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Fundamentum Astronomiae
''Fundamentum Astronomiae'' is a historic manuscript presented by Jost Bürgi to Emperor Rudolf II in 1592. It describes Bürgi's trigonometry based algorithms called Kunstweg which can be used to calculate sines at arbitrary precision.Staudacher, S., 2014. Jost Bürgi, ''Kepler und der Kaiser''. Verlag NZZ, Zürich. General Bürgi took special care to avoid his method becoming public in his time. However, Henry Briggs (mathematician) (1561-1630) was acquainted with the method, likely via a link to John Dee who knew Christoph Rothmann, a colleague of Bürgi at the court. Method Bürgi used these algorithms, including multiplication table in sexagesimal system, to compute a '' Canon Sinuum'', a table of sines to 8 sexagesimal places in steps of 2 arc seconds. Such tables were extremely important for navigation at sea. Bürgi's method only uses additions and halving, his procedure is elementary and it converges from the standard method. Johannes Kepler called the Canon Sinuum t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jost Bürgi
Jost Bürgi (also ''Joost, Jobst''; Latinisation of names, Latinized surname ''Burgius'' or ''Byrgius''; 28 February 1552 – 31 January 1632), active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician. Life Bürgi was born in 1552 Lichtensteig, Toggenburg, at the time a subject territory of the Abbey of St. Gall (now part of the canton of St. Gallen, Switzerland). Not much is known about his life or education before his employment as astronomer and clockmaker at the court of William IV in Kassel in 1579; it has been theorized that he acquired his mathematical knowledge at Strasbourg, among others from Swiss mathematician Conrad Dasypodius, but there are no facts to support this. Although an autodidact, he was already during his lifetime considered as one of the most excellent mechanical engineers of his generation. His employer, William IV, Landgrave of Hesse-Kassel, in a letter to Tycho Brahe praise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canon Sinuum (Bürgi)
The ''Canon Sinuum'' was a historic table of sines thought to have given the sines to 8 sexagesimal places between 0 and 90 degrees in steps of 2 arc seconds. Some authors believe that the table was only between 0 and 45 degrees. It was created by Jost Bürgi at the end of the 16th century. Such tables were essential for navigation at sea. Johannes Kepler called the ''Canon Sinuum'' the most precise known table of sines. This table is thought to be lost. The ''Canon Sinuum'' was computed by Bürgi's algorithms explained in his work Fundamentum Astronomiae presented to Emperor Rudolf II. in 1592.Staudacher, S., 2014. Jost Bürgi, Kepler und der Kaiser. Verlag NZZ, Zürich. These algorithms made use of differences and were one of the early uses of difference calculus. The largest trigonometrical table actually contained in the Fundamentum Astronomiae is a table giving the sines for every minute of the quadrant and to 5 to 7 sexagesimal places. The manuscript of Fundamentum A ... [...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] |
Difference Calculus
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term "fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximations
An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ''ad-'' (''ad-'' before ''p'' becomes ap- by assimilation) meaning ''to''. Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning. It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. In science, approximation can refer to u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books ''Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navigation
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, marine navigation, aeronautic navigation, and space navigation. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks. All navigational techniques involve locating the navigator's position compared to known locations or patterns. Navigation, in a broader sense, can refer to any skill or study that involves the determination of position and direction. In this sense, navigation includes orienteering and pedestrian navigation. History In the European medieval period, navigation was considered part of the set of '' seven mechanical arts'', none of which were used for long voyages across open ocean. Polynesian navigation is probably the earliest form of open-ocean navigation; it was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arc Seconds
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of Angular unit, angular measurement equal to of one Degree (angle), degree. Since one degree is of a turn (geometry), turn (or complete rotation), one minute of arc is of a turn. The nautical miles, nautical mile (nmi) was originally defined as the meridian arc, arc length of a minute of latitude on a spherical Earth, so the actual Earth circumference is very near . A minute of arc is of a radian. A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol , is of an arcminute, of a degree, of a turn, and (about ) of a radian. These units originated in Babylonian astronomy as sexagesimal subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying, and marksmanship. To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sexagesimal
Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates. The number 60, a superior highly composite number, has twelve factors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6. ''In this article, all sexagesimal digits are represented as decimal numbers, except where otherwise noted. For e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emperor Rudolf II
Rudolf II (18 July 1552 – 20 January 1612) was Holy Roman Emperor (1576–1612), King of Hungary and Croatia (as Rudolf I, 1572–1608), King of Bohemia (1575–1608/1611) and Archduke of Austria (1576–1608). He was a member of the House of Habsburg. Rudolf's legacy has traditionally been viewed in three ways:Hotson, 1999. an ineffectual ruler whose mistakes led directly to the Thirty Years' War; a great and influential patron of Northern Mannerist art; and an intellectual devotee of occult arts and learning which helped seed what would be called the Scientific Revolution. Determined to unify Christendom, he initiated the Long Turkish War (1593–1606) with the Ottoman Empire. Exhausted by war, his citizens in Hungary revolted in the Bocskai Uprising, which led to more authority given to his brother Matthias. Under his reign, there was a policy of toleration towards Judaism. Early life Rudolf was born in Vienna on 18 July 1552. He was the eldest son and successor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christoph Rothmann
Christoph Rothmann (born between 1550 and 1560 in Bernburg, Saxony-Anhalt; died probably after 1600 in Bernburg) was a German mathematician and one of the few well-known astronomers of his time. His research contributed substantially to the fact that Kassel became a European center of the astronomy in the 16th century. Life It is not known today when Rothmann was born, although it is known that his place of birth was Bernberg on the Saale, probably between 1550 and 1560. After a basic education he studied theology and mathematics in Wittenberg with support of the prince, Joachim Ernst von Anhalt. Rothmann's enthusiasm for the astronomy was substantial. Christoph Rothmann was appointed in 1577 as court mathematician in Kassel by Prince Wilhelm IV of Hessen. From 1584 to 1590 he was active in astronomy at the observatory of the prince. His research contributed substantially to the fact that Kassel became a center of the astronomical research. In 1590 he visited Tycho Brahe in Ura ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Dee
John Dee (13 July 1527 – 1608 or 1609) was an English mathematician, astronomer, astrologer, teacher, occultist, and alchemist. He was the court astronomer for, and advisor to, Elizabeth I, and spent much of his time on alchemy, divination, and Hermetic philosophy. As an antiquarian, he had one of the largest libraries in England at the time. As a political advisor, he advocated the foundation of English colonies in the New World to form a "British Empire", a term he is credited with coining. Dee eventually left Elizabeth's service and went on a quest for additional knowledge in the deeper realms of the occult and supernatural. He aligned himself with several individuals who may have been charlatans, travelled through Europe and was accused of spying for the English crown. Upon his return to England, he found his home and library vandalised. He eventually returned to the Queen's service, but was turned away when she was succeeded by James I. He died in poverty in London ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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