Copyright © Philip M. Parker, INSEAD. Terms of Use.

Definitions: Calculus |
CalculusNoun1. A hard lump produced by the concretion of mineral salts; found in hollow organs or ducts of the body. 2. An incrustation that forms on the teeth and gums. 3. The branch of mathematics that is concerned with limits and with the differentiation and integration of functions. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "calculus" was first used: 1666. (references) |
| The following table is compiled from various sources, across various languages. When English abbreviations or acronyms come from a non-English source, this is noted. | |||
| Entry | Source | Expression | Field |
| CALIBAN | English | Causal Calculus based on Nets | Computing, European Union |
Source: compiled by the editor, based on several corpora (additional references). | |||
(From Wikipedia, the free Encyclopedia)
There are two main branches of calculus:
The conceptual foundations of calculus include the function, limit, infinite sequences, infinite series, and continuity. Its tools include the symbol manipulation techniques associated with elementary algebra, and mathematical induction.
Calculus has been extended to differential equations, vector calculus, calculus of variations, time scale calculus and differential topology. The modern, formally correct version of calculus is known as real analysis.
Although Archimedes and others have used integral methods throughout history, and a great many (Barrow, Fermat, Pascal, Wallis and others) had previously invented the idea of a derivative, Gottfried Wilhelm Leibniz and Sir Isaac Newton are usually credited with the invention, in the late 1600s, of differential and integral calculus as we know it today. Leibniz and Newton, apparently working independently, arrived at similar results. It is thought that Newton's discoveries were made earlier, but Leibniz' were the first to be published. Newton (who represented derivatives as , , etc.) provided a host of applications in physics, but Leibniz' more flexible notation (, , etc.) was eventually adopted. (The simpler notation is still used in some cases where it is sufficient.)
In 1704 an anonymous pamphlet, later determined to have been written by Leibniz, accused Newton of having plagiarised Leibniz' work. That claim is easily refuted as there is ample evidence to show that Newton commenced work on the calculus long before Leibniz can possibly have done, however the resulting controversy lead to suggestions that Leibniz may not have invented the calculus independently as he claimed, but may have been influenced by reading copies of Newton's early manuscripts. This claim is not so easily dismissed and there is in fact considerable circumstantial evidence to support it. Leibnitz was not known at the time for his probity, and later admitted to falsifying the dates on certain of his manuscripts in an effort to bolster his claims. Furthermore, a copy of one of Newton's very early manuscripts with annotations by Leibniz was found among Leibniz' papers after his death, although the exact date when Leibniz first acquired this is unknown. It is also interesting to note that a similar controversy exists in philosophy over whether or not Leibniz may have appropriated the ideas of Spinoza in his writings on that subject.
The truth of the matter will never be known, and in any case is unimportant to anyone alive today. Leibniz' great contribution to calculus was his notation, and this is beyond doubt purely of Leibniz's invention. The controversy was unfortunate however in that it divided the mathematicians of Britain and Europe for many years. This set back British analysis (i.e. calculus-based mathematics) for a very long time. Newton's terminology and notation was clearly less flexible than that of Leibniz, yet it was retained in British usage until the early 19th century, when the work of the Analytical Society successfully saw the introduction of Leibniz's notation in Great Britain.
The strict limit definition of the derivative presented above was not evolved until much later, and neither Newton nor Leibniz, nor any of their followers until the mid-1800s, developed calculus with acceptable rigour. Nevertheless, the calculus was widely used, as it was a very powerful mathematical tool, but it was not until the nineteenth century that mathematicians like Augustin Louis Cauchy, Bernard Bolzano, and Karl Weierstrass were able to provide a mathematically rigorous exposition. This eventually resulted in deep explorations of the concept of infinity by Georg Cantor and others.
See also: calculus with polynomials
This usage is particularly common in mathematical logic, where a calculus is applied to compute universally true statements of a certain formal logic. Examples include the calculus of natural deduction, the sequent calculus, as well as many other calculi that are deviced in proof theory.
Derived from the Latin word for "pebble", calculus in its most general sense can mean any method or system of calculation. Other topics where the term calculus is used in this sense include:
(From Wikipedia, the free Encyclopedia)History
Further Reading
In mathematics and related fields, the term calculus more generally refers to a system of formal rules of inference and axioms that are used for computation.Calculus (dental)
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Calculus."
Synonyms: CalculusSynonyms: concretion (n), infinitesimal calculus (n), stone (n), tartar (n), the calculus (n). (additional references) |
| Context | Synonyms within Context (source: adapted from Roget's Thesaurus). |
Disease | Ague, angina pectoris, appendicitis; Asiatic cholera, spasmodic cholera; biliary calculus, kidney stone, black death, bubonic plague, pneumonic plague; blennorrhagia, blennorrhoea; blood poisoning, bloodstroke, bloody flux, brash; breakbone fever, dengue fever, malarial fever, Q-fever; heart attack, cardiac arrest, cardiomyopathy; hardening of the arteries, arteriosclerosis, atherosclerosis; bronchocele, canker rash, cardialgia, carditis, endocarditis; cholera, asphyxia; chlorosis, chorea, cynanche, dartre; enanthem, enanthema; erysipelas; exanthem, exanthema; gallstone, goiter, gonorrhea, green sickness; grip, grippe, influenza, flu; hay fever, heartburn, heaves, rupture, hernia, hemorrhoids, piles, herpes, itch, king's evil, lockjaw; measles, mumps, polio; necrosis, pertussis, phthisis, pneumonia, psora, pyaemia, pyrosis, quinsy, rachitis, ringworm, rubeola, St. Vitus's dance, scabies, scarlatina, scarlet fever, scrofula, seasickness, struma, syntexis, tetanus, tetter, tonsillitis, tonsilitis, tracheocele, trachoma, trismus, varicella, varicosis, variola, water qualm, whooping cough; yellow fever, yellow jack. |
Numeration | Noun: numeration; numbering; Verb: pagination; tale, recension, enumeration, summation, reckoning, computation, supputation; calculation, calculus; algorithm, algorism, rhabdology, dactylonomy; measurement; statistics. |
Arithmetic, analysis, algebra, geometry, analytical geometry, fluxions; differential calculus, integral calculus, infinitesimal calculus; calculus of differences. | |
| Source: adapted from Roget's Thesaurus. | |
| Domain | Usage | |
Screenplays | Mr. Calculus Teacher Man is in the hay-ouse! (Ed; writing credit: Steven Joel Kerzner) | |
Source: compiled by the editor from various references; see credits. | ||
| Domain | Title | ||
Books |
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Periodicals |
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Theater & Movies | |||
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High Tech |
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Source: compiled by the editor from various references; see credits. | |||
| Subject | Topic | Quote |
Health | Brain activity, whether one is looking at a picture, working out a problem in calculus, or simply observing the surroundings, requires energy. (references) | |
Source: compiled by the editor from ICON Group International, Inc.; see credits. | ||
| "Calculus" is generally used as a noun (singular) -- approximately 100.00% of the time. "Calculus" is used about 109 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Noun (singular) | 100% | 109 | 31,132 |
Source: compiled by the editor from several corpora; see credits.
Expressions using "calculus": absolute calculus ♦ algebraic calculus ♦ Barycentric calculus ♦ biliary calculus ♦ calculus biliary ♦ calculus I ♦ calculus II ♦ calculus in the reins ♦ calculus of Communicating Systems ♦ calculus of differences ♦ Calculus of functions ♦ Calculus of operations ♦ Calculus of probabilities ♦ Calculus of variations ♦ circuit CALculus ♦ Dental Calculus ♦ differencial calculus ♦ Differential calculus ♦ domain calculus ♦ Exponential calculus ♦ functional calculus ♦ Imaginary calculus ♦ infinitesimal calculus ♦ integral calculus ♦ intestinal calculus ♦ knights of the Lambda Calculus ♦ nasal calculus ♦ nephritic calculus ♦ predicate calculus ♦ probability calculus ♦ propositional calculus ♦ relational calculus ♦ renal calculus ♦ salivary calculus ♦ spermatic calculus ♦ the calculus ♦ tuple calculus ♦ urinary calculus. Additional references. | |
| Hyphenated Usage | |
Beginning with "calculus": calculus-based. | |
Ending with "calculus": Knights of the Lambda-Calculus, Lambada-Calculus, lambda-calculus, nu-calculus, pi-calculus, polymorphic lambda-calculus, pure lambda-calculus, Second-Order Lambda-calculus, typed lambda-calculus. | |
Containing "calculus": predicate-calculus-like. | |
| Source: compiled by the editor from various references; see credits. | |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Expression | Frequency per Day |
calculus | 6,196 |
calculus help | 163 |
pre calculus | 116 |
calculus problem | 59 |
calculus history | 56 |
calculus tutorial | 54 |
calculus integral | 50 |
ap calculus | 49 |
calculus software | 44 |
calculus limit | 43 |
| Source: compiled by the editor from various references; see credits. | |
| Language | Translations for "calculus"; alternative meanings/domain in parentheses. | |
Albanian | njehsim (calculation, computation, count, reckoning), gur (boulder, cobble, piece, rock, stone). (various references) | |
Arabic | حساب التفاضل والتكامل, حصاة المثانة أو الكلية, الحصاة الكلوية. (various references) | |
Bulgarian | камък (concretion, rock, stone), клон на висшата математика, висша математика. (various references) | |
Chinese | "石. (various references) | |
Czech | poèet (number, quantity, tally), kamének, kámen (jewel, rock, stone). (various references) | |
Danish | calculus (calculus I, gallstone), sten (concrement, concretion, gallstone, stone), konkrement (concrement, concretion, gallstone). (various references) | |
Dutch | steen (brick, cancelmatter, concrement, concretion, gallstone, gem, imposing stone, imposing surface, jewel, stone), infinitesimaalrekening (infinitesimal calculus), differentiaal- en integraalrekening (infinitesimal calculus). (various references) | |
Farsi | حساب جامعه وفاضله , سنگ (Boulder, Rock, Stone), جامع وفاضل . (various references) | |
Finnish | calculus (gallstone), kivi (cobble, cobblestone, gallstone, rock, stone). (various references) | |
French | calcul (calculation, calculus I). (various references) | |
German | Rechnung (account, arithmetic, bill, calculation, check, count, Inv., invoice, reckoning, score, statement, sum, tally), Rechenart (arithmetic, type of calculation), infinitesimalrechnung (infinitesimal calculus). (various references) | |
Greek | σύγκριμα (agglomerate, concrement, concretion, gallstone), λιθίαση, λογισμόσ (reflection, reflexion), λίθος (gallstone, gemstone, stone), διαφορικόσ λογισμόσ. (various references) | |
Hebrew | אבן כליות (kidney stone, renal calculus), אב ית ש ים (tartar), חצץ (gravel, grit, macadam). (various references) | |
Hungarian | számítás (account, anticipation, bill, calculation, calculi, cast, count, estimate, reckoning). (various references) | |
Italian | calcolo (account, calculation, calculus I, computation, count, design, estimating, gallstone, gravel, number crunching, reckoning, stone, theory). (various references) | |
Japanese Kanji | 結石 , 微積分 . (various references) | |
Japanese Katakana | びせきぶ", けっせき (absence, non-attendance). (various references) | |
Korean | 미 분학. (various references) | |
Manx | calcalys. (various references) | |
Pig Latin | alculuscay.(various references) | |
Portuguese | cálculo (account, appraisal, appraisement, calculation, cast, clearing-off, computation, compute, concretion, design, estimate, measurement, number crunching, numerator, putting, rate, reckoning, sum, tally, theory, working out). (various references) | |
Romanian | calcul (account, calculation, casting, computation, concretion, estimate, estimation, numeration, rate, sum). (various references) | |
Russian | исчисление (estimate, numeration). (various references) | |
Serbo-Croatian | račun (account, arithmetic, bill, calculation, check, chit, count, reckoning, tab), kamen (rock, stone, stony). (various references) | |
Spanish | cálculo (accounting cost, calculation, computation, computing, counting, estimate, gallstone, number crunching, reckoning, stone). (various references) | |
Swedish | sten (boulder, cobble, cobblestone, concretion, pebble, rock, stone). (various references) | |
Thai | นิ่ว, ระบบการคำนว"เกี่ยวกับจำนวนที่มีการเปลี่ยนแปลงอย่างต่อเนื่อง เช่น ความเร็วของหินที่ตกลง. (various references) | |
Turkish | taş (allusion, concretion, dig, Flint, gem, gibe, gravel, hit, innuendo, jeer, jibe, lapidary, piece, rock, stone), hesap (account, arithmetic, bill, calculation, computation, count, counting, estimate, reckoning, score, settling, sum, sums). (various references) | |
Ukranian | числення, камінь (rock, stone). (various references) | |
| Source: compiled by the editor from various translation references. | ||
| Language | Period | Translations |
| Latin | 500 BCE-Modern | calculus. (various references) |
| Source: compiled by the editor from various references. | ||
| Language | Date | Source | Isaiah Chapter 6, Verse 6 |
| Greek (transliterated) | 250 BC | Septuagint | Kai apestalh proV me en twn serafin kai en th ceiri eicen anqraka on th labidi elaben apo tou qusiasthriou |
| Latin | 405 | Vulgate | Et volavit ad me unus de seraphin et in manu eius calculus quem forcipe tulerat de altari |
| Middle English | 1395 | Wyclif | And ther fleiy to me oon of the serafyn, and in his hond a cole, that with the toenge he toc fro the auter. |
| Jacobean English | 1611 | King James | Then flew one of the seraphims unto me, having a live coal in his hand, which he had taken with the tongs from off the altar: |
| Victorian English | 1833 | Webster | Then one of the seraphim flew to me, having a live coal in his hand, which he had taken with the tongs from off the altar: |
| Basic English | 1964 | Ogden | Then a winged one came to me with a burning coal in his hand, which he had taken from off the altar with the fire-spoon. |
Source: compiled by the editor from various references; see credits. | |||
| Language | Isaiah Chapter 6, Verse 6 |
| Bulgarian | Тогава долетя при мене един от серафимите, като държеше в ръката си разпален въглен, що бе взел с щипци от олтара. |
| Cebuano | Ug unya ang usa sa mga serafin milupad nganhi kanako, nga may usa ka baga nga carbon diha sa iyang kamot nga iyang gikuha pinaagi sa mga kumpit gikan sa halaran: |
| Chinese | 有 一 '' 拉 弗 飛 到 我 跟 前 、 手 裡 拿 著 紅 炭 、 是 " 火 剪 從 壇 上 取 下 來 的 . |
| Croatian | Jedan od serafa doletje k meni: u ruci mu žerava koju uze kliještima sa žrtvenika; |
| Danish | Men en af Seraferne fløj hen til mig; og han havde i Hånden et glødende Kul, som han med en Tang havde taget fra Alteret; |
| Dutch | Maar een van de serafs vloog tot mij, en had een gloeiende kool in zijn hand, die hij met de tang van het altaar genomen had. |
| Finnish | Silloin lensi minun luokseni yksi serafeista, kädessään hehkuva kivi, jonka hän oli pihdeillä ottanut alttarilta, |
| French | Mais l`un des séraphins vola vers moi, tenant la main une pierre ardente, qu`il avait prise sur l`autel avec des pincettes. |
| German | Da flog der Seraphim einer zu mir und hatte eine glühende Kohle in der Hand, die er mit der Zange vom Altar nahm, |
| Haitian Creole | Yonn nan bèt vivan yo pran yon chabon dife tou limen ak yon pensèt sou lotèl la, li vole vin bò kote m' avèk chabon dife a nan men li. |
| Hungarian | És hozzám repült egy a szeráfok közül, és kezében eleven szén vala, a melyet fogóval vett volt az oltárról; |
| Indonesian-Bahasa Sehari-hari | Kemudian salah satu makhluk itu terbang kepada saya membawa bara yang diambilnya dengan sepit dari mezbah. |
| Indonesian-Terjemahan Lama | Tetapi dari pada segala serafim itu terbanglah seorang mendapatkan aku, dan pada tangannya adalah bara api, yang telah diambilnya dari atas mezbah dengan penyepit. |
| Italian | Allora uno dei serafini volò verso di me; teneva in mano un carbone ardente che aveva preso con le molle dall'altare. |
| Korean | 때 에 그 스 랍 의 하 나 가 " 로 단 에 서 취 한 " 핀 숯 을 손 에 가 지 내 게 로 아 와 서 |
| Maori | Na ko te rerenga mai o tetahi o nga herapima ki ahau, he waro mura i tona ringa, he mea tango mai e ia i te aata ki te kokopi. |
| Modern Greek | Τοτε επετασε προς εμε εν εκ των Σεραφειμ εχον εν τη χειρι αυτου ανθρακα πυρος, τον οποιον ελαβε δια της λαβιδος απο του θυσιαστηριου. |
| Norwegian | Da fløi en av serafene bort til mig med en gloende sten i sin hånd; med en tang hadde han tatt den fra alteret. |
| Portuguese | Então voou para mim um dos serafins, trazendo na mão uma brasa viva, que tirara do altar com uma tenaz; |
| Rumanian | Dar unul din serafimi a zburat spre mine cu un cqrbune aprins kn mknq, pe care -l luase cu clewtele de pe altar. |
| Russian | фПЗ"Б ТЙМЕФЕМ ЛП НОЕ П"ЙО ЙЪ уЕТБЖЙНПЧ, Й Ч ТХЛЕ Х ОЕЗП ЗПТСЭЙК ХЗПМШ, ЛПФПТЩК ПО ЧЪСМ ЛМЕЭБНЙ У ЦЕТФЧЕООЙЛБ, |
| Spanish | Entonces voló hacia mí uno de los serafines trayendo en su mano, con unas tenazas, un carbón encendido tomado del altar. |
| Swedish | Men en av seraferna flög fram till mig, och han hade i sin hand ett glödande kol, som han med en tång hade tagit på altaret. |
| Thai | แล้วตนหนึ่งในเสราฟิมบินมาหาข้าพเจ้า ในมือมีถ่านเพลิง ซึ่งเขาเอาคีมคีบมาจากแท่นบูชา |
| Ukrainian | І прилетів до мене один з Серафимів, а в руці його вугіль розпалений, якого він узяв щипцями з-над жертівника. |
Source: compiled by the editor from various references; see credits. | |
Derivations | |
Words beginning with "calculus": calculuses. (additional references) | |
Words ending with "calculus": precalculus. (additional references) | |
Words containing "calculus": precalculuses. (additional references) | |
| |
"Calculus" is suggested in spellcheckers for the following: calcu, calcul, calculas, calculis, calculos. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "calculus" (pronounced ka"lkyulus) |
| 6 | -k y u l u s | meticulous, miraculous, ridiculous. |
| 5 | -y u l u s | fabulous, nebulous, populace, populous, scrupulous, stimulus, tremulous, unscrupulous. |
| 4 | -u l u s | acropolis, anomalous, Carolus, frivolous, garrulous, incredulous, libelous, marvelous, megalopolis, merciless, metropolis, nautilus, necropolis, Oxalis, pendulous, perilous, querulous, scandalous, scurrilous, syphilis, tantalus. |
| 3 | -l u s | accomplice, ageless, aimless, airless, Amaryllis, atlas, bacillus, backless, balas, baseless, blameless, bloodless, bolus, boneless, bottomless, boundless, brainless, breathless, callous, callus, careless, cashless, ceaseless, childless, classless, cloudless, clueless, Colas, colorless, cordless, countless, cutlass, defenseless, digitalis, directionless, doubtless, driverless, ductless, earless, effortless, endless, expressionless, eyeless, faceless, fatherless, fearless, featherless, featureless, feckless, fellas, fenceless, flawless, flightless, frictionless, fruitless, Gallus, gladiolus, godless, graceless, groundless, guileless, guiltless, hairless, hapless, harmless, headless, heartless, helpless, homeless, hopeless, hornless, humorless, irregardless, issueless, jealous, jobless, keyless, lactobacillus, landless, lawless, leaderless, leafless, legless, lifeless, limbless, limitless, listless, loveless, luckless, malice, meaningless, meatless, mindless, motherless, motionless, nameless, necklace, needless, odorless, overzealous, painless, palace, paperless, peerless, penniless, pilotless, pitiless, pointless, polis, powerless, priceless, prothallus, purposeless, reckless, regardless, relentless, remorseless, restless, riskless, rootless, rudderless, ruthless, scoreless, seamless, selfless, senseless, sexless, shameless, shapeless, shiftless, skinless, sleepless, sleeveless, smokeless, solace, soulless, speechless, spineless, spotless, stainless, stateless, stylus, surplus, tasteless, thankless, thoughtless, ticketless, tieless, timeless, tireless, toothless, topless, treeless, trellis, useless, valueless, victimless, voiceless, warrantless, weightless, windlass, windowless, wireless, witless, wordless, worthless, zealous, zipless. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "a-c-c-l-l-s-u-u" | |
-2 letters: callus, caucus, sulcal. | |
-3 letters: calls, cauls, culls, luaus, lulus, scall, scull, usual. | |
-4 letters: alls, call, caul, cull, lacs, luau, lulu, sall, saul, sulu, ulus. | |
-5 letters: all, als, lac, las, sac, sal, sau, ulu. | |
| Words containing the letters "a-c-c-l-l-s-u-u" | |
+1 letter: calculous, calyculus. | |
+2 letters: calculuses. | |
+3 letters: canaliculus, precalculus. | |
+5 letters: precalculuses, sociocultural. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
Hexadecimal (or equivalents, 770AD-1900s) (references)43 61 6C 63 75 6C 75 73 |
| Leonardo da Vinci (1452-1519; backwards) (references)
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| American Sign Language (origins from 1620-1817 in Italy and, especially, France) (references)
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| Semaphore (1791, in France) (references)
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| Braille (1829, in France) (references)
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Morse Code (1836) (references)-.-. .- .-.. -.-. ..- .-.. ..- ... |
| Dancing Men (Sir Arthur Conan Doyle, 1903) (references)
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Binary Code (1918-1938, probably earlier) (references)01000011 01100001 01101100 01100011 01110101 01101100 01110101 01110011 |
HTML Code (1990) (references)C a l c u l u s |
ISO 10646 (1991-1993) (references)0043 0061 006C 0063 0075 006C 0075 0073 |
| British Sign Language (Fingerspelling, BSL; 1992, British Deaf Association Dictionary of British Sign Language) (references)
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Encryption (beginner's substitution cypher): (references)3767786987788785 |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Modern | 5. Usage: Commercial 6. Images: Slideshow 7. Quotations: Non-fiction 8. Usage Frequency | 9. Expressions 10. Expressions: Internet 11. Translations: Modern 12. Translations: Ancient | 13. Bible Trace 14. Abbreviations 15. Acronyms 16. Derivations | 17. Rhymes 18. Anagrams 19. Orthography 20. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.