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In the 5th century the Indian mathematician Aryabhata (476-499) wrote a small but famous work on astronomy, the Aryabhatiya. This treatise, written in 118 verses, gives in its second chapter a summary of Hindu mathematics up to that time. Two hundred years later, an Indian astronomer called Bhaskara glossed this mathematial chapter of the Aryabhatiya.

An english translation of Bhaskara’s commentary and a mathematical supplement are presented in two volumes.

Subjects treated in Bhaskara’s commentary range from computing the volume of an equilateral tetrahedron to the interest on a loaned capital, from computations on series to an elaborate process to solve a Diophantine equation.

This volume contains an introduction and the literal translation.

The introduction aims at providing a general background for the translation and is divided in three sections: the first locates Bhaskara’s text, the second looks at its mathematical contents and the third section analyzes the relations of the commentary and the treatise.

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Brahmagupta, Anania Shirakatsi, Bhāskara I. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Brahmagupta (Sanskrit: ; ( · )) (598668) was an Indian mathematician and astronomer. Brahmagupta wrote important works on mathematics and astronomy. In particular he wrote Brahmasphutasiddhanta (Correctly Established Doctrine of Brahma), in 628. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty. Brahmagupta was born in 598 CE(it is believed) in Bhinmal city in the state of Rajasthan of northwest India. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) in the empire of Harsha during the reign (and possibly under the patronage) of King Vyaghramukha. As a result, Brahmagupta is often referred to as Bhillamalacarya, that is, the teacher from Bhillamala Bhinmal. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote four texts on mathematics and astronomy: the Cadamekela in 624, the Brahmasphutasiddhanta in 628, the Khandakhadyaka in 665, and the Durkeamynarda in 672. The Brahmasphutasiddhanta (Corrected Treatise of Brahma) is arguably his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma'mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta. Although Brahmagupta was familiar with the works of astronomers following the tradition of Aryabhatiya, it is not known if he was familiar with the work of Bhaskara I, a contemporary. Brahmagupta had a p...More: http://booksllc.net/?id=297206 ... Read more

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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Brahmagupta (Sanskrit: ; (·)) (598668) was an Indian mathematician and astronomer. Brahmagupta wrote important works on mathematics and astronomy. In particular he wrote Brahmasphutasiddhanta (Correctly Established Doctrine of Brahma), in 628. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty. Brahmagupta was born in 598 CE(it is believed) in Bhinmal city in the state of Rajasthan of northwest India. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) in the empire of Harsha during the reign (and possibly under the patronage) of King Vyaghramukha. As a result, Brahmagupta is often referred to as Bhillamalacarya, that is, the teacher from Bhillamala Bhinmal. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote four texts on mathematics and astronomy: the Cadamekela in 624, the Brahmasphutasiddhanta in 628, the Khandakhadyaka in 665, and the Durkeamynarda in 672. The Brahmasphutasiddhanta (Corrected Treatise of Brahma) is arguably his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma'mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta. Although Brahmagupta was familiar with the works of astronomers following the tradition of Aryabhatiya, it is not known if he was familiar with the work of Bhaskara I, a contemporary. Brahmagupta had a plethora of criticism directed towards the work of rival astronomers, and i... More: http://booksllc.net/?id=297206 ... Read more

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Aus Wikipedia. Nicht dargestellt. Auszug: Saint Audomar (d. ca. 670 AD), better known as Saint Omer, was a Burgundy-born bishop of Thérouanne, after whom nearby Saint-Omer in northern France was named. He was born of a distinguished family towards the close of the sixth or the beginning of the seventh century, at Guldendal, Switzerland. After the death of his mother, he entered with his father the abbey of Luxeuil in the Diocese of Besançon, probably about 615. Under the direction of Eustachius, Omer studied the Scriptures, in which he acquired remarkable proficiency. When King Dagobert requested the appointment of a bishop for the important city of Terouenne, the capital of the ancient territory of the Morini in Neustria, he was appointed and consecrated in 637. Though the Morini had received Christianity from Saint Fuscian and Saint Victoricus, and later Antmund and Adelbert, nearly every vestige of Christianity had disappeared. When Saint Audomare entered upon his episcopal duties, the Abbot of Luxeuil sent to his assistance several monks, among whom are mentioned Saint Bertin, Saint Mommolin and Saint Ebertran. Saint Omer had the satisfaction of seeing the Catholic religion firmly established in a short time. About 654 he founded the Abbey of Saint Peter (now Saint Bertin's) in Sithiu, soon to equal if not surpass the old monastery of Luxeuil for the number of learned and zealous men educated there. Several years later he erected the Church of Our Lady of Sithiu, with a small monastery adjoining, which he turned over to the monks of Saint Bertin. The exact date of his death is unknown, but he is believed to have died about the year 670. The place of his burial is uncertain; most probably he was laid to rest in the church of Our Lady, later Saint-Omer Cathedral, where there is a 13th century cenotaph dedicated to him. His feast is celebrated on . ...http://booksllc.net/?l=de ... Read more

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Aus Wikipedia. Nicht dargestellt. Auszug: Wulfoald (d.680) was the mayor of the palace of Austrasia from 656 or 661, depending on when Grimoald I was removed from that office (accounts vary: see his article for details), to his death and mayor of the palace of Neustria and Burgundy from 673 to 675. He was the regent of Austrasia during the minority of Childeric II until 670. Even after Childeric achieved his majority, Wulfoald held the real power. In 673, he became the mayor of the palace in Neustria because Childeric had succeeded to its throne. But when Childeric died, Wulfoald had to flee to Austrasia. Wulfoald and the nobles proclaimed Dagobert II king, but Ebroin, the rival mayor of the palace of Neustria, tried to place Clovis III on the Austrasian throne to extend his influence. It wasn't until 676 that Wulfoald succeeded in putting Dagobert definitively on the throne. War continued on the border until 677, when Neustria recognised Austrasian independence. Dagobert was assassinated on December 23, 679. Wulfoald outlived his king for only a short while. ...http://booksllc.net/?l=de ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 372 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Andronikos I Komnenos, Afonso I of Portugal, Pope Lucius Iii, Baldwin Iv of Jerusalem, Bhāskara Ii, Ibn Tufail, Emperor Antoku, Fernando Rodríguez de Castro, Richeza of Poland, Queen of Castile, Gille Brigte of Galloway, Yahia Ben Yahi Iii, Saint Drogo, Al-Suhayli, Dietrich I, Margrave of Lusatia, Beatrice of Rethel, Kikuchi Takanao, Taira No Kagekiyo, Stefan, Stephen Hagiochristophorites, Taira No Tokiko, Alfonso Ramírez, Taira No Tomomori, Alain, Bishop of Auxerre, Taira No Munemori, Centule Iii of Bigorre, Taira No Shigehira, Silvester of Troina, Taira No Noritsune, Nur Al-Din Muhammad. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Afonso I (c. 1109, Guimarães or Viseu 6 December 1185, Coimbra), or also Affonso (Archaic Portuguese-Galician) or Alphonso (Portuguese-Galician) or Alphonsus (Latin version), sometimes rendered in English as Alphonzo or Alphonse, depending on the Spanish or French influence, more commonly known as Afonso Henriques (Portuguese pronunciation: ), nicknamed the Conqueror (Portuguese: ), the Founder (Portuguese: ) or the Great (Portuguese: ) by the Portuguese, and El-Bortukali («the Portuguese») and Ibn-Arrik (son of Henry) by the Moors whom he fought, was the first King of Portugal. He achieved the independence of the southern part of the Kingdom of Galicia -County of Portugal- from the León, in 1139, doubling its area with the Reconquista, which he carried until his death, in 1185, after 46 years of wars against the Moors. Afonso I was the son of Henry of Burgundy, Count of Portugal and Teresa of León, the illegitimate daughter of King Alfonso VI of León. He was proclaimed King on 25 July 1139, immediately after the Battle of Ourique, and died on 6 December 1185 in Coimbra. At the end of the 11th century, the Iberian Peninsula politic...More: http://booksllc.net/?id=1657 ... Read more