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         Ferrari Lodovico:     more books (15)
  1. I Sei Cartelli Di Mathematica Disfida Primamente Intorno Alla Generale Risoluzione Delle Equazioni Cubische (Italian Edition) by Lodovico Ferrari, 2010-01-10
  2. 1565 Deaths: Pope Pius Iv, Lodovico Ferrari, Nicolaus Von Amsdorf, Adrianus Turnebus, Conrad Gessner, Turgut Reis, Cipriano de Rore
  3. Italian Scientist Introduction: Lodovico Ferrari, Bartolomeo Maranta, Gaetano Arturo Crocco, Vincenzo Silvano Casulli, Agostino Gemelli
  4. 16th-Century Mathematicians: Johannes Kepler, John Napier, Niccolò Fontana Tartaglia, Gerolamo Cardano, Luca Pacioli, Lodovico Ferrari
  5. European Mathematician Introduction: Kazimierz Kuratowski, Lodovico Ferrari, Rolf Nevanlinna, Viggo Brun, Thomas Fincke, François D'aguilon
  6. People From Bologna: Guglielmo Marconi, Pope Gregory Xiii, Pope Benedict Xiv, Alessandro Algardi, Lodovico Ferrari, Pope Gregory Xv
  7. Lodovico Ferrari: An entry from Gale's <i>Science and Its Times</i>
  8. Algebraists: Max August Zorn, Lodovico Ferrari, Alexander Anderson, Hermann Grassmann, Emmy Noether, Bartel Leendert Van Der Waerden
  9. 1522 Births: Lodovico Ferrari, Albert Alcibiades, Margrave of Brandenburg-Kulmbach, Martin Chemnitz, John Jewel, Eleanor of Toledo
  10. I sei cartelli di matematica disfida primamente intorno alla generale risoluzione dell equazioni cubiche (Italian Edition) by Lodovico Ferrari, 1876-01-01
  11. La Scoperta Dell’elettricita Animale nella Corrispondenza Inedita fra Luigi Galvani e Lazzaro Spallanzani, con due Lettere di Mariano Fontana e Bartolomeo Ferrari. by Luigi] BARBIERI, Lodovico. [GALVANI, 1938
  12. IL CONCILIO, OVERO CONSIGLIO, ET I CONSIGLIERI DEL PRENCIPE. Tradotta di Lingua Spagnuola Nella Volgare Italiana, per M. Lodovico Dolce. by Fadrique Furio Ceriol, 1560-01-01
  13. Il Libro del Cortegiano del Conte Baldesar Castiglione; Nuovamente con Diligenza Revisto per M. Lodovico Dolce, Secondo l'Esemplare del Proprio Autore by Baldesar Castiglione, 1560
  14. I Fatti De Greci Xenophonte by Xenophon;Translated By M Lodovico Domenich, 1548

41. Biography-center - Letter F
ferrari, lodovico wwwhistory.mcs.st-and.ac.uk/~history /Mathematicians/ferrari.html;ferrari, Enzo www.uwgb.edu/galta/ 333/ferrari.htm; ferrari, Gaudenzio
http://www.biography-center.com/f.html
Visit a
random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish
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448 biographies

42. Bibliography
ferrari, lodovico, 15221565, Cartelli di sfida matematica / di lodovico ferrarie Niccol`o Tartaglia, Brescia, Ateneo, 1974. ferraris, Galileo, 1847-1897
http://www.library.cornell.edu/math/bibliography/display.cgi?start=F&

43. GrandPrix.com > GP Encyclopedia > Races > 1964 Results > Italian GP
The Italian GP featured all the World Championship regulars and a variety ofadditional entries including a third ferrari for lodovico Scarfiotti.
http://www.grandprix.com/gpe/rr129.html
Location: GrandPrix.com GP Encyclopedia Races Supplier of the motorsport database to the FIA
GRAND PRIX RESULTS: ITALIAN GP, 1964
Italian GP
Monza

Sep 6, 1964
78 Laps, 5.75
The Italian GP featured all the World Championship regulars and a variety of additional entries including a third Ferrari for Lodovico Scarfiotti. Phil Hill had disappeared from the Cooper team and had been replaced by Rhodesian driver John Love who had showed well with Ken Tyrrell (the Cooper team manager) in Formula Junior. Surtees was fastest in practice and lined up on the front row alongside Dan Gurney 's Brabham and Graham Hill 's BRM Jim Clark shared the second row with Bruce McLaren 's Cooper while the third row featured Jo Siffert in his privately-entered Brabham- BRM , Ferrari's Lorenzo Bandini (the winner of the previous race in Austria) and Mike Spence in the second Lotus
At the start of the race McLaren took the lead from the second row with Gurney and Surtees chasing but Hill was left on the grid for the second consecutive race, this time with a clutch failure. Monza provided the usual exciting slipstreaming battle and McLaren was quickly pushed back to third behind Gurney and Surtees. The two managed to get slightly ahead and spent most of the afternoon switching places until Gurney dropped back in the closing stages with engine trouble.

44. Le Mans 24 Hours News And History From "Maison Blanche"
PHIL HILL 4451.255 km 1963 ferrari 250 P lodovico SCARFIOTTI, LORENZO BANDINI4561.710 km 1964 ferrari 275 P NINO VACCARELLA, JEAN GUICHET 4695.310 km
http://www.maisonblanche.co.uk/winners.html
race winners - 1923 to 2003
to print this page full width on A4 paper, print in "landscape" format

45. Cardano, Girolamo (1501-1570)
had sworn not to reveal it, and became embroiled with Cardano in a decadelongfight), and the quartic was solved by Cardano s student lodovico ferrari.
http://www.daviddarling.info/encyclopedia/C/Cardano.html
Return to The Worlds of David Darling
INDEX LATEST NEWS ARCHIVE ... Z
entire Web this site
Cardano, Girolamo (1501-1570)
A celebrated Renaissance mathematician, physician, astrologer, and gambler, whose writings on the use of negative numbers are the earliest known in Europe. As a physician, he gave one of the first clinical descriptions of typhoid fever. The illegitimate child of a mathematically gifted lawyer who was a friend of Leonardo da Vinci, he entered the University of Pavia in 1520 and later studied medicine at Padua. His eccentric and confrontational style earned him few friends and he had trouble finding work. Eventually, he won reputation as a physician and his services were highly valued at the courts. Today, Cardano is mostly remembered for his achievements in algebra . He published the solutions to the cubic and quartic equations in his book Ars magna (1545). The solution to the cubic was communicated to him by Niccolo

46. Chronology Of Pure And Applied Mathematics
1540, lodovico ferrari solves the quartic equation. 1596, Ludolf van Ceulencomputes pi to twenty decimal places using inscribed and cirumscribed polygons.
http://www.3rd1000.com/chronology/chrono23.htm
Chronology of Pure and Applied Mathematics Egyptian mathematicians employ primitive fractions. Pythagoras studies propositional geometry and vibrating lyre strings. Eudoxus states the method of exhaustion for area determination. Aristotle discusses logical reasoning in Organon. Euclid studies geometry as an axiomatic system in Elements and states the law of reflection in Catoptrics. Archimedes computes pi to two decimal places using inscribed and cirumscribed polygons and computes the area under a parabolic segment. Apollonius writes On Conic Sections and names the ellipse, parabola, and hyperbola. Diophantus writes Arithmetica, the first systematic treatise on algebra. Tsu Ch'ung-Chih and Tsu Keng-Chih compute pi to six decimal places. Hindu mathematicians give zero a numeral representation in a positional notation system. Leonardo Fibonacci demonstrates the utility of Arabic numerals in his Book of the Abacus. Ghiyathal-Kashi computes pi to sixteen decimal places using inscribed and cirumscribed polygons. Scipione Ferro develops a method for solving cubic equations.

47. Ferrari Club Potenza Picena Web Site
ferrari nel 1960 per le grandi gare di durata e per i campionati europei
http://www.ferrariclubpp.it/LODOVICO.htm
HOME CLUB ORGANI PROGRAMMI ... LINKS
Un corridore di casa nostra Il nonno paterno era stato uno dei fondatori e il primo presidente della Fiat; il padre, Luigi, un appassionato pilota. Lodovico Scarfiotti cominciò a guidare a cinque anni, una piccola monoposto fatta a sua misura. A 23 era campione italiano con le Gran Turismo. Naturale l'approdo alla Ferrari nel 1960 per le grandi gare di durata e per i campionati europei della salita con le vetture Sport. Sull'onda di una prestigiosa vittoria nella 24 Ore di Le Mans con la 250 P, nel 1963 Scarfiotti ottenne l'agognato esordio in Formula 1: sesto nel Gran Premio d'Olanda, poi un serio incidente in prova. Ferrari lo giudicava "esuberante, irruente oltre misura: la sua tecnica di guida non si conciliava con l'affinamento necessario per la Formula 1". Così, continuò a impegnarlo con le Sport, centellinandogli le partecipazioni nei Gran Premi. Nel 1966, la grande occasione: la nuova

48. Quiz Access
d. First mathematician to examine a general approach (for all powers) for Fermat sLast Theorem. 5. lodovico ferrari
http://www.mathsci.appstate.edu/~sjg/class/3110/mathfestalg2000/quiz1.html
alert("Your time is up. Please submit your quiz now.") 3110 Quiz 1 Name DrSarah Greenwald Start Time: Apr 03, 2000 13:11 Time Allowed: 14 min Number of Questions:
Question 1 (10 points)
Is x^5-2x^3-8x-2 solvable by radicals? yes no sometimes, but not always
Question 2 (10 points)
Match the mathematician with their math 1. Sophie Germain a. Proved the Epsilon Conjecture which says that Taniyama-Shimura implies Fermat's Last Theorem 2. Andrew Wiles b. Worked on the solution of a quintic by radicals 3. Niels Abel
c. Proved Fermat's Last Theorem by proving Taniyama-Shimura 4. Ken Ribet d. First mathematician to examine a general approach (for all powers) for Fermat's Last Theorem 5. Lodovico Ferrari e. Worked on the solution of a quartic by radicals Choose Match a b c d e Choose Match a b c d e Choose Match a b c d e Choose Match a b c d e Choose Match a b c d e
Question 3 (10 points)
Match the the following definitions 1. f is a function if for all x, there exists y s.t. f(x)=y, and a. for all y, there exists x s.t. f(x)=y 2. f is one-to-one if 3. f is onto if

49. Quiz Homepage
6. lodovico ferrari. f. Z_3 is a finite field. 7. Evariste Galois. g. proved thatx^3+y^3=z^3 has no nonzero whole number solutions.
http://www.mathsci.appstate.edu/~sjg/class/3110/mathfestalg2000/finalexam2.html
3110 Final Exam Login ID: drsarah Attempt: Max. Score: Quiz Started: May 08, 2000 8:46 Quiz Finished: May 08, 2000 9:00 Time Spent: 14 min., 35 sec. Student finished 1 hr., 15 min., 25 sec. ahead of the 90 min. time limit.
Question 1 (9 points)
Match the equation to the corresponding functional qualities. y=cos(x) y is 1-1 and onto y=e^x y is not a function y=x^3-x y is onto but not 1-1 y=x y is 1-1 but not onto x=y^2 y is neither 1-1 nor onto Student Response: y=cos(x) y is neither 1-1 nor onto Correct y=e^x y is 1-1 but not onto Correct y=x^3-x y is onto but not 1-1 Correct y=x y is 1-1 and onto Correct x=y^2 y is not a function Correct Score:
Question 2 (9 points)
Match the polynomials to the corresponding statements. x^5-2x^3-8x-2 If at all reducible, then solvable by radicals x^5 always solvable by radicals x^5-1 partially reducible, solvable by radicals 5th degree polynomials completely reducible, solvable by radicals 4th or lower degree polynomials irreducible, not solvable by radicals Student Response: x^5-2x^3-8x-2 irreducible, not solvable by radicals Correct x^5 completely reducible, solvable by radicals

50. The Writer's Almanac, Jan. 29 - Feb. 4, 1996
Birthday of Italian mathematician, lodovico ferrari, born in 1522. Writer MarkTwain first used his pen name on this day in 1863.
http://writersalmanac.publicradio.org/docs/96_01_29.htm
January 29 - February 4 Monday Tuesday Wednesday Thursday ... Other Weeks
MONDAY 1/29 Today's reading: "Brian O'Linn" an Irish ballad by an anonymous author.
  • The first Librarian of Congress, John James Beckley, was appointed on this day in 1802.
  • Birthday of painter John Calcott Horsley, designer of first Christmas card, was born in London in 1817.
  • Novelist Anton Pavlovitch Chekhov was born in Ukraine in 1860.
  • Actor W. C. Fields was born in Philadelphia in 1880.
  • Birthday of Oprah Winfrey, born in Mississippi in 1954.

TUESDAY 1/30 Today's reading: "Ode to Healing" by John Updike from COLLECTED POEMS, published by Alfred A. Knopf.
  • King Charles I of England was beheaded on this day in 1649.
  • In 1847 the town of Yerba Buena, California changed its name to San Francisco
  • Birthday of Franklin Delano Roosevelt, born in Hyde Park, New York in 1882.
  • The Lone Ranger radio program was first broadcast in 1933 in Detroit, Michigan.
  • Birthday of author Richard Brautigan, born in Tacoma, Washington in 1935.

WEDNESDAY 1/31 Today's reading: "Life Study" by Stephen Orlen from THE MORROW ANTHOLOGY OF YOUNGER AMERICAN POETS, published by William Morrow & Co.

51. Lodovico Ferrari Matemático Bolonhês Que Chegou A Casa De Gerônimo
Translate this page lodovico ferrari. Matemático bolonhês que chegou a casa de Gerônimo Cardano aoscatorze anos para ser seu empregado. Cardano logo percebeu sua excepcional
http://www.educ.fc.ul.pt/docentes/opombo/seminario/renascenca/ferrari.htm
[Home] [O Episódio] [Os personagens] [O problema] ... [Quem somos] Lodovico Ferrari Matemático bolonhês que chegou a casa de Gerônimo Cardano aos catorze anos para ser seu empregado. Cardano logo percebeu sua excepcional capacidade de ler e escrever e nomeou-o seu secretário, além de lhe ensinar matemática. Seu discípulo não o decepcionou e logo se tornou num grande geómetra e herdou o posto do mestre na Fundação Piatti, em Milão (1540), derrotando facilmente um concorrente num debate decisivo pelo posto. Posteriormente tornou-se professor em Bolonha mas manteve sempre uma estreita ligação com o seu mestre e protector colaborando com ele em diversos trabalhos, designadamente na resolução de equações. [Topo]

52. Lexikon Lodovico Ferrari
lodovico ferrari aus der freien EnzyklopädieWikipedia und steht unter der GNU Lizenz. Die Liste der Autoren ist
http://lexikon.freenet.de/Lodovico_Ferrari

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Sie sind hier: Startseite Lexikon Lodovico Ferrari
Lodovico Ferrari
Lodovico Ferrari 2. Februar in Bologna Italien 5. Oktober in Bologna) war ein Mathematiker Ferrari war Professor der Mathematik in Mailand und Bologna. Er fand auf Anregung seines Lehrers Gerolamo Cardano die Aufl¶sung der Gleichungen vierten Grades und f¼hrte groŸe geod¤tische Vermessungen in Oberitalien aus. Einen heftigen Streit f¼hrte Ferrari mit dem Mathematiker Tartaglia darum, wer als erster die L¶sung f¼r kubische Gleichungen fand. Siehe auch: Cardanische Formeln
Personendaten
NAME Ferrari, Lodovico ALTERNATIVNAMEN KURZBESCHREIBUNG italienischer Mathematiker GEBURTSDATUM 2. Februar

53. Math 489
Gerolamo Cardano, lodovico ferrari Rafael Bombelli François Viète Simon StevinJohn Napier Marin Mersenne René Descartes Pierre de Fermat
http://orion.math.iastate.edu/lhogben/classes/math489.html
Math 489 History of Mathematics
Spring 2005
New Information
Final 12-2 PM Monday May 2 in the regular classroom 2 Carver. Extended time is allowed.
4/28 Updated topics list for the final.

The final is comprehensive but also emphasizes material since test 2.
Algebraic Symbolism slides
Index
General Course Information
2:10-3:30 TTh Room 2 Carver Hall Objective
The objective of this course is not merely to know what mathematics was discovered when and by whom, but to understand the how the development of mathematical ideas was influenced by knowledge and notation available, realize the intellectual struggles involved in the development of new mathematical concepts, and appreciate mathematics as a part of human culture.
Text: History of Mathematics: Brief Version, by Victor J. Katz
The course will cover the entire text as outlined in the reading schedule.

54. Louis Ferrari - Wikipédia
Translate this page (Redirigé depuis lodovico ferrari). Louis ferrari (2 février 1522 - 5 octobre1565) est un ferrari se retire relativement jeune (42 ans) et assez riche.
http://fr.wikipedia.org/wiki/Lodovico_Ferrari
Wikim©dia a besoin de votre aide notre page de collecte de fonds pour plus de d©tails.
Louis Ferrari
Un article de Wikip©dia, l'encyclop©die libre.
(Redirig© depuis Lodovico Ferrari
Louis Ferrari 2 f©vrier 5 octobre ) est un math©maticien italien. N©   Bologne , il est l'©l¨ve et le collaborateur de J©r´me Cardan . Il est extrªmement brillant et Cardan commence   lui enseigner les math©matiques. Il est c©l¨bre pour avoir r©solu l'©quation du quatri¨me degr© en la ramenant   une ©quation du troisi¨me degr©. Ferrari se retire relativement jeune (42 ans) et assez riche. Il retourne dans sa ville natale pour tenir un poste de professeur de math©matiques en 1565. Quelque temps plus tard il meurt d'un empoisonnement   l' arsenic , apparemment assassin© par sa sœur. R©cup©r©e de « http://fr.wikipedia.org/wiki/Louis_Ferrari Cat©gories Math©maticien italien Affichages Outils personels Navigation Rechercher Bo®te   outils Autres langues

55. Selected Twentieth Century Works: B
nella corrispondenza inedita fra Luigi Galvani e Lazzaro Spallanzani, con duelettere di Mariano Fontana e Bartolomeo ferrari di lodovico Barbieri.
http://www.thebakken.org/library/books/20b.htm
Books and Manuscripts
Selected Twentieth Century Works: B
Previous
Page Next page
6 p. 24.1 cm. "Extrait des Bulletins et mémoires de la Société médicale des Hôpitaux de Paris. (Séance du 30 Novembre 1906.)" Babinski was a renowned French neurologist who succeeded Charcot at Salpetriere in 1893 and devoted his life to clinical neurology. He was the first to recognize the diagnostic significance of the cutaneous plantor reflex in 1898. (Babinski sign, a lesion of the pyramidal tract that produces extension of the great toe and flexing of the other toes when the sole of the foot is stroked.) 4 p. 24.2 cm. "Extrait des Bulletins et mémoires de la Société des Hôpitaux de Paris. (Séance du 7 Novembre 1902)." "Extrait des Comptes rendus des séances de la Société de Biologie (Séance du 26 janvier 1901)." 234 p. 24.9 cm. Provenance: Author's signed presentation copy to, "Emile Picard". [4] p. 24.3 cm.

56. Lexikon: Lodovico Ferrari - Begriff

http://lexikon.donx.de/?action=details&show=Lodovico Ferrari

57. EVENTS IN SCIENCE AND MATHEMATICS
1540 lodovico ferrari solves the quartic equation; 1543 Andreas Vesalius publishesDe Fabrica Corporis Humani which corrects Greek medical errors and
http://www.physics.ohio-state.edu/~wilkins/science/sciehist.html
EVENTS IN SCIENCE AND MATHEMATICS
  • a.c
  • 1400 p.c
  • 1700 p.c
  • 1800 p.c ...
  • 1900 p.c
  • -3000 The abacus is invented in the Tigris-Euphrates valley
  • -1700 Egyptian mathematicians employ fractions
  • -586 Thales of Miletus predicts a solar eclipse in 585 B.C.
  • -530 Pythagoras studies propositional geometry and vibrating lyre strings
  • -380 Hippocrates begins the scientific study of medicine
  • -370 Eudoxus states the method of exhaustion
  • -300 Euclid studies geometry as a deductive system in Elements and states the law of reflection in Catoptrics
  • -230 Archimedes writes The Sand-Reckoner
  • -200 Apollonius writes On Conic Sections and names the ellipse, parabola, and hyperbola
  • -200 Eratosthenes roughly determines the radius of the Earth
  • -130 Hipparchus creates the magnitude scale of stellar apparent luminosities and discovers the precession of the equinoxes
  • -46 Julius Caesar orders the development of the Julian calendar
  • 50 Cleomedes studies refraction
  • 60 Hero of Alexandria writes Metrica Mechanics Catoptrics , and Pneumatics
  • 130 Claudius Ptolemy tabulates angles of refraction for several media
  • 250 Diophantus writes Arithmetica , the first systematic treatise on algebra
  • 550 Hindu mathematicians give a numeral representation to zero
  • 1054 Chinese and American Indian astronomers observe the Crab supernova explosion
  • 1202 Leonardo Fibonacci demonstrates the utility of Arabic numerals in his Book of the Abacus
  • 1248 Roger Bacon writes formulas for gunpowder in his

58. History Of Astronomy: Persons (F)
ferrari, Ludovico lodovico (15221565). Biographical data and references Short biography and references (MacTutor Hist. Math.
http://www.astro.uni-bonn.de/~pbrosche/persons/pers_f.html
History of Astronomy Persons
History of Astronomy: Persons (F)
Deutsche Fassung
  • Fabricius, David (1564-1617)
  • Fabricius, Johannes (1587-1616)
  • Fabry, Marie Paul Auguste Charles (1867-1945)
  • Fairbank, William Martin (1917-1989)
  • Fairfax Somerville, Mary: see Somerville, Mary Fairfax Greig (1780-1872)
  • Falck, Anders (1740-1796)
  • Faraday, Michael (1791-1867)
  • Fatou, Pierre Joseph Louis (1878-1929)
  • Faulkner, Don (20th c.)
  • Fermat, Pierre de (1601-1665)
  • 59. Lodovico Pavoni, Biography (1784-1849)
    Blessed lodovico Pavoni was born in Brescia on 11 September 1784 and, after 30years of service to Fr Carlo Domenico ferrari, future Bishop of Brescia.
    http://www.vatican.va/news_services/liturgy/2002/documents/ns_lit_doc_20020414_p
    LODOVICO PAVONI photo Blessed Lodovico Pavoni was born in Brescia on 11 September 1784 and, after 30 years of service to young people, died in Saiano, outside Brescia, on 1 April 1849. For 30 years he followed his inspiration to serve the needs of the young boys on the streets with positive methods of education. He began by opening his own oratory (catechetical and recreation centre) that in 1821 he expanded it into a hostel for their shelter and a school to teach them a trade. In 1825 he founded a religious congregation of priests and brothers to run the educational and industrial activities that grew out of his intuition. Lodovico was a lively and bright child, interested in the world around him and quick to grasp the social problems of his day. He prepared for the priesthood by receiving his theological formation at the home of the Domenican, Fr Carlo Domenico Ferrari, future Bishop of Brescia. During the Napoleonic era in Italy (1799-1814), the French Emperor closed seminaries. In Brescia, in 1807, he was ordained a priest and first launched the oratory. A book by Pietro Schedoni Moral Influences listed the reasons for the "rebellion" of young boys: leaving inadequate schools for a job, bad influences of adult workers, and peer pressure. The author confirmed Lodovico in his personalist approach: to concentrate on the personal and social formation of the young with a positive and preventative approach.

    60. Quadratic Etc Equations
    Cardan encouraged his own student, lodovico ferrari, to examine quartic equations.ferrari managed to solve the quartic with perhaps the most elegant of
    http://physics.rug.ac.be/Fysica/Geschiedenis/HistTopics/Quadratic_etc_equations.
    Quadratic, cubic and quartic equations
    Previous topic Next topic History Topics Index
    It is often claimed that the Babylonians (about 400 BC) were the first to solve quadratic equations. This is an over simplification, for the Babylonians had no notion of 'equation'. What they did develop was an algorithmic approach to solving problems which, in our terminology, would give rise to a quadratic equation. The method is essentially one of completing the square. However all Babylonian problems had answers which were positive (more accurately unsigned) quantities since the usual answer was a length. In about 300 BC Euclid developed a geometrical approach which, although later mathematicians used it to solve quadratic equations, amounted to finding a length which in our notation was the root of a quadratic equation. Euclid had no notion of equation, coefficients etc. but worked with purely geometrical quantities. Hindu mathematicians took the Babylonian methods further so that Brahmagupta (598-665 AD) gives an, almost modern, method which admits negative quantities. He also used abbreviations for the unknown, usually the initial letter of a colour was used, and sometimes several different unknowns occur in a single problem. The Arabs did not know about the advances of the Hindus so they had neither negative quantities nor abbreviations for their unknowns. However

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