgis, -io, ilgumas; комната длиною въ три сажени – kambarys trijų s.; ширина – plotis (dydis); platumas; толщина – storis, -io, storumas.

1.2. Terms of non-Lithuanian origin

Most international mathematical terms have survived in present-day ma-

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thematics: axiom, algebra, arithmetic, coefficient, logarithm, minus, plus, percentage, progression, proportion, proportionality, radical, system, theorem. Financial terms have also survived: capitolas (now capitalas), vekselis.

The term tabelė (logarithm tables, multiplication table) is no longer used in mathematics; it has now been replaced by the Lithuanian term lentelė, whose use was advocated by A. Jakštas (alongside the term tabelė), since books (logarithm books) are wholly unsuitable in this case: “What kind of books can these be, when they contain nothing but digits and mathematical symbols?! The simplest name for them is logarithm tables (cf. Russian tablicy, German Tafeln, French Fables). Why oppose the whole world and call ‘books’ something that contains not a single living word? If Mr. M. does not like tables, he can call his publication ‘logarithm tabelės,’ although tabelės are no better than tables” (Jakštas 1919 1: 359). M. Šikšnys proposed replacing the component tabelė in the compound term daugybos tabelė with a Lithuanian one: daugybos abėcėlė.

1.2.1. TERMS OF VARIOUS ORIGINS: SYNONYMS

There are few synonyms for terms of various origins in the Glossary: sometimes preference is given to a term of foreign origin, and sometimes to a Lithuanian term.

The international term kvadratas is treated as the main term; the Lithuanian ketvirtainis is given in parentheses and treated as secondary. These terms were also used synonymously in the textbooks of A. Busilas (1921) and Masing (1922; translated by A. Smetona), but later only kvadratas became established (see Šilobritaitė 2007: 150 for more details).

In the Glossary, the international term kubas is considered secondary (it is given only in parentheses); the main term is the Lithuanian šeštainis, but it did not take hold. Kubas had already been used in the oldest printed Lithuanian textbook, P. Matulionis and J. Spudulis (compiled by J. Gailutis), Užduotinas, tai ira Rankius užduocziu Aritmetikos arba Rakundos mokslo (1885) (the manuscript of the textbook used kubikas) (Rumšas 1974: 4). In the Mathematics Terminology Project, šeštainis is considered secondary, while the main term is kūbas (= kubas) (Šikšnys 1918: 322). This term then became established in textbooks of the period; only in Masing’s 1922 textbook were these terms still considered synonyms.

Although the Lithuanian terms dėjinys and dėtinys, which did not take hold in mathematics, are also given alongside the international term suma in the Glossary, textbooks (both M. Šikšnys’s and those by other authors) use only suma (in the textbook of V. Budrevičius (1919), translated by A. Smetona (1922), suma and dėjinys are used synonymously).

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M. Šikšnys unsuccessfully attempted to Lithuanize the term formula: formulė; see solution. Sprendinys now has a different meaning: solution in mathematics, “the result of solving a problem” (DŽ₆). In the project on mathematical terminology, formula is preferred, while the Lithuanian term is given in parentheses as a secondary form: “Two algebraic expressions joined by an equality or inequality sign form a formula (solution)” (Šikšnys 1918: 322). Formula was already used in textbooks of that period and became established.

M. Šikšnys’s attempt to Lithuanize the term numeration (numeracija; see “calculation”) also failed—both terms are used in mathematics. Z. Žemaitis wrote: “In order to find out the number of things, they must be counted, or reckoned, and thus what is called ‘schisleniye’ in Russian should be called skaičiavimas or skaitymas in Lithuanian; in this sense, perhaps it would be better to use only the first word (skaičiavimas), since the second (skaitymas) has its own widely used meaning” (Žemaitis 1917). According to P. Rumšas, the meaning of numeration is “the expression of a number (orally or in writing); counting” (Rumšas 1975: 64).

It is difficult to determine whether the terms dvinaris and binomas are synonymous: in the Russian section of the Glossary, alongside the Lithuanian term dvinaris, the international term binomas is also given, whereas in the Lithuanian section the terms are listed separately. In a textbook published in 1939, M. Šikšnys treats them as synonyms (Šikšnys 1939: 110). MTŽ 1994 does not regard these terms as synonymous in every instance (for more, see Šilobritaitė 2007: 148).

2. ZIGMAS ŽEMAITIS’S COLLECTION OF GEOMETRY AND TRIGONOMETRY TERMS

Zigmas Žemaitis (1884–1969) – žymus XX amžiaus matematikas, profesorius, pedagogas ir mokslininkas. Jo pagrindinė, mokslinė ir pedagoginė, veikla skirta matematikos dėstymo metodikai, matematikos istorijai. Z. Žemaitis, kaip ir M. Šikšnys, prisidėjo prie lietuviškų matematikos terminų kūrimo ir vienodinimo. Vienas iš svarbių jo darbų, skirtų matematikai, yra Geometrijos ir trigonometrijos terminų rinkinėlis (1920).

The collection is small in scope. It is a two-part glossary comprising 99 small-format pages. The first part contains Russian–Lithuanian terms (pp. 3–45), and the second part Lithuanian–Russian terms (pp. 47–99). In the Lithuanian section, Z. Žemaitis presents about 720 terms—not only from geometry and trigonometry, but also from algebra and higher mathematics. About 340 headwords are nouns (single-word terms).

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Grammatical categories are indicated for the headwords: for both nouns and adjectives, the singular genitive ending is given, e.g.: aksiomė, ės, algebra, os, analizis, io, (analizė, ės), apibendrinimas, o, didinimas, o, didumas, o, dvejėjimas, o, dvejinimas, o, absoliutinis, ė, abypusis, ė, daugiasienis, ė, daugiaženklis, ė, daugiareikšmis, ė, dešimtainis, ė, etc.

In the collection, Z. Žemaitis gives as headwords not only single-word terms but also multiword terms: alternate interior angles (middle, external), common measure, necessary and sufficient condition, great circle of a sphere, solid geometry, alternate angles (middle, external), lunes (crescents) of Hippocrates, position geometry, similar figures, skew lines, corresponding angles, one-sided broken line. Such terms also have synonyms, which are given after a comma, an equals sign, or in parentheses. In some cases, the synonymous elements are secondary components of a term: piercing point, point of piercing; vertical line=static line; vertical angles=crossed angles; expressed, explicit function; non-common-denominator (common-denominator) fractions; linear (plane) angle; in other cases—a single-word term is given instead of a multiword one (in parentheses or after a comma): sum of sides (perimeter); plane-table, menzula; right angle (right-angled angle). Z. Žemaitis defines one multiword term: geometric locus of points (set)=a line whose points have a common property.

Some terms are marked with stress, though not always with the correct intonation: figūrą, netrukūs (Russian непрерывный), pastovūs, ribà, tyrà, tašà, tiesioginis, trūkūs, but elipsoidas, hipérbolė, hipérbolinis, hipérboliškas, matériinis, milimétrinis, paràbolė, paràbolinis, pènkelias, sinusóidė, stereométrinis, tangensóidė, taškų bégale, transcendéntinis.

2.1. Terms of Lithuanian origin

Z. Žemaitis lists more than 230 one-word Lithuanian nominal terms. Most of these terms are still used in mathematical science today: generalization, circumference, circle, circularity, axis, segment, answer, distance, altitude, height, infinity, drafting, edge, polyhedron, line, division, division, multiplication, polygon, polygon, combination, law, increase, enlargement, space, parallelogram, parallelepiped, length, net, cutout (=cutout), proof, diagonal, hypotenuse, set square, angle, change, quadrilateral, tetrahedron, variation, side, cone, solid, degree, arc, remainder, tangency, etc. Two surviving terms

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have spelling variants (the stem of the spelling variant is given in parentheses): apibriežimas, o (–brež), briežinys (brež.).

The booklet also contains terms that did not become established in mathematical terminology and were replaced by others for various reasons.

Like M. Šikšnys, Z. Žemaitis gives two separate terms for the remainder of a division: išdalos, ų and liekana.

The term ieškinys (teorėmės) (Russian заключение (теоремы)) did not catch on. In LKŽ_e, ieškinys ³ is marked neol. (neologism) and defined as “unknown, sought-for”: Dviejų ieškinių (ieškomųjų) lygybės J. Jablonskis. Today ieškinys (Russian заключение (теоремы)) is no longer used in the mathematical sense; instead, the term išvada is used (the booklet gives išvadas – вывод, слѣдствіе): conclusion of a theorem – Russian вывод, слѣдствіе, заключеніе: слѣдствіе теоремы; English conclusion, deduction, inference, corollary, consequence, implication: corollary of a theorem (MTŽ 1994).

The mast as proposed by both Z. Žemaitis and J. Jablonskis to denote scale also failed to become established (for more detail, see Klimavičius 2005: 143–146).

Z. Žemaitis later proposed replacing the names for lines that had not caught on in mathematics—liečiamoji (linija), kerta-moji, kreivoji, šios, tiesioji (linija)—with shorter nouns. Only his proposed kreivė and tiesė caught on. However, lietėja, kirtėja (proposed by J. Jablonskis) were later replaced by the terms liestinė, kirstinė.

Other terms that failed to catch on: a) terms no longer used in the mathematical sense (like the terms ieškinys, mastas mentioned above): atmaina, os (now keitimas), braiža, os (now braižymas), dalinėjimas, o (Russian послѣдовательное дѣленіе) (now nuoseklusis dalijimas), davinys, io (now duomuo), įvardinimas, o (now žymėjimas), klostinėjimas, o (paeilinis) (now atidėjimas), pagrindinė, ės (now pagrindo linija), priedėlis, io (now papildinys, papildymas (?)), sankryža, os (now susikirtimo (sankirtos) taškas), visetas, o (now visuma), žymė, ės (now požymis); b) terms that disappeared because of semantic obscurity or ambiguity (like išdalos): apklotis, ies (now uždėjimas), artimavimas (of circles, lines) (now santykiavimas), ketverėjimas, o (now keturgubinimas), liesmas, o (now lietimas), linkmatis, čio – Russian измѣреніе (мѣры); трију линкмачію кунас – Russian тѣло трех измѣреній (now matmuo), pakeičiamybė, ės (now apgręžiamumas), priklotis, ies (now pridėjimas), rietiklė, ės (now kreivinė liniuotė, lekalas), skretė, ės (now diskas), skrieplūksnis, io (now braižiklis).

2.1.1. TERMS OF LITHUANIAN ORIGIN — SYNONYMS

All the terms mentioned above (except kitėjimas (kitimas)) are presented by Z. Žemaitis as separate terms without synonyms. But synonyms of terms are unavoidable in the Rin-

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kinelyje—in certain cases, several terms are given to name one concept (in parentheses, after a comma, dash, semicolon, or equals sign).

Terms given in parentheses are considered secondary (they were still used in some textbooks of the time) and are not listed as headwords: ištyrimas, o (tyra, os), kitėjimas (kitimas), o, plokšmė, ės (plokštumas, o) (Z. Žemaitis proposed the term plokštė because, in his view, “a term is needed that would denote not a property or quality of a surface, but the infinite surface itself; such a word-term could be (terminus technicus) plokšmė, plokštis” (Žemaitis 1966: 198)), šakniženkis, io (šaknies ženklas), radikalas (radikalas is a headword, but it is unclear why its synonym is considered to be the Lithuanian term šaknis: radikalas, o (šaknis, es – padūkar), veiksm ženklis, io (veiksmo ženklas). Sometimes a term given in parentheses is also listed as a headword, but is corrected (the appropriate term is given after an equals sign): apskritimas, o (skraja, os), o (skraja, os)=apskritimas, o; pagrindas, o (pamatas, o), o pamatas, o=pagrindas, o.

Not all of the headwords proposed by Z. Žemaitis took hold: neither ištyrimas, nor tyra is used anymore (the term used for this concept is tyrimas (Rinkineliyje it is also found), nor plokšmė or plokštumas (plokštuma took hold). Terms not considered primary that did take hold were kitėjimas, šakniženkis, veiksm ženklis, while their secondary variants became established: kitimas, radikalas (šaknies ženklas), veiksmo ženklas.

Z. Žemaitis strongly criticized these Lithuanian terms: laipsnėjimas, liesmataškis, tikrumas ir vaisius. In his view, the mathematical terms given after the equals sign are better: laipsnėjimas=laipsniavimas (now neither is used anymore, only kelimas laipsniu), liesmataškis, o=lietimo taškas (now lietimosi taškas), tikrumas, o=tikslumas, o (now tikslumas), vaisius, aus=gavinys, io (now rezultatas, which Z. Žemaitis strongly criticized). As can be seen, his proposed terms did not prove accurate and correct in every case.

Z. Žemaitis apparently considered terms given after a dash to be synonyms: delčios–mėnuliai (Russian луночки). MTŽ 1994 gives mėnulis (Russian лун(оч)ка, English lune, biangle). Also given after a dash are svara, os–svoris, io (Russian вnc). MTŽ 1994 gives only svoris (Russian вес, English weight).

Especially common are cases in which one Russian term corresponds to two (or more) Lithuanian terms, presented: a) after a semicolon: atsakas, o; atsakymas, o (now only atsakymas); atstumas, o; nuotolis, io; nutolimas, o (the Russian-language part of the glossary also gives tolis, which

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presented separately in the Lithuanian section; now only distance is used); abundance, -ė; infinity, -ė (now, as in M. Šikšnys’s Glossary, they are treated as different terms); parallelogram, -o; parallelogram, -o (only parallelogram); deterioration, -o; simplification, -o (now simplification) or b) after cable: position, -ies; place, -os (both are now used, but they are not considered synonyms); rotation, turning (now rotation, turn – they are not always considered synonyms: turn: about an axis, about a center, about a point and rotation: about an axis, about a point, but rotation of axes, rotation of a line segment, elementary rotation, elliptical rotation and so on); verification, checking, -o (now only verification); finding, -o, discovery, -o (now only finding).

There are cases in which synonymous terms are listed in separate term entries but have the same single Russian equivalent: practice, exercise – упражнение and exercise – упражнение (now only exercise); application, os, adaptation, o – приложение and appendage, ies – приложение (now only adaptation); continuation, os – продолжение and continuation – продолжение (now continuation).

Z. Žemaitis, like M. Šikšnys, had already tried to distinguish terms that are not considered synonyms in present-day terminology either: height – вышина (как величина) and height, o – вышина (размер высоты), magnitude, džio – величина and size, o – размер; значение (величины)², speed – скорость (как величина) and speed, o – скорость (размер скорости), length – длина (величина) and length, o – длина (размер длины), width, čio – ширина (как величина) and width, o (width magnitude) – ширина (значение), thickness – толщина (как величина) and thickness, o – толщина (значение величины), distance, io – даль; расстояние and distance, o – расстояние; дальность, capacity – вместимость and capacity, o – вместительность.

The author of the little glossary also tried to distinguish other terms: calculation, o (Russian вычисление; измерение; вычисление, измерение объема, площади), accounting, os (Russian вычисление) and computation (Russian вычисление). A single term, calculation (MTŽ 1994), is now used to designate these concepts; it was absent from the Glossary. Likewise, dash, io (Russian черта) and stroke, os (Russian черта (линия)); doubling, o (Russian удвоение (как процесс)) and doubling, o (Russian удвоение (дѣйствіе)); outside, ės (Russian внѣ находящееся (на поверхности)) and exterior, ės (Russian внѣ находящееся (в пространстве)). Now

² The concept of magnitude was most often expressed by the word didumas. In 1919, A. Dambrauskas recommended using the word dydis (Rumšas 1980: 76), although S. Antanaitis’s 1918 review still stated that “the word didumas, or the word ‘dydis’ that has entered usage <...> is unsuitable for expressing the concept in question, because in people’s speech didumas, dydis mean stature, height <...>. ‘Didybė’ is the best fit here, and it is already in use” (Antanaitis 1918: 56).

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only dash, doubling (Russian удваивание, удвоение (MTŽ 1994)) and exterior are now used respectively to denote the aforementioned concepts.

2.2. Terms of non-Lithuanian origin

Almost all the terms of non-Lithuanian origin presented in Z. Žemaitis’s Glossary, which lack Lithuanian equivalents, took hold. These include names of branches of mathematics: algebra, arithmetic, geometry, trigonometry; units of length: centimeter, inch, kilometer, meter, millimeter; units of measurement (of angles and arcs): minute, ės, radian, o, second, ės; names of geometric figures: figure, cube (now cube), square, rhombus, trapezoid; names of lines and related concepts: ellipsoid, o, hyperbola, ės, hyperboloid, o, line, os, normal, ės, parabola, ės, paraboloid, o (now paraboloid), and other general terms: astrolabe, os (now astrolabe), center, o, element, o, function, os, matter, os, plane, o, period, o, projection, os, proportion, os, proportionality, o, symmetry, os, logarithm, logarithmic scale; logarithmization, o.

Considerable discussion was prompted by the variants attributed to Z. Žemaitis: analizis, io and analize, ės, bazis, io and bazė, ės (in the Russian section of the Glossary, bazis has the Lithuanian synonym pamatas; it is not recorded in the Lithuanian section), sintezis, io and sintezė. Z. Žemaitis gives both terms, but for a long time maintained the view that analizis, bazis and sintezis are better terms: “There is no reason at all to adopt Greek terms that sound entirely Lithuanian—analizis, sintezis—in a form already twice distorted (in French and German) (cf. analizė, sintezė), and to decline them as follows: analizė, analizės, analizei…, when the word can be perfectly well declined according to its original basic form, while preserving the Greek accent &lt;…&gt;” (Žemaitis 1966: 199–200). But analizė, bazė, sintezė prevailed. Unsuccessful Lithuanization efforts include the forms aksiomė, ės (now aksioma), formula (now formulė), lėmė, ės (now lema), limbė, ės (now limbas (this term is absent from MTŽ 1994)), teoremė, ės (now teorema) (in M. Šikšnys’s terminology glossary: aksioma, formulė; teorema).

The grammatical form of the Greek-derived term elipsis, sio also changed (the current term elipsė is not listed in the Glossary).

Variation was also unavoidable in presenting the names of trigonometric functions and related concepts: cosecant (this), cotangent, o (this, o), secant, o, secant-related, ės, tangent, o (ntas, o), tangent-related, ės, tangenoid, ės, cosecant-related, ės (tinė, ės), cotangent-related, ės (tinė, ės), cosine-related, ės (cosinus-related, ės), cosine, aus (sas, so), cosinoid, ės, sine, aus (sinus, o), sine-related, ės (sinus-related, ės), sinusoid, ės. Not only mathematicians but also linguists were

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There were differing opinions about Lithuanian endings and declension: “<...> it was proposed to treat the words sinus, cosinus as nominatives in Lithuanian as well and to decline them accordingly: sinus, sinaus, sinui, etc. Apparently, J. Jablonskis’s view prevailed that their nominatives should be Lithuanianized, i.e., written sinusas, kosinusas. It was then argued that tangens, cotangens, sekans should be called tangensas, cotangensas, rather than tangent as, kotangent as..., as J. Jablonskis demanded, relying on the principle that Lithuanian nominative endings should be attached to the genitive stem of the foreign-language word” (Žemaitis 1966: 198). In A. Jakštas’s view, “sinusai, kosinusai” and “tangentai, kotangentai” are no better than “sinus and kosinus,” “tangensus, kotangensus” (Jakštas 1919 1: 359). The present forms of the terms tangentas, kotangentas, sekantas, kosekantas were established by P. Mašiotas, although 50 years later, under the influence of Russian, tangensas, kotangensas, sekansas, kosekansas spread again (for more, see Klimavičius 1969: 18–21). Perhaps for this reason Z. Žemaitis gives both names for the subtraction sign: minus, aus (minusas, o).

2.2.1. TERMS OF DIFFERENT ORIGINS: SYNONYMS

In the collection, alongside non-Lithuanian terms, Z. Žemaitis sometimes also gives Lithuanian ones. Some took root, others did not. A. Jakštas, an advocate of terms of non-Lithuanian origin, was particularly indignant that terms “which have become international and are used in the mathematical literature of almost all languages” were being Lithuanianized: “It seems to us they have been Lithuanianized without need, especially since their Lithuanian character is by no means successful in every case” (Jakštas 1919 2: 360). Neither J. Jablonskis nor the mathematicians of the time (including Z. Žemaitis) agreed.

Z. Žemaitis corrected some terms of non-Lithuanian origin quite rigorously. In such cases, Lithuanian terms (sometimes single-word, sometimes compound) are given after an equals sign: binomas, o=dvin aris, io, bisektrisė, ēs=pusiaukampinė, ēs, chordė, ēs=styga, os, cilind eris, io=ritinys, io (A. Jakštas disagreed with the use of the term ritinys: “Ritinis can never mean a cylinder” (for more, see Rumšas 1974: 17)), cirkielis, io=skriestuvas, katetas, o=statinis, io, kontro-lė, ēs=tikrinimas; patikrinimas, kūbatura, os=tūrio apskaitymas, matavimas; medianė, ēs=pusiaukraštinė, ēs, ortocentras, o=aukštinių sankryža, radiusas, o=spindulys, io (A. Jakštas proposed radijus instead of radiusas (for more, see Rumšas 1974: 10)), rezultatas, o=gavinys, io; vaisius, aus, segmentas, o=nuopiova, os, sekt oras, o=išpiova, os, stereometrija, os=erdvės geometrija; after a dash: (liniuotė, es)–tiesiklė, es, kvadratūra, os–ploto apskaitymas or with the reference “see”: diametras, o see skersmuo, ens.

For it is understandable why, while Lithuanianizing terms, Z. Žemaitis nevertheless leaves

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diagonal and hypotenuse, indicating that a Lithuanian term should be replaced with a term of foreign origin: diagonalė, ės (įstrižainė, ės) and įstrižainė, ės=diagonalė, ės; hipotenuzė, ės (įžambinė, ės) and įžambinė, ės=hipotenuzė, ės.

Only rarely are Lithuanian and foreign-origin terms presented in the same terminology entry and separated by a comma or semicolon: postulatas (–tetas)³, dešnis – постулат; principas, dešnis – принцип; pavidalas, o; forma, os – форма; вид. It is unclear, however, why the headwords dešnis and forma have no synonyms: dešnis, io – положение, предложение; принцип; постулат and forma – форма. In MTŽ 1994, pavidalas and forma are also sometimes treated as synonyms: pavidalas: algebrinis, diagonalusis, diferencialinis and so on (cf. forma: algebrinė, diagonalioji, diferencialinė, but only apipusė forma, antis imetrinė forma, antroji kvadratinė forma, and so on). Postulatas and dešnis; principas and dešnis are not treated as synonyms in MTŽ 1994: postulatas (Russian постулат, English postulate, axiom), dešnis (Russian закон, English law, distribution, principle, rule), principas (Russian принцип, English principle, law, axiom).

Radikalas gave Z. Žemaitis doubts. The Lithuanian term šaknis, given in parentheses, apparently seemed unsuitable even to him: šaknis is not given in the entry for radikalas, but is treated as a synonym of šakniženklis. The term currently used for the sign indicating extraction of a root is radikalas.

Z. Žemaitis also considered the term apotemė (now apotema) in need of replacement, so he put it in parentheses (although it is a headword in the collection), followed by an explanation of the term after the hyphen: the radius of the inscribed circle (in a regular polygon).

The Lithuanian term tieseklė also failed to take root; Z. Žemaitis regarded the current term liniuotė as its synonym (he gave it in parentheses).

3. CONCLUSIONS

The beginning of the 20th century was a very important period in the development of mathematical terminology: many mathematics textbooks and problem books in Lithuanian were published, as well as the first glossaries of mathematical terms.

M. Šikšnys’s Aritmetikos ir algebros terminų žodynėlis and Z. Žemaitis’s Geometrijos ir trigonometrijos terminų rinkinėlis were the first Lithuanian glossaries of terms, published in an independent Lithuania that had already regained its independence. They laid the foundations for present-day mathematical terminology: most of the terms (both Lithuanian and international) became established.

However, not all the terms presented in the glossaries survived and are still used

³ This is a variant form of the term postulate.

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in mathematics. Cases in which terms presented in them are no longer used in their mathematical sense are particularly common (įvardijimas, luomas, skyrius (M. Šikšnys); atmaina, ieškinys, priedėlis (Z. Žemaitis)). In some cases, only the form of the terms has changed: išvadas (= išvada), lygtys (= lygtis); sudarymas (= darymas), lyginimas (= palyginimas) (M. Šikšnys). Only a few terms listed in the glossaries are no longer used at all in contemporary language (išdalos (M. Šikšnys); prasmas, skretė (Z. Žemaitis)).

The examples presented show the authors’ inclination to purify and Lithuanize mathematical terms. However, attempts to Lithuanize international terms were not always successful: the international terms that had long been in use became established in mathematics (formulė, kubas (M. Šikšnys); postulatas, principas (Z. Žemaitis)).

An analysis of the terminology in the first mathematical glossaries shows that the second decade of the 20th century was an important period in the formation of mathematical terminology. The synonymy of terms and unsuccessful attempts to Lithuanize certain international terms are natural features of the development of terminology.

MAIN SOURCES

Šikšnys M. 1919: Aritmetikos ir algebros terminų žodynėlis. Vilnius.

Žemaitis Z. 1920: Geometrijos ir trigonometrijos terminų rinkinėlis, Kaunas.

OTHER SOURCES

Antanaitis 1918: Trumpas aritmetikos vadovėlis. – Lietuvos mokykla 3, 55–57.

LKŽ_e 2005: Lietuvių kalbos žodynas (elektroninis leidimas), Vilnius.

MTŽ 1994: Matematikos terminų žodynas. Sud. V. Bagdonavičius, P. Golokvoščius, R. Kašuba, J. Kubilius (vadovas), Vilnius.

Šikšnys M. 1918: Matematikos terminų projektas. – Lietuvos mokykla 11, 321–328.

Šikšnys M. 1923: Geometrija, Kaunas.

Šikšnys M. 1939: Aritmetika ir algebra 1, Kaunas.

LITERATŪRA

DŽ₂ 1972: Dabartinės lietuvių kalbos žodynas, Vilnius.

DŽ₃ 1993: Dabartinės lietuvių kalbos žodynas, Vilnius.

DŽ₅ 2003: Dabartinės lietuvių kalbos žodynas (elektroninis leidimas), Vilnius.

Jakštas A. 1919 1: Logaritmų knygos penkiais dešimtainiais skaitmenimis. – Draugija 7–8, 359.

Jakštas A. 1919 2: Pr. Mašiotas. Geometrijos uždavinynas. – Draugija 7–8, 359–360.

Klimavičius J. 1969: Tangensas, sekansas ar tangentas, sekantas. – Kalbos kultūra 16, 18–21.

Klimavičius J. 2003: Lietuvių terminografija: praeities bruožai, dabarties sunkumai ir uždaviniai. – Terminologija 10, 9–32.

Klimavičius J. 2005. Terminas prie termino. II. – Terminologija 12, 143–146.

Rumšas P. 1974: Lietuviškų geometrijos terminų istorija. – Mūsų kalba 2, 4–19.

Rumšas P. 1975: Matematikos terminai „Dabartinės lietuvių kalbos žodyne“. – Kalbos kultūra 28, 3–16.

Rumšas P. 1979: Prie matematikos terminijos ištakų. – Zigmas Žemaitis, 52–58.

Rumšas P. 1980: Lietuvių aritmetikos terminai XX amžiaus pradžioje. – Kalbotyra XXXI(1), 69–78.

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Šikšnys M. 1962: Mano lietuvių kalbos pamokos ir atsiminimai apie J. Jablonskį. – Kalbotyra 5, 81–87.

Šilobritaitė D. 2007: Vienažodžių matematikos terminų sinonimija matematikos vadovėliuose (1910–1940). – Terminologija 14, 146–158.

TŽŽe 2002: Interleksis. Kompiuterinis tarptautinių žodžių žodynas (elektroninis leidimas). Ats. red. A. Kinderys, Vilnius.

Žemaitis Z. 1917: Dėl aritmetikos terminologijos. – Santara 28.

Žemaitis Z. 1966: Lietuviškos matematinės terminologijos istorijai. – Lietuvių kalbotyros klausimai 8, 195–201.

TERMINOLOGY OF THE FIRST DICTIONARIES OF MATHEMATICS

The beginning the 20^th century is a very important stage of the creation of terms of mathematics – a lot of textbooks and exercise books of mathematics and, most importantly, first dictionaries of mathematics were published.

Aritmetikos ir algebros terminų žodynėlis (Dictionary of terms of arithmetic and algebra) by M. Šikšnys and Geometrijos ir trigonometrijos terminų rinkinėlis (A collection of terms of geometry and trigonometry) by Z. Žemaitis were the first Lithuanian dictionaries of terms published in already restored independent Lithuania. They laid the foundations for the modern terminology of mathematics – the majority of terms from them took root in the language. However not all terms presented in dictionaries survived and were used in mathematics. The important thing is that special meanings of these terms, but not terms themselves vanished, because these words are still being used (įvardijimas (naming), luomas (caste, estate), skyrius (section, chapter) (M. Šikšnys); atmaina (species, variety), ieškinys (plaint, lawsuit, claim), priedėlis (appendage) (Z. Žemaitis)). There are some cases when only grammatical form of terms or their word-formation changed (išvadas (= išvada) (conclusion), lygt ys (= lygtis) (equation), sudarymas (= darymas) (formation), lyginimas (= palyginimas) (congruence) (M. Šikšnys); liečiamoji (= liestinė) (tangent), kertamoji (= kirstinė) (secant line), veiksmaženklis (= veiksmo ženklas) (action sign) (Z. Žemaitis)). Only few terms from these dictionaries fell out of the usage in the modern language completely (išdalos (M. Šikšnys); prasmas, skretė (Z. Žemaitis)).

In the earlier mentioned dictionaries there are some synonyms of terms (of the same or different origin), which are presented in brackets, after comma, dash or equal sign. However it is quite difficult to judge the synonymy, because rather frequently one Russian term has two or three equivalents, which in Lithuanian parts of dictionaries are presented as separate terms and in Russian parts – in the same term entry.

The wish to purify terms and make them more Lithuanian is a particularly noticeable tendency. Terms of the foreign origin are not numerous (especially in the dictionary of M. Šikšnys). Almost all of them have Lithuanian equivalents, which are viewed as main variants. However, not all attempts to substitute international terms with Lithuanian terms were successful. There are few international terms the textbooks of mathematics, which were in usage for a long time (formulė (formula), kubas (cube) (M. Šikšnys); postulatas (postulate), principas (principle) (Z. Žemaitis)).

Gauta 2008-12-05

Diana Šilobritaitė Lietuvių kalbos institutas P. Vileišio g. 5, LT-10308 Vilnius E. paštas: [email protected]

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