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105-504: The word "lever" entered English around AD 1300 from Old French : levier . This sprang from the stem of the verb lever , meaning "to raise". The verb, in turn, goes back to Latin : levare , itself from the adjective levis , meaning "light" (as in "not heavy"). The word's primary origin is the Proto-Indo-European stem legwh- , meaning "light", "easy" or "nimble", among other things. The PIE stem also gave rise to

210-638: A ( F A ⋅ e A ⊥ ) − b ( F B ⋅ e B ⊥ ) = a F A − b F B , {\displaystyle F_{\theta }=\mathbf {F} _{A}\cdot {\frac {\partial \mathbf {v} _{A}}{\partial {\dot {\theta }}}}-\mathbf {F} _{B}\cdot {\frac {\partial \mathbf {v} _{B}}{\partial {\dot {\theta }}}}=a(\mathbf {F} _{A}\cdot \mathbf {e} _{A}^{\perp })-b(\mathbf {F} _{B}\cdot \mathbf {e} _{B}^{\perp })=aF_{A}-bF_{B},} where F A and F B are components of

315-426: A b . {\displaystyle MA={\frac {F_{2}}{F_{1}}}={\frac {a}{b}}.\!} This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming a weightless lever and no losses due to friction, flexibility or wear. This remains true even though the "horizontal" distance (perpendicular to

420-402: A b . {\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}}.} This is the law of the lever , which was proven by Archimedes using geometric reasoning. It shows that if the distance a from the fulcrum to where the input force is applied (point A ) is greater than the distance b from fulcrum to where the output force is applied (point B ), then the lever amplifies

525-406: A and b are distances from the fulcrum to points A and B and the force F A applied to A is the input and the force F B applied at B is the output, the ratio of the velocities of points A and B is given by a/b , so we have the ratio of the output force to the input force, or mechanical advantage, is given by: M A = F B F A =

630-493: A and b are the perpendicular distances between the forces and the fulcrum. Since the moments of torque must be balanced, T 1 = T 2 {\displaystyle T_{1}=T_{2}\!} . So, F 1 a = F 2 b {\displaystyle F_{1}a=F_{2}b\!} . The mechanical advantage of a lever is the ratio of output force to input force. M A = F 2 F 1 =

735-553: A mixed language or a creole —a theory called the Middle English creole hypothesis . Although the great influence of these languages on the vocabulary and grammar of Modern English is widely acknowledged, most specialists in language contact do not consider English to be a true mixed language. English is classified as a Germanic language because it shares innovations with other Germanic languages including Dutch , German , and Swedish . These shared innovations show that

840-644: A 2012 official Eurobarometer poll (conducted when the UK was still a member of the EU), 38 percent of the EU respondents outside the countries where English is an official language said they could speak English well enough to have a conversation in that language. The next most commonly mentioned foreign language, French (which is the most widely known foreign language in the UK and Ireland), could be used in conversation by 12 percent of respondents. A working knowledge of English has become

945-658: A distinct language from Modern English and is virtually impossible for 21st-century unstudied English-speakers to understand. Its grammar was similar to that of modern German: nouns, adjectives, pronouns, and verbs had many more inflectional endings and forms , and word order was much freer than in Modern English. Modern English has case forms in pronouns ( he , him , his ) and has a few verb inflections ( speak , speaks , speaking , spoke , spoken ), but Old English had case endings in nouns as well, and verbs had more person and number endings. Its closest relative

1050-400: A fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot. As the lever rotates around the fulcrum, points further from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point further from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity. If

1155-490: A foreign language, make up the "expanding circle". The distinctions between English as a first language, as a second language, and as a foreign language are often debatable and may change in particular countries over time. For example, in the Netherlands and some other countries of Europe, knowledge of English as a second language is nearly universal, with over 80 percent of the population able to use it, and thus English

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1260-413: A lever long enough and a fulcrum on which to place it, and I shall move the world." Autumn Stanley argues that the digging stick can be considered the first lever, which would position prehistoric women as the inventors of lever technology. A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in

1365-520: A more standard version of English. They have many more speakers of English who acquire English as they grow up through day-to-day use and listening to broadcasting, especially if they attend schools where English is the medium of instruction. Varieties of English learned by non-native speakers born to English-speaking parents may be influenced, especially in their grammar, by the other languages spoken by those learners. Most of those varieties of English include words little used by native speakers of English in

1470-695: A number of other Anglic languages, including Scots and the extinct Fingallian dialect and Yola language of Ireland. Like Icelandic and Faroese , the development of English in the British Isles isolated it from the continental Germanic languages and influences, and it has since diverged considerably. English is not mutually intelligible with any continental Germanic language, as it differs in vocabulary , syntax , and phonology . However, some of these, such as Dutch or Frisian, do show strong affinities with English, especially with its earlier stages. Unlike Icelandic and Faroese, which were isolated,

1575-684: A requirement in a number of occupations and professions such as medicine and computing. English has become so important in scientific publishing that more than 80 percent of all scientific journal articles indexed by Chemical Abstracts in 1998 were written in English, as were 90 percent of all articles in natural science publications by 1996 and 82 percent of articles in humanities publications by 1995. International communities such as international business people may use English as an auxiliary language , with an emphasis on vocabulary suitable for their domain of interest. This has led some scholars to develop

1680-407: A rich inflectional morphology and relatively free word order to a mostly analytic pattern with little inflection and a fairly fixed subject–verb–object word order . Modern English relies more on auxiliary verbs and word order for the expression of complex tenses , aspects and moods , as well as passive constructions , interrogatives , and some negation . The earliest form of English

1785-758: A significant minority speaks English. The countries with the most native English speakers are, in descending order, the United States (at least 231 million), the United Kingdom (60 million), Canada (19 million), Australia (at least 17 million), South Africa (4.8 million), Ireland (4.2 million), and New Zealand (3.7 million). In these countries, children of native speakers learn English from their parents, and local people who speak other languages and new immigrants learn English to communicate in their neighbourhoods and workplaces. The inner-circle countries provide

1890-447: A verb ending ( present plural): From the 8th to the 11th centuries, Old English gradually transformed through language contact with Old Norse in some regions. The waves of Norse (Viking) colonisation of northern parts of the British Isles in the 8th and 9th centuries put Old English into intense contact with Old Norse , a North Germanic language. Norse influence was strongest in the north-eastern varieties of Old English spoken in

1995-563: Is Old Frisian , but even some centuries after the Anglo-Saxon migration, Old English retained considerable mutual intelligibility with other Germanic varieties. Even in the 9th and 10th centuries, amidst the Danelaw and other Viking invasions, there is historical evidence that Old Norse and Old English retained considerable mutual intelligibility, although probably the northern dialects of Old English were more similar to Old Norse than

2100-451: Is a simple machine operating on the premise that the resistance from one lever in a system of levers acts as effort for the next, and thus the applied force is transferred from one lever to the next. Almost all scales use some sort of compound lever to work. Other examples include nail clippers and piano keys. A lever arm uses the fulcrum to lift the load using and intensifying an applied force . In practice, conditions may prevent

2205-400: Is also the most widely learned second language in the world, with more second-language speakers than native speakers. English is either the official language or one of the official languages in 59 sovereign states (such as India , Ireland , and Canada ). In some other countries, it is the sole or dominant language for historical reasons without being explicitly defined by law (such as in

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2310-466: Is also undergoing change under the influence of American English, fuelled by the strong presence of American English in the media and the prestige associated with the United States as a world power. As of 2016 , 400 million people spoke English as their first language , and 1.1 billion spoke it as a secondary language. English is the largest language by number of speakers . English

2415-610: Is also widely used in media and literature, and the number of English language books published annually in India is the third largest in the world after the US and UK. However, English is rarely spoken as a first language, numbering only around a couple hundred-thousand people, and less than 5% of the population speak fluent English in India. David Crystal claimed in 2004 that, combining native and non-native speakers, India now has more people who speak or understand English than any other country in

2520-407: Is an official language of countries populated by few descendants of native speakers of English. It has also become by far the most important language of international communication when people who share no native language meet anywhere in the world. The Indian linguist Braj Kachru distinguished countries where English is spoken with a three circles model . In his model, Kachru based his model on

2625-538: Is called Old English or Anglo-Saxon ( c.  450–1150 ). Old English developed from a set of West Germanic dialects, often grouped as Anglo-Frisian or North Sea Germanic , and originally spoken along the coasts of Frisia , Lower Saxony and southern Jutland by Germanic peoples known to the historical record as the Angles , Saxons , and Jutes . From the 5th century, the Anglo-Saxons settled Britain as

2730-434: Is no mechanical advantage. This is not usually the goal of a compound lever system, though in rare situations the geometry may suit a specific purpose. The distances used in calculation of mechanical advantage are measured perpendicular to the force. In the example of a nail clipper on the right (a compound lever made of a class 2 and a class 3 lever), because the effort is applied vertically (that is, not perpendicular to

2835-536: Is often arbitrarily defined as beginning with the conquest of England by William the Conqueror in 1066, but it developed further in the period from 1150 to 1500. With the Norman conquest of England in 1066, the now-Norsified Old English language was subject to another wave of intense contact, this time with Old French , in particular Old Norman French , influencing it as a superstrate. The Norman French spoken by

2940-405: Is operated by applying an input force F A at a point A located by the coordinate vector r A on the bar. The lever then exerts an output force F B at the point B located by r B . The rotation of the lever about the fulcrum P is defined by the rotation angle θ in radians. Let the coordinate vector of the point P that defines the fulcrum be r P , and introduce

3045-424: Is routinely used to communicate with foreigners and often in higher education. In these countries, although English is not used for government business, its widespread use puts them at the boundary between the "outer circle" and "expanding circle". English is unusual among world languages in how many of its users are not native speakers but speakers of English as a second or foreign language. Many users of English in

3150-517: Is spoken by communities on every continent and on islands in all the major oceans. The countries where English is spoken can be grouped into different categories according to how English is used in each country. The "inner circle" countries with many native speakers of English share an international standard of written English and jointly influence speech norms for English around the world. English does not belong to just one country, and it does not belong solely to descendants of English settlers. English

3255-481: Is the generalized coordinate that defines the configuration of the lever, and the generalized force associated with this coordinate is given by F θ = F A ⋅ ∂ v A ∂ θ ˙ − F B ⋅ ∂ v B ∂ θ ˙ =

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3360-777: Is the third person pronoun group beginning with th- ( they, them, their ) which replaced the Anglo-Saxon pronouns with h- ( hie, him, hera ). Other core Norse loanwords include "give", "get", "sky", "skirt", "egg", and "cake", typically displacing a native Anglo-Saxon equivalent. Old Norse in this era retained considerable mutual intelligibility with some dialects of Old English, particularly northern ones. Englischmen þeyz hy hadde fram þe bygynnyng þre manner speche, Souþeron, Northeron, and Myddel speche in þe myddel of þe lond, ... Noþeles by comyxstion and mellyng, furst wiþ Danes, and afterward wiþ Normans, in menye þe contray longage ys asperyed, and som vseþ strange wlaffyng, chyteryng, harryng, and garryng grisbytting. Although, from

3465-485: The Augustinian canon Orrm , which highlights the blending of both Old English and Anglo-Norman elements in English for the first time. In Wycliff'e Bible of the 1380s, the verse Matthew 8:20 was written: Foxis han dennes, and briddis of heuene han nestis . Here the plural suffix -n on the verb have is still retained, but none of the case endings on the nouns are present. By the 12th century Middle English

3570-546: The Danelaw area around York, which was the centre of Norse colonisation; today these features are still particularly present in Scots and Northern English . The centre of Norsified English was in the Midlands around Lindsey . After 920 CE, when Lindsey was incorporated into the Anglo-Saxon polity, English spread extensively throughout the region. An element of Norse influence that continues in all English varieties today

3675-552: The European Free Trade Association , Association of Southeast Asian Nations (ASEAN), and Asia-Pacific Economic Cooperation (APEC) set English as their organisation's sole working language even though most members are not countries with a majority of native English speakers. While the European Union (EU) allows member states to designate any of the national languages as an official language of

3780-536: The Germanic language branch, and as of 2021 , Ethnologue estimated that there were over 1.5 billion speakers worldwide. Old English emerged from a group of West Germanic dialects spoken by the Anglo-Saxons . Late Old English borrowed some grammar and core vocabulary from Old Norse , a North Germanic language . Then, Middle English borrowed vocabulary extensively from French dialects , which are

3885-767: The Low Saxon and Frisian languages . English is an Indo-European language and belongs to the West Germanic group of the Germanic languages . Old English originated from a Germanic tribal and linguistic continuum along the Frisian North Sea coast, whose languages gradually evolved into the Anglic languages in the British Isles , and into the Frisian languages and Low German /Low Saxon on

3990-668: The United Nations at the end of World War II , English had become pre-eminent and is now the main worldwide language of diplomacy and international relations. It is one of six official languages of the United Nations. Many other worldwide international organisations, including the International Olympic Committee , specify English as a working language or official language of the organisation. Many regional international organisations such as

4095-518: The palatalisation of consonants that were velar consonants in Proto-Germanic (see Phonological history of Old English § Palatalization ). The earliest varieties of an English language, collectively known as Old English or "Anglo-Saxon", evolved from a group of North Sea Germanic dialects brought to Britain in the 5th century. Old English dialects were later influenced by Old Norse -speaking Viking invaders and settlers , starting in

4200-564: The "outer circle" countries are countries such as the Philippines , Jamaica , India , Pakistan , Singapore , Malaysia and Nigeria with a much smaller proportion of native speakers of English but much use of English as a second language for education, government, or domestic business, and its routine use for school instruction and official interactions with the government. Those countries have millions of native speakers of dialect continua ranging from an English-based creole to

4305-425: The 3rd century BC and were provided by Archimedes . " Give me a place to stand, and I shall move the earth with a lever " is a remark attributed to Archimedes, who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria). One of the earliest examples of a compound lever is from Han dynasty (202 BC - 220 AD) crossbow trigger mechanisms which featured a triple compound lever. Such

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4410-617: The 8th and 9th centuries. Middle English began in the late 11th century after the Norman Conquest of England, when a considerable amount of Old French vocabulary was incorporated into English over some three centuries. Early Modern English began in the late 15th century with the start of the Great Vowel Shift and the Renaissance trend of borrowing further Latin and Greek words and roots, concurrent with

4515-608: The Angles. English may have a small amount of substrate influence from Common Brittonic, and a number of possible Brittonicisms in English have been proposed, but whether most of these supposed Brittonicisms are actually a direct result of Brittonic substrate influence is disputed. Old English was divided into four dialects: the Anglian dialects ( Mercian and Northumbrian ) and the Saxon dialects ( Kentish and West Saxon ). Through

4620-524: The British Empire in the 1950s and 1960s, former colonies often did not reject English but rather continued to use it as independent countries setting their own language policies. For example, the view of the English language among many Indians has gone from associating it with colonialism to associating it with economic progress, and English continues to be an official language of India. English

4725-547: The Early Modern period includes the works of William Shakespeare and the translation of the Bible commissioned by King James I . Even after the vowel shift the language still sounded different from Modern English: for example, the consonant clusters /kn ɡn sw/ in knight , gnat , and sword were still pronounced. Many of the grammatical features that a modern reader of Shakespeare might find quaint or archaic represent

4830-655: The English Language , which introduced standard spellings of words and usage norms. In 1828, Noah Webster published the American Dictionary of the English language to try to establish a norm for speaking and writing American English that was independent of the British standard. Within Britain, non-standard or lower class dialect features were increasingly stigmatised, leading to the quick spread of

4935-412: The English word "light". The earliest evidence of the lever mechanism dates back to the ancient Near East c.  5000 BC , when it was first used in a simple balance scale . In ancient Egypt c.  4400 BC , a foot pedal was used for the earliest horizontal frame loom . In Mesopotamia (modern Iraq) c.  3000 BC , the shadouf , a crane-like device that uses a lever mechanism,

5040-557: The English-speaking inner circle countries outside Britain helped level dialect distinctions and produce koineised forms of English in South Africa, Australia, and New Zealand. The majority of immigrants to the United States without British ancestry rapidly adopted English after arrival. Now the majority of the United States population are monolingual English speakers. English has ceased to be an "English language" in

5145-554: The Roman economy and administration collapsed . By the 7th century, this Germanic language of the Anglo-Saxons became dominant in Britain , replacing the languages of Roman Britain (43–409): Common Brittonic , a Celtic language , and British Latin , brought to Britain by the Roman occupation. At this time, these dialects generally resisted influence from the then-local Brittonic and Latin languages. England and English (originally Ænglaland and Ænglisc ) are both named after

5250-494: The Union, in practice English is the main working language of EU organisations. Although in most countries English is not an official language, it is currently the language most often taught as a foreign language . In the countries of the EU, English is the most widely spoken foreign language in nineteen of the twenty-five member states where it is not an official language (that is, the countries other than Ireland and Malta ). In

5355-519: The United States and United Kingdom ). It is a co-official language of the United Nations , the European Union , and many other international and regional organisations. It has also become the de facto lingua franca of diplomacy, science , technology, international trade, logistics, tourism, aviation, entertainment, and the Internet . English accounts for at least 70% of total speakers of

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5460-407: The base from which English spreads to other countries in the world. Estimates of the numbers of second language and foreign-language English speakers vary greatly from 470 million to more than 1 billion, depending on how proficiency is defined. Linguist David Crystal estimates that non-native speakers now outnumber native speakers by a ratio of 3 to 1. In Kachru's three-circles model,

5565-453: The basis for the required controlled natural languages Seaspeak and Airspeak, used as international languages of seafaring and aviation. English used to have parity with French and German in scientific research, but now it dominates that field. It achieved parity with French as a language of diplomacy at the Treaty of Versailles negotiations in 1919. By the time of the foundation of

5670-400: The beginning, Englishmen had three manners of speaking, southern, northern and midlands speech in the middle of the country, ... Nevertheless, through intermingling and mixing, first with Danes and then with Normans, amongst many the country language has arisen, and some use strange stammering, chattering, snarling, and grating gnashing. John Trevisa , c.  1385 Middle English

5775-638: The consensus of educated English speakers around the world, without any oversight by any government or international organisation. American listeners readily understand most British broadcasting, and British listeners readily understand most American broadcasting. Most English speakers around the world can understand radio programmes, television programmes, and films from many parts of the English-speaking world. Both standard and non-standard varieties of English can include both formal or informal styles, distinguished by word choice and syntax and use both technical and non-technical registers. The settlement history of

5880-701: The continent. The Frisian languages, which together with the Anglic languages form the Anglo-Frisian languages , are the closest living relatives of English. Low German/Low Saxon is also closely related, and sometimes English, the Frisian languages, and Low German are grouped together as the North Sea Germanic languages, though this grouping remains debated. Old English evolved into Middle English , which in turn evolved into Modern English. Particular dialects of Old and Middle English also developed into

5985-476: The development of English was influenced by a long series of invasions of the British Isles by other peoples and languages, particularly Old Norse and French dialects . These left a profound mark of their own on the language, so that English shows some similarities in vocabulary and grammar with many languages outside its linguistic clades —but it is not mutually intelligible with any of those languages either. Some scholars have argued that English can be considered

6090-419: The distance traveled is greater, then the output force is lessened. T 1 = F 1 a , T 2 = F 2 b {\displaystyle {\begin{aligned}T_{1}&=F_{1}a,\quad \\T_{2}&=F_{2}b\!\end{aligned}}} where F 1 is the input force to the lever and F 2 is the output force. The distances

6195-476: The distinct characteristics of Early Modern English. In the 1611 King James Version of the Bible, written in Early Modern English, Matthew 8:20 says, "The Foxes haue holes and the birds of the ayre haue nests." This exemplifies the loss of case and its effects on sentence structure (replacement with subject–verb–object word order, and the use of of instead of the non-possessive genitive), and

6300-401: The early period of Old English were written using a runic script . By the 6th century, a Latin alphabet was adopted, written with half-uncial letterforms . It included the runic letters wynn ⟨ ƿ ⟩ and thorn ⟨ þ ⟩ , and the modified Latin letters eth ⟨ ð ⟩ , and ash ⟨ æ ⟩ . Old English is essentially

6405-551: The educational reforms of King Alfred in the 9th century and the influence of the kingdom of Wessex , the West Saxon dialect became the standard written variety . The epic poem Beowulf is written in West Saxon, and the earliest English poem, Cædmon's Hymn , is written in Northumbrian. Modern English developed mainly from Mercian, but the Scots language developed from Northumbrian. A few short inscriptions from

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6510-695: The elite in England eventually developed into the Anglo-Norman language . Because Norman was spoken primarily by the elites and nobles, while the lower classes continued speaking English, the main influence of Norman was the introduction of a wide range of loanwords related to politics, legislation and prestigious social domains. Middle English also greatly simplified the inflectional system, probably in order to reconcile Old Norse and Old English, which were inflectionally different but morphologically similar. The distinction between nominative and accusative cases

6615-408: The expanding circle use it to communicate with other people from the expanding circle, so that interaction with native speakers of English plays no part in their decision to use the language. Non-native varieties of English are widely used for international communication, and speakers of one such variety often encounter features of other varieties. Very often today a conversation in English anywhere in

6720-400: The forces that are perpendicular to the radial segments PA and PB . The principle of virtual work states that at equilibrium the generalized force is zero, that is F θ = a F A − b F B = 0. {\displaystyle F_{\theta }=aF_{A}-bF_{B}=0.\,\!} Thus, the ratio of the output force F B to

6825-721: The growing economic and cultural influence of the United States and its status as a superpower following the Second World War has, along with worldwide broadcasting in English by the BBC and other broadcasters, caused the language to spread across the planet much faster. In the 21st century, English is more widely spoken and written than any language has ever been. As Modern English developed, explicit norms for standard usage were published, and spread through official media such as public education and state-sponsored publications. In 1755, Samuel Johnson published his A Dictionary of

6930-412: The hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the law of the lever . The mechanical advantage of a lever can be determined by considering the balance of moments or torque , T , about the fulcrum. If

7035-479: The history of English was Early Modern English (1500–1700). Early Modern English was characterised by the Great Vowel Shift (1350–1700), inflectional simplification, and linguistic standardisation. The Great Vowel Shift affected the stressed long vowels of Middle English. It was a chain shift , meaning that each shift triggered a subsequent shift in the vowel system. Mid and open vowels were raised , and close vowels were broken into diphthongs . For example,

7140-407: The history of how English spread in different countries, how users acquire English, and the range of uses English has in each country. The three circles change membership over time. Countries with large communities of native speakers of English (the inner circle) include Britain, the United States, Australia, Canada, Ireland, and New Zealand, where the majority speaks English, and South Africa, where

7245-403: The inner-circle countries, and they may show grammatical and phonological differences from inner-circle varieties as well. The standard English of the inner-circle countries is often taken as a norm for use of English in the outer-circle countries. In the three-circles model, countries such as Poland, China, Brazil, Germany, Japan, Indonesia, Egypt, and other countries where English is taught as

7350-426: The input force F A is obtained as M A = F B F A = a b , {\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}},} which is the mechanical advantage of the lever. This equation shows that if the distance a from the fulcrum to the point A where the input force is applied is greater than the distance b from fulcrum to

7455-419: The input force. On the other hand, if the distance a from the fulcrum to the input force is less than the distance b from the fulcrum to the output force, then the lever reduces the input force. The use of velocity in the static analysis of a lever is an application of the principle of virtual work . A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever

7560-531: The introduction of loanwords from French ( ayre ) and word replacements ( bird originally meaning "nestling" had replaced OE fugol ). By the late 18th century, the British Empire had spread English through its colonies and geopolitical dominance. Commerce, science and technology, diplomacy, art, and formal education all contributed to English becoming the first truly global language. English also facilitated worldwide international communication. English

7665-475: The introduction of the printing press to London. This era notably culminated in the King James Bible and the works of William Shakespeare . The printing press greatly standardised English spelling, which has remained largely unchanged since then, despite a wide variety of later sound shifts in English dialects. Modern English has spread around the world since the 17th century as a consequence of

7770-489: The island of Great Britain . The namesake of the language is the Angles , one of the ancient Germanic peoples that migrated to Britain . It is the most spoken language in the world, primarily due to the global influences of the former British Empire (succeeded by the Commonwealth of Nations ) and the United States . English is the third-most spoken native language , after Standard Chinese and Spanish ; it

7875-431: The languages have descended from a single common ancestor called Proto-Germanic . Some shared features of Germanic languages include the division of verbs into strong and weak classes, the use of modal verbs , and the sound changes affecting Proto-Indo-European consonants, known as Grimm's and Verner's laws . English is classified as an Anglo-Frisian language because Frisian and English share other features, such as

7980-442: The lengths a = | r A − r P | , b = | r B − r P | , {\displaystyle a=|\mathbf {r} _{A}-\mathbf {r} _{P}|,\quad b=|\mathbf {r} _{B}-\mathbf {r} _{P}|,} which are the distances from the fulcrum to the input point A and to the output point B , respectively. Now introduce

8085-409: The lever), distances to the respective fulcrums are measured horizontally, instead of along the lever. In this example, W/F is ⁠ 7 + 1 / 1 ⁠ × ⁠ 6 / 6 + 2 ⁠ = 6. Note that (7 + 1) cm = 8 cm is the distance from the point of application of the effort to the fulcrum of the first lever, perpendicular to the applied effort. A few examples of the compound lever are

8190-401: The levers and they rub against the wheels, using friction to slow and eventually stop the train. These are everyday applications of this mechanism. A piano key is a compound lever of the first-class, since the fulcrum is between the weight to be moved and the power. The purpose of this lever is to translate a small movement (depression of the key) into a larger and fast movement of the hammer on

8295-529: The mechanical advantage, W/F can be calculated as ⁠ 10 / 3 ⁠ × ⁠ 9 / 4 ⁠ = 7.5, meaning that an applied force of 1 pound (or 1 kg) could lift a weight of 7.5 lb (or 7.5 kg). Alternatively, if the position of the fulcrum on lever AA' were moved so that A1 = 4 units and A2 = 9 units, then the mechanical advantage W/F is calculated as ⁠ 4 / 9 ⁠ × ⁠ 9 / 4 ⁠ = 1, meaning that an applied force will lift an equivalent weight and there

8400-414: The next, and thus the applied force is transferred from one lever to the next. Examples of compound levers include scales, nail clippers and piano keys. The malleus , incus and stapes are small bones in the middle ear , connected as compound levers, that transfer sound waves from the eardrum to the oval window of the cochlea . The lever is a movable bar that pivots on a fulcrum attached to

8505-538: The point B where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point A is less than from the fulcrum to the output point B , then the lever reduces the magnitude of the input force. English language English is a West Germanic language in the Indo-European language family , whose speakers, called Anglophones , originated in early medieval England on

8610-560: The points A and B are obtained as v A = θ ˙ a e A ⊥ , v B = θ ˙ b e B ⊥ , {\displaystyle \mathbf {v} _{A}={\dot {\theta }}a\mathbf {e} _{A}^{\perp },\quad \mathbf {v} _{B}={\dot {\theta }}b\mathbf {e} _{B}^{\perp },} where e A and e B are unit vectors perpendicular to e A and e B , respectively. The angle θ

8715-426: The prestige varieties among the middle classes. In modern English, the loss of grammatical case is almost complete (it is now only found in pronouns, such as he and him , she and her , who and whom ), and SVO word order is mostly fixed. Some changes, such as the use of do-support , have become universalised. (Earlier English did not use the word "do" as a general auxiliary as Modern English does; at first it

8820-411: The pull of gravity) of both a and b change (diminish) as the lever changes to any position away from the horizontal. Levers are classified by the relative positions of the fulcrum, effort and resistance (or load). It is common to call the input force "effort" and the output force "load" or "resistance". This allows the identification of three classes of levers by the relative locations of the fulcrum,

8925-678: The reign of Henry V . Around 1430, the Court of Chancery in Westminster began using English in its official documents , and a new standard form of Middle English, known as Chancery Standard , developed from the dialects of London and the East Midlands . In 1476, William Caxton introduced the printing press to England and began publishing the first printed books in London, expanding the influence of this form of English. Literature from

9030-423: The resistance and the effort: These cases are described by the mnemonic fre 123 where the f fulcrum is between r and e for the 1st class lever, the r resistance is between f and e for the 2nd class lever, and the e effort is between f and r for the 3rd class lever. A compound lever comprises several levers acting in series: the resistance from one lever in a system of levers acts as effort for

9135-404: The rule is that force multiplied by the force arm equals the weight multiplied by the weight arm. The output from one lever becomes the input for the next lever in the system, and so the advantage is magnified. The figure on the left illustrates a compound lever formed from two first-class levers, along with a short derivation of how to compute the mechanical advantage. With the dimensions shown,

9240-411: The scale, train brakes , and a common type of nail clippers . Another example is the elbow-joint press, which is used in printing, molding or handloading bullets, minting coins and medals, and in hole punching. Compound balances are used to weigh heavy items. These all use multiple levers to magnify force to accomplish a specific purpose. The train brake translates the force of pushing back the stick to

9345-468: The sense of belonging only to people who are ethnically English . Use of English is growing country-by-country internally and for international communication. Most people learn English for practical rather than ideological reasons. Many speakers of English in Africa have become part of an "Afro-Saxon" language community that unites Africans from different countries. As decolonisation proceeded throughout

9450-483: The source of approximately 28% of Modern English words , and from Latin , which is the source of an additional 28% . As such, though most of its total vocabulary comes from Romance languages , Modern English's grammar, phonology, and most commonly used words in everyday use keep it genealogically classified under the Germanic branch. It exists on a dialect continuum with Scots and is then most closely related to

9555-474: The southern dialects. Theoretically, as late as the 900s AD, a commoner from certain (northern) parts of England could hold a conversation with a commoner from certain parts of Scandinavia. Research continues into the details of the myriad tribes in peoples in England and Scandinavia and the mutual contacts between them. The translation of Matthew 8:20 from 1000 shows examples of case endings ( nominative plural, accusative plural, genitive singular) and

9660-409: The strings. The quality of the resulting tone depends on whether the final speed is brought about by gradual or sudden movement of the key. The malleus , incus and stapes are small bones (ossicles) in the middle ear , connected as compound levers, that transfer sound waves from the eardrum to the oval window of the cochlea . The earliest remaining writings regarding levers date from

9765-455: The study of English as an auxiliary language. The trademarked Globish uses a relatively small subset of English vocabulary (about 1500 words, designed to represent the highest use in international business English) in combination with the standard English grammar. Other examples include Simple English . The increased use of the English language globally has had an effect on other languages, leading to some English words being assimilated into

9870-448: The unit vectors e A and e B from the fulcrum to the point A and B , so r A − r P = a e A , r B − r P = b e B . {\displaystyle \mathbf {r} _{A}-\mathbf {r} _{P}=a\mathbf {e} _{A},\quad \mathbf {r} _{B}-\mathbf {r} _{P}=b\mathbf {e} _{B}.} The velocity of

9975-412: The use of a single lever to accomplish the desired result, e.g., a restricted space, the inconvenient location of the point of delivery of the resultant force, or the prohibitive length of the lever arm needed. In these conditions, combinations of simple levers, called compound levers, are used. Compound levers can be constructed from first, second and/or third-order levers. In all types of compound lever,

10080-436: The vocabularies of other languages. This influence of English has led to concerns about language death , and to claims of linguistic imperialism , and has provoked resistance to the spread of English; however the number of speakers continues to increase because many people around the world think that English provides them with opportunities for better employment and improved lives. Compound lever The compound lever

10185-473: The word bite was originally pronounced as the word beet is today, and the second vowel in the word about was pronounced as the word boot is today. The Great Vowel Shift explains many irregularities in spelling since English retains many spellings from Middle English, and it also explains why English vowel letters have very different pronunciations from the same letters in other languages. English began to rise in prestige, relative to Norman French, during

10290-785: The world may include no native speakers of English at all, even while including speakers from several different countries. This is particularly true of the shared vocabulary of mathematics and the sciences. English is a pluricentric language , which means that no one national authority sets the standard for use of the language. Spoken English, including English used in broadcasting, generally follows national pronunciation standards that are established by custom rather than by regulation. International broadcasters are usually identifiable as coming from one country rather than another through their accents , but newsreader scripts are also composed largely in international standard written English . The norms of standard written English are maintained purely by

10395-539: The world, but the number of English speakers in India is uncertain, with most scholars concluding that the United States still has more speakers of English than India. Modern English, sometimes described as the first global lingua franca , is also regarded as the first world language . English is the world's most widely used language in newspaper publishing, book publishing, international telecommunications, scientific publishing, international trade, mass entertainment, and diplomacy. English is, by international treaty,

10500-438: The worldwide influence of the British Empire and the United States. Through all types of printed and electronic media in these countries, English has become the leading language of international discourse and the lingua franca in many regions and professional contexts such as science, navigation , and law. Its modern grammar is the result of a gradual change from a dependent-marking pattern typical of Indo-European with

10605-405: Was adopted in parts of North America, parts of Africa, Oceania, and many other regions. When they obtained political independence, some of the newly independent states that had multiple indigenous languages opted to continue using English as the official language to avoid the political and other difficulties inherent in promoting any one indigenous language above the others. In the 20th century

10710-518: Was fully developed, integrating both Norse and French features; it continued to be spoken until the transition to early Modern English around 1500. Middle English literature includes Geoffrey Chaucer 's The Canterbury Tales , and Thomas Malory 's Le Morte d'Arthur . In the Middle English period, the use of regional dialects in writing proliferated, and dialect traits were even used for effect by authors such as Chaucer. The next period in

10815-496: Was invented. In ancient Egypt , workmen used the lever to move and uplift obelisks weighing more than 100 tons. This is evident from the recesses in the large blocks and the handling bosses which could not be used for any purpose other than for levers. The earliest remaining writings regarding levers date from the 3rd century BC and were provided, by common belief, by the Greek mathematician Archimedes , who famously stated "Give me

10920-505: Was lost except in personal pronouns, the instrumental case was dropped, and the use of the genitive case was limited to indicating possession . The inflectional system regularised many irregular inflectional forms, and gradually simplified the system of agreement, making word order less flexible. The transition from Old to Middle English can be placed during the writing of the Ormulum . The oldest Middle English texts that were written by

11025-533: Was only used in question constructions, and even then was not obligatory. Now, do-support with the verb have is becoming increasingly standardised.) The use of progressive forms in -ing , appears to be spreading to new constructions, and forms such as had been being built are becoming more common. Regularisation of irregular forms also slowly continues (e.g. dreamed instead of dreamt ), and analytical alternatives to inflectional forms are becoming more common (e.g. more polite instead of politer ). British English

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