Gujarati Mathematical Vocabulary
Gujarati Numbers • Vocabulary
Compiled
by
Babu Suthar
Lecturer in Gujarati University of Pennsylvania South Asia Regional Studies 820 William Halls 36th and Spruce Philadelphia PA 19143 USA
2
Gujarati Numbers
Gujarati numerals are of three types: (1) cardinals, (2) ordinals, and (3) fractions. The basic number figures are ten and each figure bears a name. (1) Number figures and their names
0 È mI6u& 5 Í pa&c6o 1 É Aek6o 6 Î 2g6o 2 Ê bg6o 7 Ï sat6o 3 Ë tg6o 8 Ð Aa56o 4 Ì cog6o 9 Ñ nv6o
Cardinals
1 É Aek 13 ÉË ter 2 Ê be 14 ÉÌ cOd 3 Ë {a8 15 ÉÍ p&dr 4 Ì car 16 ÉÎ soX 5 Í pa&c 17 ÉÏ s]ar 6 Î 2 18 ÉÐ A7ar 7 Ï sat 19 ÉÑ Aog8Is 8 Ð Aa5 20 ÊÈ vIs 9 Ñ nv 21 ÊÉ AekvIs 10 ÉÈ ds 22 ÊÊ bavIs 11 ÉÉ Aigyar 23 ÊË tevIs 12 ÉÉ bar 24 ÊÌ covIs 3
25 ÊÍ pCcIs 52 ÍÊ bavn 26 ÊÎ 2vIs 53 ÍË tepn 27 ÊÏ s]aavIs 54 ÍÌ copn 28 ÊÐ A¹avIs 55 ÍÍ p&cavn 29 ÊÑ Aog8{aIs 56 ÍÎ 2Ppn 30 ËÈ {aIs 57 ÍÏ s]aavn 31 ËÉ Aek{aIs 58 ÍÐ A¹avn 32 ËÊ b{aIs 59 ÍÑ Aog8sa;5 33 ËË te{aIs 60 ÎÈ sa;5 34 ËÌ co{aIs 61 ÎÉ Aeks5 35 ËÍ pa&{aIs 62 ÎÊ bas5 36 ËÎ 2{aIs 63 ÎË tes5 37 ËÏ sa6{aIs 64 ÎÌ cos5 38 ËÐ Aa6{aIs 65 ÎÍ pa&s5 39 ËÑ Aog8calIs 66 ÎÎ 2as5 40 ÌÈ calIs 67 ÎÏ s6s5 41 ÌÉ AektalIs 68 ÎÐ A6s5 42 ÌÊ betalIs 69 ÎÑ Ag8ois]aer 43 ÌË tetalIs 70 ÏÈ is]aer 44 ÌÌ cu&malIs 71 ÏÉ ;kotr 45 ÌÍ ipStalIs 72 ÏÊ boter 46 ÌÎ 2etalIs 73 ÏË toter 47 ÌÏ su6talIs 76 ÏÎ 2oter 51 ÍÉ Aekavn 77 ÏÏ isTyotr 52 ÍÊ bavn 78 ÏÐ ;5yotr 51 ÍÉ Aekavn 79 ÏÑ Ag*yaAe&sI 4
80 ÐÈ Ae&sI 90 ÑÈ nevu& 81 ÐÉ AekyasI 91 ÑÉ Aeka8u& 82 ÐÊ ByasI 92 ÑÊ ba8u& 83 ÐË TyasI 93 ÑË ta8u& 84 ÐÌ coyaRsI 94 ÑÌ cora8u& 85 ÐÍ p&casI 95 ÑÍ p&ca8u& 86 ÐÎ 2yasI 96 ÑÎ 2Nn&u 87 ÐÏ isTyasI 97 ÑÏ s]aa8u& 88 ÐÐ ;5yasI 98 ÑÐ A¹a8u& 89 ÐÑ neVyasI 99 ÑÑ nVva8u&
A hundred and higher figures are as under:
100 ÉÈÈ so, Aekso 200 ÊÈÈ bso 300 ËÈÈ {a8so 400 ÌÈÈ carso 500 ÍÈÈ pa&cso 600 ÎÈÈ 2so 700 ÏÈÈ satso 800 ÐÈÈ Aa5so 900 ÑÈÈ nvso 1,000 É,ÈÈÈ hjar, Aek hjar 10,000 ÉÈ,ÈÈÈ ds hjar 100,000 ÉÈÈ,ÈÈÈ la`, Aek la` 5
1,000,000 É,ÈÈÈ,ÈÈÈ ds la` 10,000,000 ÉÈ,ÈÈÈ,ÈÈÈ kro6 100,000,000 ÉÈÈ,ÈÈÈ,ÈÈÈ ds kro6 1,000,000,000 É,ÈÈÈ,ÈÈÈ,ÈÈÈ Abj 10,000,000,000 ÉÈ,ÈÈÈ,ÈÈÈ,ÈÈÈ ds Abj
Note: There is no concept of ‘million’ in Gujarati
While reading a number of more than two digits, no ‘and’ is required as in English. Examples: ÊÎÑ bso Ag8ois]aer Ë,ÎÐÏ {a8 jhar 2so isTyasI Í,ÉÐ,ÑÈÍ pa&c la`, A7ar hjar, nvso pa&c
However, while doing counting the conjunction ne may be used while reading the last two digits. If the penultimate digit is 0 (zero) the ne may be used with the last digit. Examples: ÊÎÑ bsone Ag8ois]aer Ë,ÎÐÏ {a8 jhar 2sone isTyasI Í,ÉÐ,ÑÈÍ pa&c la`, A7ar hjar, nvsone pa&c
Ordinals The ordinals behave like adjectives and agree with the nouns in gender.
English Masculine Feminine Neuter Ordinals 6
First phelo phelI phelu& Élo ÉlI Élu&
Second bIjo bI@ bIju& 2nd Êjo Ê@ Êju&
Third {aIjo {aI@ {aIju& 3rd Ëjo Ë@ Ëju&
Fourth co9o co9I co9u& 4th Ì9o Ì9I Ì9u&
Fifth pa&cmo pa&cmI pa&cmu& 5th Ímo ÍmI Ímu&
Sixth 2¹o 2¹I 2¹u& 6th ιo ιI ιu&
Seventh satmo satmI satmu& 7th Ïmo ÏmI Ïmu&
For each of the higher ordinal use mo, mI, mu& as the case may be.
Fractions Following are the terms for Gujarati fractions:
Simple
¼ pa ½ A60u& 7
¾ po8u&
Plus
Examples
Plus ¼ sva 1 ¼ sva Aek Plus ½ sa6a 3 ½ sa6a {a8 Plus ¾ po8u& 2 ¾ po8a {a8
Notes:
(1) The A60u& And po8u& agree with the noun in gender and number. Examples:
A60o kagX ‘half paper’ A60a kagX ‘half of the papers’ A60I kerI ‘half mango’ A60I kerIAo ‘half of the mangos A60u& keXu& ‘half banana’ A60a& keXa& ‘half of the bananas’
(2)
For 1 ½ and 2 ½ always use A7I and do7 respectively. 8
Vocabulary*
* Derived with a few modifications from "wCcgi8tnI pir-aqa" 1966. (Terminology of higher mathematics), Publisher: Gujarat University, Ahmedabad, India. 9
A alternately AekaNtre absolute inrpex alternating function p/its&imt iv0ey absolute term Aclpd alternating series p/its&imt [ae7I absolute value inrpex mULy analysis p<(9kr8, ive¿leq8 absurd As> analytical geometry vE¿leiqk -Uimit accuracy coksa: angle `U8o acute angle l3uko8 angle at the center keN±S9 `U8o acute angled triangle l3ui{ako8 angle at the circumferemce capS9 ko8 additon srvaXo, v]aakar angle of contact Sp=R`U8o adjacent angle s&lGn ko8 angle of depression Avse0 adjacent sides s&lGn bajuAo angle of elevation wTse0 admissible solution SvIkayR wkel angular ko8Iy admissible value SvIkayR ik&mt angular diagram v 10 approximately Aa=re, lg-g average srera=, m)yk, srasrI a priori pUvRSvIk circle vtuRX, v<]a bisector iµ-ajk circular vtUXakar, v<]aIy bivariate iµcl circular determinants ck/Iy inyamko bounding line pirre`a circular diagram v<]aak C circular test ck/Iy pirx8 calculating machine g8trIy&{a circulating decimals Aav<]a d=a&= calculation g8trI circumcenter pirkeN± calculus kln gi8t circumference piri0, pir3 cancel w6a6I devu& circumpolar pir0/uvIy canonical variation iviht cln circum-radius piri{ajya capacity xmta circumscribed circle pirv<]a cardinal g8naTmk circumscribing pirgt cantesinal =ta&=k class vgR central keN±Iy class magnitude vgRman central moments keiN±y p/3at characteristic (of log) pU8aR&k classification vgIRkr8 12 co-effecient A&k, gu8k, cone =&ku shgu8k conical point =&kupat colliner smre` conical projection =&kup/xep collinearity smre`ta conicoids =&kuj column kolm, St&- conjugate Anub&0 combination s&cy conoid =&kva-as common samaNy conormal points smi-l&b ib&duAo common multiple samaNy AvyvI consecutive k/imk common system (of Log) samaNy d=a0ar consequent w]arpd commutative law k/mno inym consistency s>ta comparision test tulna pirx8 constant Acl complete differential pU8R ivkl constituent 34k complete the squares pU8R vgR krvo construction of index numbers Aa&krcna component equations 34k smIkr8 contavarient p/itcl components 34ko covective equilibrium s&vahI s&iS9it composite im[a converse Wl4u&, p/it composite hypothesis s&yukt pirkLpna co-ordinate yam composite number -ajy pU8aR&k co-ordination smNvy compound s&yukt coplaner smtlIy correlation shs&b&0 computation Ai-g8na computer Ai-g8k corollary wpp/mey 13 corresponding Anu£p camulants yog3at corresponding angle Anuko8 cumulative s&cyI co-terminal angles smsIm `U8a curve vk/re`a, vk/ couple blyuGm, yuGm curve fitting vk/ ANvayojn covariance shivcr8 curve surface vk/tl covarient shcl curve tracing vk/ale`n cross-multiplication SviStkgu8n curve in space i{aimt vk/ ityRk gu8n curvilinear vk/Iy cross-ration of pencil re`avilnu& ityRk p/ma8 cusp ini=t cube 3n, sm3n cuspidal locus ini=t ib&dup9 cube root 3nmUX, t D w6a6I devu& damped Avm&idt demand curve magvk/ damping factor Avm&dn Avyv denominator 2ed dash 6e= denote d=aRvvu& data Aa&k6a, maihtI derivative ivklnfl decagon d=ko8 ivkilt decimal d=a&= derivative of an arc capnu& ivkln decimal fraction d=a&= ApU8aR&k derived function ingimt iv0ey deciles d=a&=k descending wtrtu& decreasing 34tu& descending node AvrohI pat deduce ingmn krvu& descriptive statistics v8RnaTmk Aa&k6a=aS{a deduction ingmn determinant in¾ayk definite suini¾t deviation ivcln definite integral inyt s&kl diagonal ivk8R definition Vya~ya diagonal points ivk8R ib&duAo degree A&= diagonal triangle ivk8R i{ako8 degree ma{aa diagram Aak difference equation A&trsmIkr8 delete dUr krvu& 15 difference table A&trkoQ4k divisor -ajk differentiable ivklnIy domain xe{a differentiability ivkLyta double bm8u&, iµgui8t differential ivkl double contact iµSp=R differential calculus ivklnivd\ya double integral iµs&kl differential coefficien ivklngu8 double line iµkre`a differential equation ivkl smIkr8 double point iµib&du differential of an arc capno ivkl double root iµkbIj differentiation ivkln double sampling iµind=Rn differentiation under the integral sign s&kl ich\nma& ivkln double star yuGmtark digit Aa&k6o double tabulation iµiv0 koQ4k dihendral angle iµtlko8 doublet vIjyuGm dimension pirma8 doubly infinite (system of curves) iµAn&t distribution iv-ajn, ivtr8 equal brabr, sr`u&, sman distributed ivxoi-t equal in all respect svaR&gsm, Aek£p dividend -ajy aequality saMy, smanta dividendo ivyogp/ma8 equate smIkvu& divisibility inŠ=eq -ajyta equation smIkr8 division -agakar equations involving reciprocals of unknowns VyitkraTmk smIkr8 division transformation -agakr ivi0 16 equations involving reciprocals of center wTkeN±s&Skar estimate Aag8n krvu& equations involving reciprocals of motion estimate AnUman, Aag8k gitsmIkr8 estimated Anuimit equations involving reciprocals of three moments i{a-ajk smIkr8 Euler's exponential values Ao:lrnu& 3ata&kIy mULy equations involving reciprocals of trigonometrical i{ako8mItIy smIkr8 even bekI equiangular smko8 even function smiv0ey equiangular spiral smko8avtR example da`lo, wdahr8 equiconjugate diameter smanub)0 ex-center bihQkeN± keN±re`a expend ivStr8 krvu& equi-cross smityRk\ expansion ivStr8 equidistant sr`e A&tre expected frequency Apeixt Aav expected value Apeixt mULy equivalent smpirma8I explicit SpQ4 equivalent sman exponent 3ata&k equivalent equations smbIj exponential 3ata&kIy equivalent equation pyaRiyk smIkr8 exponential value 3ata&kIy £p equivalent system sms&iht express d=aRvvu& error {au4I expression pdavil, rai= escribed circle bihv 18 geometric average smgu8o]ar srera= grouping of data Aa&knu& vgIRkr8 maihtInu& vgIRkr8 geometric mean smgu8o]ar growth rate v ingress p/ve= independent inrpex intial Aad\y indetermination Aini¾tta initial line Aad\yre`a index 3ata&k in perspective sm±Q4 index number 3ata&k n&br iradius A&tŠiS{ajy indicatrix vk/indeR= inscribed circle A&tv integration in series [ae7I£p s&kln inverse (circle) p/tIp interior angle A&tŠko8 inverse circular function v<]aIy p/itiv0ey interior opposite angle A&tŠs&mu`ko8 inverse curves p/tIp vk/o interminable division An&t -agakr inverse function p/itiv0ey in terms of arch capIy, ainverse hyperbolic functions AitvlyI cayp/clI p/itiv0ey internal A&tirt inverse line. etc. p/i{ajya vgere internal bisector A&tiµR-ajk inverse operations Wl4I ik/yaAo inverse ivprIt inverse operator p/itkark inverse interpolation ivpirt A&tveR=n inverse order Wl4o k/m interpolation with equal intervals inverse point p/tIp ib&du sma&tr A&tveR=n interpolation with unequal intervals inverse probability ivprIt s&-avna Asma&tr A&tveR=n interpretation A9R34n inverse proportion VySt p/ma8 interquartile range ctu9Rk A&tr inverse ration VySt gu8o]ar intersect 2edvu& inverse variation VySt cln intersect prthogonally l&b2ed 9vo inversely similar p/itÝsm£p l&b2ed krvo inversion p/tIpn interclass correlation vgaR&t shs&b&0 invertendo VyStp/ma8 intrinsic Svay]a investigation ANve=n ainvariable in¾l investigator ANveqk inverse VySt, WL4u& 22 involute p/itkeN±j law of Indices 3ata&kno inym involution 3atik/ya law of larage numbers mhas&~yaAono inym involution smuTk/m8 law of Statistical regularity Aa&k6aAonI involution pencil smuTk/m8 re`avil inyimttaAono is)0a&t involution range smuTk/m8 ib&dup&ikt leading term Ag/pd irrational As&mey leading constituent Ag/34k isogonal smnt leading diagonal Ag/ivk8R isolated point Aeka&kI ib&du least l3u]am isoperimetric smpirimitk least square Nyuntm vgR isosceles tetrahedron iµsm ctuQflk left hand vam isosceles triangle iµsm i{ako8 left hand side 6abI baju, pUvRpx J Jacobians jekoibyn lemma pUvRp/mey joint frequency distributions s&yuky Aav like (terms) sjatIy latus-rectum nai-l&b likelyhood function ivs&-avna iv0ey law of inverse square VySt vgRno inym 23 likelyhod ration test ivs&-avna gu8o]ar prIx8 literal coeffecient v8Rgu8k like parallel forces sjatIy sma&tr locus ib&dup9 bXo logarithm l3ug8k like (signs) smich\n logarithmic series l3ug8kIy [ae8I limit lx logical tkRs> limited sImIt lower quartile p/9m ctu9Rk limiting sImaNt M limiting points lxib&du major arc gurucap limiting value lx manifold classification bhuiv0 vgIRkr8 limitless inŠsIm manifold tabulation bhuiv0 koQ4krcna line re`a mantissa A&=k line at infinity An&t re`a marginal sImavtIR linear re`Iy, sure` mathematical analysis gi8tIy iv¿leq8 line integral re`as&kl mathematical inducation gi8tIy Anuman line of centers keN±re`a matrix [aei8k line of curvature vk/tare`a maximum Ai0ktm line of force blre`a maximum likelihood Ai0ktm line of greatest slope mh]am 7aXnI s&-avna re`a mean srera=, m)yk, line of regression inyt s&b&0 re`a m)ym literal equation v8R smIkr8 mean anomaly m)ym ko8 24 mean derivation srera= ivcln minimum value NyUntm mULy mean parallax m)yman S9an-ed minor wpin¾ayk mean proportional m)ym p/ma8pd minor arc l3ucap mean value m)ykman minus bad, Ao2a, ¢8 mean theoram m)ykmannu& p/mey mixed fraction im[a ApU8aR&k measure map, man monotonic AeksU{aI measure of association s&b&0man multinominal bhupdI measurement of angles ko8mapn multinominal distribution bhupdI ivtr8 ko8map multinominal expression bhupdI pdavil medial section m)ymey 2ed multiple gui8t median m)yga method of detached coefficient multiple angles gui8t `U8aAo p<9k gu8a&konI rIt multiple correlation bhuclIy metod of differences A&trivi0 shs&b&0 method of divisors -ajkivi0 multiple integral bhus&kl method of expansion ivStr8ivi0 multiple point bhul ib&du method of substitution Aade=nI rIt multiple regression bhuclIy inyt s&b&0 method of undermined multipliers Aini8Rt gu8konI multiple root bhugui8t bIj rIt middle term m)ypd multiplicand gu*y mid-point m)yib&du& multiplication gu8akar minimum NyUntm multiplication rule gu8akarno inym 25 multiplier gu8k norm of angles ko8ad=R multivariate bhucl norm of sides -ujad=R multiple analysis bhucl p<(9kr8 notation p/tIkVyvS9a, s&ketn multivariate distribution bhucl ivtr8 nucleus nai- mutual prSpr, parSpirk null hypothesis inrakr8Iy N pikLpna nadir p/itm)y null line =UNy -/amk re`a natural logarithm p/ak order of figurate numbers s£p s&~ya [ae8I obtuse angle guruko8 order of powers 3atk/m obtuse angled triangle gurui{ako8 order of surds kr8I3at octagon AQ4ko8 ordinal k/maTmk octahedron AQ4flk ordinal numbers k/maTmk s&~yaAo odd AekI s&~ya, Asm ordinary (differential equations) odd functions Asm iv0ey samaNy ordinate koi4 ogive curve s&ymI Aav percentage 4ka point equation ib&dusmIkr8 percentiles =ta&=k point estimation ib&duAag8n perfect cube pU8R 3n point of application p/yogib&du, kayRib&du perimeter pirimit point of bisection m)yib&du permutation k/mcy points of concurrence s&gmib&du permutation with repetition AavtIR k/mcy points of contact Sp=Rib&du permutation with restriction =rtI k/mcy points of intersection 2ednib&du perpendicular l&b points of suspension Avl&bn ib&du perpendicular bisector l&b iµ-ajk points of symmetry simitkeN± perpendicular line l&bre`a points of trisection i{a-agib&du perturbations ivxo- polygon bhuko8 plane smtl apolygonal numbers bhukoi8k s&~yaAo plane angle smtl ko8 polyhedron bhuflk plane circuit smtl sikR4 polynominal bhupdI plane of floation Plvntl polynominal regression bhupidk inyt plane of section smtlC2ed s&b&0 plumb line AoX&banI re`a position iS9it planimeters xe{amapk positive 0n, 0naTmk plot (the points) Aale`vu& positive correlation 0n shs&b&0 point ib&du power 0at 29 principle section p/C2ed power function sam(yR iv0ey principle solution p/bIj power series 3at [ae7I principle value of logarithm p/mULy power of a test prIx8 sam(yR prinicple of superimposition A)yaropno inym preceding pUvRgamI principle part p/0an A&=, prediction p/ak\k9n mu~y A&= prime (mutually) sapex Aiv-ajy prism ip/zm prime function Aiv-ajy probable s&-ivt pdavil probable error s&-ivt {au4I prime meridian Aar&i-k yamo]ar probability s&-avna prime modulus mUl mana&k problem smSya, kU4p/½ prime number Aiv-ajy pU8aR&k product gu8akar prime vertical pUvaRpr wd\v<]a product formula gu8akarsU{a primitive pUvRg progression [ae8I primitive root mU~y bIj projectile p/ixPt principle inym, is)0aNt projective p/xepI principle axes mu~y Axo projective geometry p/xep -Uimit principle directions p/id=a projective property p/xep]v principle normal p/ai-l&b proof saibtI, isi)0 principle plane p/flk proper fraction wict ApU8aR&k principle radius p/i{ajya property gu80mR 30 proporation p/ma8 quadratic surd vgRkr8I, vgaRTmk kr8I proporational p/ma8 quadrature xe{akln proporational mean m)ym p/ma8pd quadrilateral gu8aTmk Aa&k6a propositionally p/ma8sr quantiles ivyojko proposition p/mey, sa)y quantitative data manaTmk Aa&k6a aprotracter ko8mapk quantity rai= prove saibt krvu&, quantum index mana&k is)0 krvu& pure geometry =u)0 -Uimit quartic curve ctu4aRtI vk/ pure mathematics =u)0 gi8t quartile deviation ctu9Rk ivcln purposive sampling shetuk ind=Rn questionnaire p/½avil O quotient -agakar Q.E.D. :it is)0m\ quotient (continued fraction) -agfl C.E.F. :it k 32 reciprocal relation p/ityog s&b&0 reminder theorem =eq p/mey reciprocal root VySt bIj represent d=aRvvu&, in£p8 krvu&, reciprocal theorem p/ityog p/mey s&ketn krvu& reciprocally proportional VySt p/ma8ma& representation s&ketna, in£p8 reciprocation VyStIkr8 representative sample p/itini0 ind=Rn rectangle l&bcors residual error Avi=Q4 doq rectangular array Aaytsr8I residues Av=eq, v¥I rectangular axis l&ba=o residues of powers of numbers pU8aR&k3atav=eq rectangular distribution Aayat ivtr8 resolve into factors Avyv p<(9kr8 rectangular hyperbola l&baitvly respectively Anuk/me rectification capkln result pir8am rectifying plane Sp=aRi-l&b tl resultant pir8amI rectiliner figure sure` Aak Rule (additional) yoginym score p/aPta&k rule of cross multiplication SviStk gu8n secant 2edk re`a inym sector of circle v 35 singular point AsamaNy ib&du spherical polygon golIy bhuko8 size kd spherical radius golIy i{ajya sketch Aak 36 statistics (as a science) Aa&k6a=aS{a, sum formula yogsU{a s&~yaiv}aan, sa&i~ykI sum of a series [ae7Ifl step pd summation srvaXo, yogik/ya straight angle sure` ko8 summation formula [ae7I flsU{a, yogsU{a straight line sure`a supplementary angle pUrk ko8 stratum Str surd kr8I sub-duplicate ration vgRmUl gu8o]ar surd index kr8I 3ata&k subject of formula sU{ano ktaR survey sveR, moj8I sub-multiple wpgui8t symbol p/tIk, s&ket, sub-multiple angles wpgui8t `U8aAo ich\n, s&}aa subordinate root gO8 bIj smmetric smimt substitution Aade= symmetric determinant smimt in¾yaTmk substraction badbakI symmetrical smimt subtriplicate ration 3nmUl gu8o]ar symmetric equation smimt smIkr8 successsive reduction k/imk l3ukr8, k/imk s&xepn asymmetric expression smimt pdavil, smimt rai= successive terms k/imk pdo symmetry smimt sufficient pyaRPt synthetic division s&ixPt -agakar sufficient statistic pyaRPt Aag8k T sufficiency pyaRiPt table koQ4k sum srvaXo, yog 37 tabular logarithm koQ4kIy l3ug8k transformation (of equation) £paNtr tabulation koQ4krcna transit circle yoMyotr v<]a term pd translation S9anetr test (verb) cksavu&, transversal 2edk re`a meXvI jovu& trapezium sml&bk test (noun) prIx8, kso4I triangle i{ako8 theoretical =aS{aIy, sE)0aiNtk triangle of forces bli{ako8 theorem p/mey triangle of reference Aa0ar i{ako8 theorem of the equivalent layer triangular prism i{apa¼R ip/zm tULy p U vector si±= unequal Asm vector field si±= xe{a unit Aekm vector product si±= gu8akar universal savRi{ak vectorial angle si±= ko8 univariate Aekcl verification taXo, `atrI unlimited inŠsIm, Apirimt vertex i=roib&du unlike (signs) Asm vertical w)vR, l&bk unlike term ivjatIy vertical angle i=rŠko8 V vertical plane W)vR smtl valid p/ma8 vertical circle W)vRv<]a validity p/ma8ta, p/ama*y vertical line W)vR re`a, le`a&k re`a value ik&mt, mULy vertically opposite angle Ai-ko8 variable cl vinculum re`akO&s variable (adjective) cilt volume 3nfX variable rate ivcilt dr W 39 w.r.t (with respect to) na ivqe without reminder inŠ=eq whole number pU8R=&k s&~ya Y No word Z zero =UNy zero produce =UNy gu8akar