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Arithmetica Logarithmica
''Arithmetica'' ( grc-gre, Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus () in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations. Summary Equations in the book are presently called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the ''Arithmetica'' problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of the form 4n + 3 cannot be the sum of two squares. Diophantus also appears to know that every number can be written as the sum of four squares. If he did know this result (in the sense of having proved it as opposed to merely conjectured it), his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the Roman Republic it became the dominant language in the Italian region and subsequently throughout the Roman Empire. Even after the fall of Western Rome, Latin remained the common language of international communication, science, scholarship and academia in Europe until well into the 18th century, when other regional vernaculars (including its own descendants, the Romance languages) supplanted it in common academic and political usage, and it eventually became a dead language in the modern linguistic definition. Latin is a highly inflected language, with three distinct genders (masculine, feminine, and neuter), six or seven noun cases (nominative, accusative, genitive, dative, ablative, and vocative), five declensions, four verb conjuga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qusta Ibn Luqa
Qusta ibn Luqa (820–912) (Costa ben Luca, Constabulus) was a Syrian Melkite Christian physician, philosopher, astronomer, mathematician and translator. He was born in Baalbek. Travelling to parts of the Byzantine Empire, he brought back Greek texts and translated them into Arabic. Personal life Qusta ibn Luqa al-Ba'albakki, i. e. from Baalbek or Heliopolis, modern-day Lebanon, a Melkite Christian, was born in 820 and flourished in Baghdad. He was a philosopher, physician, mathematician and astronomer. He died in Armenia possibly in A.D. 912/913. Translations Translations of Diophantos, Theodosius of Bithynia's ''Sphaerica'', ''On Days and Nights (Περὶ ἡμερῶν καὶ νυκτῶν -De diebus et noctibus)'', ''On the places of habitation'' (''Περὶ οἰκήσεων - De habitationibus''), Autolycus' ''On the moving sphere'' (''Περὶ κινουμένης σφαίρας'' - ''De sphaera quae movetur), On Risings and Settings'' (''Περὶ ἐπιτολ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digamma
Digamma or wau (uppercase: Ϝ, lowercase: ϝ, numeral: ϛ) is an archaic letter of the Greek alphabet. It originally stood for the sound but it has remained in use principally as a Greek numeral for 6. Whereas it was originally called ''waw'' or ''wau'', its most common appellation in classical Greek is ''digamma''; as a numeral, it was called ''episēmon'' during the Byzantine era and is now known as '' stigma'' after the Byzantine ligature combining σ-τ as ϛ. Digamma or wau was part of the original archaic Greek alphabet as initially adopted from Phoenician. Like its model, Phoenician waw, it represented the voiced labial-velar approximant and stood in the 6th position in the alphabet between epsilon and zeta. It is the consonantal doublet of the vowel letter upsilon (), which was also derived from waw but was placed near the end of the Greek alphabet. Digamma or wau is in turn the ancestor of the Latin letter F. As an alphabetic letter, it is attested in archaic a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archaic Greek Alphabets
Many local variants of the Greek alphabet were employed in ancient Greece during the archaic and early classical periods, until around 400 BC, when they were replaced by the classical 24-letter alphabet that is the standard today. All forms of the Greek alphabet were originally based on the shared inventory of the 22 symbols of the Phoenician alphabet, with the exception of the letter Samekh, whose Greek counterpart Xi () was used only in a sub-group of Greek alphabets, and with the common addition of Upsilon () for the vowel . The local, so-called ''epichoric'', alphabets differed in many ways: in the use of the consonant symbols , and ; in the use of the innovative long vowel letters ( and ), in the absence or presence of Η in its original consonant function (); in the use or non-use of certain archaic letters ( = , = , = ); and in many details of the individual shapes of each letter. The system now familiar as the standard 24-letter Greek alphabet was originally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of The Greek Alphabet
The history of the Greek alphabet starts with the adoption of Phoenician letter forms in the 9th–8th centuries BC during early Archaic Greece and continues to the present day. The Greek alphabet was developed during the Iron Age centuries after the loss of Linear B, the syllabic script that was used for writing Mycenaean Greek until the Late Bronze Age collapse and Greek Dark Age. This article concentrates on the development of the alphabet before the modern codification of the standard Greek alphabet. The Phoenician alphabet was strictly speaking one that was consistently explicit only about consonants, though even by the 9th century BC it had developed '' matres lectionis'' to indicate some, mostly final, vowels. This arrangement is much less suitable for Greek than for Semitic languages, and these ''matres lectionis'', as well as several Phoenician letters which represented consonants not present in Greek, were adapted according to the acrophonic principle to represent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iota
Iota (; uppercase: Ι, lowercase: ι; ) is the ninth letter of the Greek alphabet. It was derived from the Phoenician letter Yodh. Letters that arose from this letter include the Latin alphabet, Latin I and J, the Cyrillic І (І, і), Yi (Cyrillic), Yi (Ї, ї), and Je (Cyrillic), Je (Ј, ј), and Iotation, iotated letters (e.g. Yu (Cyrillic), Yu (Ю, ю)). In the system of Greek numerals, iota has a value of 10. Iota represents the close front unrounded vowel . In early forms of ancient Greek, it occurred in both long and short versions, but this distinction was lost in Koine Greek phonology, Koine Greek. Iota participated as the second element in falling diphthongs, with both long and short vowels as the first element. Where the first element was long, the iota was lost in pronunciation at an early date, and was written in polytonic orthography as iota subscript, in other words as a very small ι under the main vowel. Examples include ᾼ ᾳ ῌ ῃ ῼ ῳ. The former d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epsilon
Epsilon (, ; uppercase , lowercase or lunate ; el, έψιλον) is the fifth letter of the Greek alphabet, corresponding phonetically to a mid front unrounded vowel or . In the system of Greek numerals it also has the value five. It was derived from the Phoenician letter He . Letters that arose from epsilon include the Roman E, Ë and Ɛ, and Cyrillic Е, È, Ё, Є and Э. The name of the letter was originally (), but it was later changed to ( 'simple e') in the Middle Ages to distinguish the letter from the digraph , a former diphthong that had come to be pronounced the same as epsilon. The uppercase form of epsilon is identical to Latin E but has its own code point in Unicode: . The lowercase version has two typographical variants, both inherited from medieval Greek handwriting. One, the most common in modern typography and inherited from medieval minuscule, looks like a reversed number "3" and is encoded . The other, also known as lunate or uncial epsilon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta
Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labiodental fricative while in borrowed words is instead commonly transcribed as μπ. Letters that arose from beta include the Roman letter and the Cyrillic letters and . Name Like the names of most other Greek letters, the name of beta was adopted from the acrophonic name of the corresponding letter in Phoenician, which was the common Semitic word ''*bait'' ('house'). In Greek, the name was ''bêta'', pronounced in Ancient Greek. It is spelled βήτα in modern monotonic orthography and pronounced . History The letter beta was derived from the Phoenician letter beth . Uses Algebraic numerals In the system of Greek numerals, beta has a value of 2. Such use is denoted by a number mark: Β′. Computing Finance Beta is used i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic Greece, Archaic and early Classical Greece, Classical times, the Greek alphabet existed in Archaic Greek alphabets, many local variants, but, by the end of the 4th century BCE, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today. The letter case, uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , /ς, , , , , , . The Greek alphabet is the ancestor of the Latin script, Latin and Cyrillic scripts. Like Latin and Cyrillic, Greek originally had only a single form of each letter; it developed the letter case distinction between uppercase and lowercase in parallel with Latin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alpha
Alpha (uppercase , lowercase ; grc, ἄλφα, ''álpha'', or ell, άλφα, álfa) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph , which is the West Semitic word for " ox". Letters that arose from alpha include the Latin letter A and the Cyrillic letter А. Uses Greek In Ancient Greek, alpha was pronounced and could be either phonemically long ( ː or short ( . Where there is ambiguity, long and short alpha are sometimes written with a macron and breve today: Ᾱᾱ, Ᾰᾰ. * ὥρα = ὥρᾱ ''hōrā'' "a time" * γλῶσσα = γλῶσσᾰ ''glôssa'' "tongue" In Modern Greek, vowel length has been lost, and all instances of alpha simply represent the open front unrounded vowel . In the polytonic orthography of Greek, alpha, like other vowel letters, can occur with several diacritic marks: any of three accent symbols (), and either of two breathing mark ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hellenistic Civilization
In Classical antiquity, the Hellenistic period covers the time in History of the Mediterranean region, Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in 31 BC and the conquest of Ptolemaic Kingdom, Ptolemaic Egypt the following year. The Ancient Greek word ''Hellas'' (, ''Hellás'') was gradually recognized as the name of Greece, name for Greece, from which the word ''Hellenistic'' was derived. "Hellenistic" is distinguished from "Hellenic" in that the latter refers to Greece itself, while the former encompasses all ancient territories under Greek influence, in particular the East after the conquests of Alexander the Great. After the Macedonian invasion of the Achaemenid Empire in 330 BC and its disintegration shortly after, the Hellenistic kingdoms were established throughout Southwest Asia, south-west Asia (Seleucid Empire, Attalid dynasty, Kingdom of Pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abūl Wafā' Būzjānī
Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī ( fa, ابوالوفا بوزجانی or بوژگانی) (10 June 940 – 15 July 998) was a Persian mathematician and astronomer who worked in Baghdad. He made important innovations in spherical trigonometry, and his work on arithmetics for businessmen contains the first instance of using negative numbers in a medieval Islamic text. He is also credited with compiling the tables of sines and tangents at 15 ' intervals. He also introduced the secant and cosecant functions, as well studied the interrelations between the six trigonometric lines associated with an arc. His ''Almagest'' was widely read by medieval Arabic astronomers in the centuries after his death. He is known to have written several other books that have not survived. Life He was born in Buzhgan, (now Torbat-e Jam) in Khorasan (in today's Iran). At age 19, in 959 AD, he moved to Baghda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
