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Topic: Arithmetica

Related Topics

Diophantine equation

Algebra

Cubic equation

Quadratic equation

Diophantus

Timeline of mathematics

	Arithmetica
		Arithmetica understands that need, and thus allows you to add on to the last expression executed, without retyping it.
		Due to the many types of expressions held by Arithmetica, Problems with the syntax are expected.
		Arithmetica will Return 0 as the value of that variable, and inform you of the problem.
	www.duke.edu /~pas7/cps108/arithmetica/Umanual.html (750 words)

	Arithmetica Users Manual
		Section 1 ~ Intro to and General Overview of Arithmetica
		To begin the program, enter arithmetica at the prompt.
		It would be the same implementation as parentheses, but with these function names as part of the operator, and can be evaluated in exptree.
	www.duke.edu /~kyc/cps108/arithmetica/users.html (389 words)

	arithmetica
		His book Arithmetica is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations.
		Arithmetica and its author are often mentioned as the origin of algebra, but there is no doubt that most of what was written in this work was known by the Babylonians.
		Nevertheless, Arithmetica was a remarkable achievement as it gave a collection of indeterminate problems that was not fully appreciated until the 17th century.
	www.mathsisgoodforyou.com /artefacts/diphantusarithmetica.htm (264 words)

	[No title] (Site not responding. Last check: )
		Diophantus wrote three works: Arithmetica, his most important one and of which six out of thirteen books are extant, On Polygonal Numbers, of which only a fragment is extant, and Porisms which is lost.
		The Arithmetica is an analytical treatment of algebraic number theory and marks the author as a genius in this field.
		The Arithmetica can best be dealt with under three main headings, (1) the notation and definitions, (2) the principal methods employed, so far as they can be classified, (3) the nature of the contents, including the assumed Porisms, with some typical examples of the devices by which the problems are solved (Heath 476).
	home.olemiss.edu /~gdbradle/mathresearch.doc (1393 words)

	Arithmetica - Wikipedia, the free encyclopedia
		Arithmetica, an ancient text on mathematics written by classical period Greek mathematician Diophantus in the second century AD is a collection of 130 algebra problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations.
		The method for solving these equations is known as Diophantine analysis.
		Most of the Arithmetica problems lead to quadratic equations.
	en.wikipedia.org /wiki/Arithmetica (93 words)

	Pierre de Fermat \| Fermat's Last Theorem (Site not responding. Last check: )
		It was written by Diophantus, a man about whom little is known apart from that he lived around AD 250, and spent much of his life in Alexandria.
		'Arithmetica' is a collection of 13 books containing all that was known about the subject at the time.
		After the final attack, the victorious Caliph Omar ordered all material contrary to the Koran be destroyed, and he also declared that any which conformed to the Koran was superfluous, and so should also be destroyed.
	www.adrianbailey.co.uk /fermat/flt.html (577 words)

	Arithmetica et algebra - Introduzione
		Arithmetica data: in quibus multa a Boethio, Iordanoque pretermissa demonstrantur.
		Nella descrizione dei lavori che Maurolico riunisce sotto il titolo di Arithmetica speculativa, si riconoscono gli stessi temi descritti in precedenza, i quali corrispondono ai due libri aritmetici che ci sono pervenuti: il primo riguarda i numeri figurati, il secondo l'aritmetica pratica delle grandezze razionali ed irrazionali.
		Arithmetica nostra speculativa: in qua multa circa triangulos, quadratos, hexagonos, cubosque numeros et alias eorum species, ab aliis praetermissa acutissime demonstrantur; tum circa praxim arithmeticam tam rationalium, quam irrationalium magnitudinum, quae in decimo elementorum, praecepta cum minime negligenda, tum ad practicas quaestiones necessaria.
	www.maurolico.unipi.it /edizioni/arithmet/intro.htm (3343 words)

	[No title]
		Gow notes that historians do not think that the propositions of Arithmetica are now found in the order in which they were originally written, and that essential discussions of determinate quadratic equations and indeterminate simple equations are excluded (102).
		A critic and historian of mathematics from the latter part of the nineteenth century by the name of Hankel describes the Arithmetica as having included one hundred and thirty problems each of which could be classified into fifty different types (Heath D 54).
		Heath continues to illustrate higher order double equations by citing examples from Arithmetica, and he must make conjectures a bout what he perceives to be Diophantus' intended method, since they "lack generality" (Heath D 93).
	www.math.rutgers.edu /courses/436/436-s00/Papers2000/kirschm.html (3982 words)

	[No title] (Site not responding. Last check: )
		Although mathematicians in India and Arabia had since made significant contributions to the subject, mathematics had remained largely frozen since Diophantus, and Fermat and his contemporaries were attempting to resurrect the subject and discover new truths.
		Arithmetica was devoted to problems related to whole numbers, and as such it became Fermat's Bible.
		In particular, Arithmetica asked its reader to find solutions to Pythagoras' equation, such that x, y, and z could be any whole number, except zero.
	www.prometheus.demon.co.uk /01/01fermat.htm (4279 words)

	Henry Briggs
		Briggs is especially known for his publication of tables of logarithms to the base 10, first Logarithmorum chilias prima, 1617, and later Arithmetica logarithmetica, 1624.
		He also composed a work on trigonometry (basically tables, both of the functions and of the logs of sines and tangents) that was left unfinished at his death; Gellibrand completed and published it.
		Arithmetica Logarithmica, logs to 14 places, since functions to 15 places, tangent and secant functions to 10 places.
	www.thocp.net /biographies/briggs_henry.html (1022 words)

	BOEARI2 TEXT
		Quemadmodum constitutis altrinsecus duobus terminis arithmetica, geometrica et armonica inter eos medietas alternetur; in quo de eorum generationibus.
		Hic enim aequa semper proportio custoditur, numeri quantitas multitudoque neglegitur, contrarie quam in arithmetica medietate, ut sunt I. vel in tripla proportione I. vel si quadrupla vel si quincupla vel si in quamlibet multiplicitatem numerorum sit constituta distensio.
		Arithmetica prima I. Geometrica secunda I. Armonica tertia III.
	www.music.indiana.edu /tml/6th-8th/BOEARI2_TEXT.html (13663 words)

	Solution: A Scholarly Lesson (Site not responding. Last check: )
		In the center grid, you should end up with "Arithmetica Logarithmica scriptor." Scriptor is latin for "author," and "Arithmetic Logarithmica" was one of Briggs' greatest mathematical works.
		You have to realize that the words are Latin, and that scriptor is "author." Arithmetica translates only to arithmetic, and logarithmica doesn't translate.
		So the clue phrase is basically "Arithmetica Logarithmica author," which clues for Briggs.
	www.mit.edu /~puzzle/04/timbuktu/4KX/answer.html (421 words)

	Institutio Arithmetica; Medeltidshandskrift 1; S:t Laurentius digital manuscript library
		In comparison to diagrams and schemas in related works on the liberal arts by Cassiodorus and the Corpus Agrimensorum, with which De Arithmetica was often associated, there is a striking similarity in execution independent of the manuscript's date or place of origin.
		In the case of the Corpus Agrimensorum, which is preserved in both 6th century manuscripts and later copies, it can be stated that the Carolingian artists followed their exemplars very closely.
		The mediatory role played by the insular monasteries during the 7th and 8th centuries to promote classical learning is well known, and De Arithmetica was translated by Alfred the Great in the 9th century.
	laurentius.lub.lu.se /volumes/Mh_1/detailed (1398 words)

	[Arithmetica logarithmica]. Logarithmicall arithmetike. Or Tables of logarithmes for absolute numbers from an unite to ...
		Or Tables of logarithmes for absolute numbers from an unite to 100000; as also for sines, tangents and secantes for every minute of a quadrant: with a plaine description of their use in arithmetike, geometrie, geographie, astronomie, navigation, &c.Éfirst invented by John Neper.
		ÒBriggs' [1556-1630] Arithmetica logarithmica was the first to publish logarithmic tables based on the decimal system such that log 1=0 and log 10=1; the common logarithmic tables currently in use are derived from those of Briggs.
		Briggs learned of logarithms from their inventor John Napier, with whom he worked on the development of logarithms during the two years before Napier's death; the parts taken by each of them in this task are described in the first part of Arithmetica logarithmica.
	www.mrtbooksla.com /si/12082.html (419 words)

	Fermat's last theorem
		It was found by Samuel written as a marginal note in his father's copy of Diophantus's Arithmetica.
		Fermat almost certainly wrote the marginal note around 1630, when he first studied Diophantus's Arithmetica.
		It may well be that Fermat realised that his remarkable proof was wrong, however, since all his other theorems were stated and restated in challenge problems that Fermat sent to other mathematicians.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Fermat's_last_theorem.html (2143 words)

	Diophantus Summary
		Diophantus is sometimes known as the "father of Algebra" perhaps because his unusual syncopated notation seems reminiscent of the fully symbolic algebra that would develop much later.
		The editio princeps of Diophantus was published in 1575 by Xylander, and editions of Arithmetica exerted a profound influence on the development of algebra in Europe in the late sixteenth and through the seventeenth and eighteenth centuries.
		In 1637, while reviewing his copy of Diophantus' Arithmetica Pierre de Fermat wrote his famous "Last Theorem" in the margins of his copy of Bachet's 1621 edition of the Arithmetica.
	www.bookrags.com /Diophantus (1657 words)

	Arithmetica (Site not responding. Last check: )
		Luca Pacioli published his Summa de arithmetica, geometria proportioni et proportionalita...
		The Summa de arithmetica was not his first book, but it made...
		MAGAZINES American Scientist 5/1/2001 Gouvea, Fernando Q. the 1630s, began to read Diophantus's Arithmetica, he probably had no idea that he was...
	enciclopedia.cc /Arithmetica (349 words)

	Diophantus of Alexandria and the 10-th Problem of Hilbert
		The second chapter comments that Diophantus extended the notion of number to include negatives and rationals, describes his symbols for exponents from -6 to 6, and notes that he moved beyond Greek traditions in permitting addition of non-homogeneous magnitudes.
		More than a thousand years later, in 1570, 6 of the 13 chapters of Arithmetica were found in a library in Germany.
		Fermat studies Arithmetica and among other discoveries he claims that he has a beautiful solution for the well known Last Theorem but he has not enough place to provide the solution as his son later tells us.
	www.mlahanas.de /Greeks/Diophantus.htm (1178 words)

	Diophantus (Site not responding. Last check: )
		The title, “father of algebra”;, was not one that I came up with myself, but given to me by historians and mathematicians.
		My work on Arithmetica has also been seen as a great contribution to the development of algebra.
		Arithmetica is a collection of 130 problems that gives numerical solutions of determinate equations, which have a unique solution, and indeterminate equations.
	www.3villagecsd.k12.ny.us /wmhs/Departments/Math/OBrien/dio.html (529 words)

	Biography of Diophantus
		Diophantus worked during the middle of the third century and is best known for his Arithmetica, a work on the theory of numbers.
		The most details we have (and these may not be accurate) say that he married at the age of 33 and had a son who died at the age of 42, four years before Diophantus himself died at approximately 84.
		The Arithmetica, Diophantus's book, is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations.
	www.andrews.edu /~calkins/math/biograph/199899/biodioph.htm (419 words)

	Arithmetica: Todas las informaciones en Arithmetica de Enciclopedia-Gratuita.com
		Arithmetica: Todas las informaciones en Arithmetica de Enciclopedia-Gratuita.com
		La Arithmetica no es propiamente un texto de Ã¡lgebra sino una colecciÃ³n de problemas.
		En honor de Diofanto las ecuaciones con coeficientes enteros cuyas soluciones son tambiÃ©n enteras se denominan ecuaciones diofÃ¡nticas o ecuaciones diofantinas.
	www.enciclopedia-gratuita.com /a/ar/arithmetica.html (79 words)

	235 A.D. (Site not responding. Last check: )
		His greatest work was a set of thirteen books called "Arithmetica." All the translations of this work, including the early Arabic ones, contain only six of the books.
		In "Arithmetica," Diophantus solves 130 determinate and indeterminate equations, some being of fourth and sixth degree.
		One example is that no number of the form 8n-7, where n is a non-negative integer, could be rewritten as the sum of three squares.
	faculty.oxy.edu /jquinn/home/Math490/Timeline/235AD.html (237 words)

	Diophantus
		On the other hand he is quoted by Theon of Alexandria (who observed an eclipse at Alexandria in AD 365); and his work was the subject of a commentary by Theon's daughter Hypatia (died in 415).
		The Arithmetica, the greatest treatise on which the fame of Diophantus rests, purports to be in thirteen Books, but none of the Greek manuscripts which have survived contain more than six (though one has the same text in seven Books).
		The "Porisms" quoted are interesting propositions in the theory of numbers, one of which was clearly that the difference between two cubes can be resolved into the sum of two cubes.
	www.nndb.com /people/744/000104432 (442 words)

	Diophantus (Site not responding. Last check: )
		The most details we have of Diophantus's life come from the Greek Anthology, compiled by Metrodorus around 500, which implies that he married at the age of 26, and had a son who died at the age of 42, 4 years before Diophantus himself died aged 84.
		Diophantus is best known for his Arithmetica, the most outstanding work on algebra in Greek mathematics.
		Diophantus himself refers to another work which consists of a collection of lemmas, but this book is entirely lost.
	www.stetson.edu /~efriedma/periodictable/html/Dy.html (516 words)

	Shalen Abstract UGA Math (Site not responding. Last check: )
		If we are very ambitious we might want to describe all possible rational solutions to our equation.
		For example, problem VI.17 of Diophantus's {\it Arithmetica} asks for a positive rational solution to $x^8 + x^4 + x^2 = y^2$.
		As is typical in the {\it Arithmetica}, Diophantus provides a solution to this problem, namely $x = 1/2$ and $y= 9/16$.
	www.math.uga.edu /~szwang/colloquium/abst-wetherell.html (217 words)

	SFORTUNATI,Giovanni of Siena., Nuovo Lume Libro di Arithmetica. (Site not responding. Last check: )
		SFORTUNATI,Giovanni of Siena., Nuovo Lume Libro di Arithmetica.
		Smith, in Rara Arithmetica, writes that "Sfortunati wrote his treatise along the lines followed by Borghi and Feliciano, and in his preface he acknowledges his indebtedness to them and to 'Maestro Luca dal Borgo dell' ordine di fanto Francesco' and to the 'operetta di Filippo Caladri Cittadino Fiorentino'.
		Like these authors, he was a popular writer, as the seven editions of his book go to prove.
	www.polybiblio.com /hamish/B87.html (168 words)

	Hypatia's work on Diophantus (Site not responding. Last check: )
		Heath in 1885 was doubtful that Hypatia wrote on Diophantus at all.
		By 1921, Heath spoke more positively of both Hypatia, as the first Diophantus commentator, and of "the attractive hypothesis of Tannery that Hypatia's commentary extended only to our six Books, and that this accounts for their survival when the rest were lost" [17, 453].
		Tannery hypothesized that Hypatia's commentary preserved part of the Arithmetica as Eutocius preserved part of the Conics [47].
	www.mathsci.appstate.edu /~sjg/womeninmath/diophantus.html (628 words)

	Ivars Peterson's MathTrek - The Amazing ABC Conjecture
		The equation of Fermat's last theorem is one example of a type known as a Diophantine equation -- an algebraic expression of several variables whose solutions are required to be rational numbers (either whole numbers or fractions, which are ratios of whole numbers).
		In fact, it was in the margin of a page of a Latin translation of Arithmetica that Fermat first set down the proposition that came to be known as Fermat's last theorem.
		Interestingly, the Wiles proof of Fermat's last theorem was a by-product of his deep inroads into proving the Shimura-Taniyama-Weil conjecture.
	www.maa.org /mathland/mathtrek_12_8.html (1286 words)

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