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Menelaus's Theorem
Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ''ABC'', and a transversal line that crosses ''BC'', ''AC'', and ''AB'' at points ''D'', ''E'', and ''F'' respectively, with ''D'', ''E'', and ''F'' distinct from ''A'', ''B'', and ''C''. A weak version of the theorem states that : \frac \times \frac \times \frac = 1, where '', AB, '' is taken to be the ordinary length of segment ''AB'': a positive value. The theorem can be strengthened to a statement about signed lengths of segments, which provides some additional information about the relative order of collinear points. Here, the length ''AB'' is taken to be positive or negative according to whether ''A'' is to the left or right of ''B'' in some fixed orientation of the line; for example, ''AF''/''FB'' is defined as having positive value when ''F'' is between ''A'' and ''B'' and negative otherwise. The signed version of Menelaus's theorem stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Almagest
The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canonized a geocentric model of the Universe that was accepted for more than 1,200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus. It is also a key source of information about ancient Greek astronomy. Ptolemy set up a public inscription at Canopus, Egypt, in 147 or 148. N. T. Hamilton found that the version of Ptolemy's models set out in the ''Canopic Inscription'' was earlier than the version in the ''Almagest''. Hence the ''Almagest'' could not have been completed before about 150, a quarter-century after Ptolemy began observing. Names The name comes from Arabic ', with ' meaning "the", and ''magesti'' bei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Al-Sijzi
Abu Sa'id Ahmed ibn Mohammed ibn Abd al-Jalil al-Sijzi (c. 945 - c. 1020, also known as al-Sinjari and al-Sijazi; fa, ابوسعید سجزی; Al-Sijzi is short for "Al-Sijistani") was an Iranian Muslim astronomer, mathematician, and astrologer. He is notable for his correspondence with al-Biruni and for proposing that the Earth rotates around its axis in the 10th century. He dedicated work to 'Adud al-Daula, who was probably his patron, and to the prince of Balkh. He also worked in Shiraz making astronomical observations from 969 to 970. Mathematics Al-Sijzi studied intersections of conic sections and circles. He replaced the old kinematical trisection of an angle by a purely geometric solution (intersection of a circle and an equilateral hyperbola.) Earth's rotation Al-Biruni tells us that Al-Sijzi invented an astrolabe, called "al-zūraqī", whose design was based on the idea that the Earth rotates: Al-Biruni also referred to Al-Sijzi as a prominent astronomer who d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nasir Al-Din Al-Tusi
Muhammad ibn Muhammad ibn al-Hasan al-Tūsī ( fa, محمد ابن محمد ابن حسن طوسی 18 February 1201 – 26 June 1274), better known as Nasir al-Din al-Tusi ( fa, نصیر الدین طوسی, links=no; or simply Tusi in the West), was a Persian polymath, architect, philosopher, physician, scientist, and theologian. Nasir al-Din al-Tusi was a well published author, writing on subjects of math, engineering, prose, and mysticism. Additionally, al-Tusi made several scientific advancements. In astronomy, al-Tusi created very accurate tables of planetary motion, an updated planetary model, and critiques of Ptolemaic astronomy. He also made strides in logic, mathematics but especially trigonometry, biology, and chemistry. Nasir al-Din al-Tusi left behind a great legacy as well. Tusi is widely regarded as one of the greatest scientists of medieval Islam, since he is often considered the creator of trigonometry as a mathematical discipline in its own right. The Muslim sch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sharaf Al-Din Al-Tusi
Sharaf al-Dīn al-Muẓaffar ibn Muḥammad ibn al-Muẓaffar al-Ṭūsī ( fa, شرفالدین مظفر بن محمد بن مظفر توسی; 1135 – 1213) was an Iranian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages). Biography Tusi was probably born in Tus, Iran. Little is known about his life, except what is found in the biographies of other scientistsO'Connor & Robertson (1999) and that most mathematicians today can trace their lineage back to him. Around 1165, he moved to Damascus and taught mathematics there. He then lived in Aleppo for three years, before moving to Mosul, where he met his most famous disciple Kamal al-Din ibn Yunus (1156-1242). This Kamal al-Din would later become the teacher of another famous mathematician from Tus, Nasir al-Din al-Tusi. According to Ibn Abi Usaibi'a, Sharaf al-Din was "outstanding in geometry and the mathematical sciences, having no equal in his time". Mathematics Al-Tusi has been credited ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thabit Ibn Qurra
Thabit ( ar, ) is an Arabic name for males that means "the imperturbable one". It is sometimes spelled Thabet. People with the patronymic * Ibn Thabit, Libyan hip-hop musician * Asim ibn Thabit, companion of Muhammad * Hassan ibn Sabit (died 674), poet and companion of Muhammad * Khuzaima ibn Thabit (died 657), companion of Muhammad * Sinan ibn Thabit (c. 880 – 943), physician and mathematician * Zayd ibn Thabit (c. 610 – 660), personal scribe of Muhammad * Abdullah Thabit (born 1973), Saudi Arabian poet, novelist and journalist People with the given name * Thabit ibn Qays, companion of Muhammad * Thabit ibn Qurra (c. 826 – 901), Baghdadi mathematician and astronomer See also * Thabit number * Tabit (town) (or Thabit), Sudan * Upsilon Orionis or Thabit – a star in the constellation Orion * Sabit Sabit is an Arabic masculine given name, meaning "firmly in place”, “stable”, “unshakable”, "dhilaman", from Thabit (ثابت). Notable people with the name include: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine Rule
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, \frac \,=\, \frac \,=\, \frac \,=\, 2R, where , and are the lengths of the sides of a triangle, and , and are the opposite angles (see figure 2), while is the radius of the triangle's circumcircle. When the last part of the equation is not used, the law is sometimes stated using the reciprocals; \frac \,=\, \frac \,=\, \frac. The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the triangle is not uniquely determined by this data (called the ''ambiguous case'') and the technique gives two possible values for the enclosed angle. The law of sines is one of two trigonometric equations commonly appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Al-Khazin
Abu Jafar Muhammad ibn Husayn Khazin ( fa, ابوجعفر خازن خراسانی; 900–971), also called Al-Khazin, was an Iranian Muslim astronomer and mathematician from Khorasan. He worked on both astronomy and number theory. Al-Khazin was one of the scientists brought to the court in Ray, Iran by the ruler of the Buyid dynasty, Adhad ad-Dowleh, who ruled from 949 to 983 AD. In 959/960 Khazin was required by the Vizier of Ray, who was appointed by ad-Dowleh, to measure the obliquity of the ecliptic. One of Al-Khazin's works ''Zij al-Safa'ih'' ("Tables of the disks of the astrolabe") was described by his successors as the best work in the field and they make many references to it. The work describes some astronomical instruments, in particular an astrolabe fitted with plates inscribed with tables and a commentary on the use of these. A copy of this instrument was made, but it vanished in Germany at the time of World War II. A photograph of this copy was taken and examined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Al-Nayrizi
Abū’l-‘Abbās al-Faḍl ibn Ḥātim al-Nairīzī ( ar, أبو العباس الفضل بن حاتم النيريزي, la, Anaritius, Nazirius, c. 865–922) was a Persian mathematician and astronomer from Nayriz, Fars Province, Iran. He flourished under al-Mu'tadid, Caliph from 892 to 902, and compiled astronomical tables, writing a book for al-Mu'tadid on atmospheric phenomena. Nayrizi wrote commentaries on Ptolemy and Euclid. The latter were translated by Gerard of Cremona. Nairizi used the so-called umbra (versa), the equivalent to the tangent, as a genuine trigonometric line (but he was anticipated in this by al-Marwazi). He wrote a treatise on the spherical astrolabe, which is very elaborate and seems to be the best Persian work on the subject. It is divided into four books: #Historical and critical introduction. #Description of the spherical astrolabe; its superiority over plane astrolabes and all other astronomical instruments. #Applications. #Applications. He ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Al-Biruni
Abu Rayhan Muhammad ibn Ahmad al-Biruni (973 – after 1050) commonly known as al-Biruni, was a Khwarazmian Iranian in scholar and polymath during the Islamic Golden Age. He has been called variously the "founder of Indology", "Father of Comparative Religion", "Father of modern geodesy", and the first anthropologist. Al-Biruni was well versed in physics, mathematics, astronomy, and natural sciences, and also distinguished himself as a historian, chronologist, and linguist. He studied almost all the sciences of his day and was rewarded abundantly for his tireless research in many fields of knowledge. Royalty and other powerful elements in society funded Al-Biruni's research and sought him out with specific projects in mind. Influential in his own right, Al-Biruni was himself influenced by the scholars of other nations, such as the Greeks, from whom he took inspiration when he turned to the study of philosophy. A gifted linguist, he was conversant in Khwarezmian, Persian, Ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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