61. Tartaglia By Tom Purvis This earned him the nickname tartaglia, or stammerer, a name he therefore usedinstead of the name niccolo fontana that had been given him at birth. http://mathforum.org/epigone/math-history-list/whildixspal/zwlbngse77f7@forum.sw

Tartaglia by Tom Purvis reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Tartaglia Author: tpurvis@WENET.NET Date: Fri, 12 Feb 1999 00:37:55 -0500 It seems likely that Tartaglia was the source of this vaudeville character. Boyer's History of Mathematics, p. 312, says the following about Tartaglia, after he won a contest for solving cubic equations about the year 1541: "News of Tartaglia's triumph reached Cardan, who promptly invited the winner to his home, with a hint that he would arrange to have him meet a prospective patron. Tartaglia had been without a substantial source of support, partly perhaps because of his speech impediment. As a child he had received a sabre cut in the fall of Brescia to the French in 1512, which inparied his speech. This earned him the nickname Tartaglia, or stammerer, a name he therefore used instead of the name Niccolo Fontana that had been given him at birth." The Math Forum

62. Ballistics And Gunnery In The Smoothbore Era of Nova Scientia by an Italian mathematician, niccolo fontana (1499 1559). withan impediment in his speech - plus the nickname tartaglia (stutterer) which http://riv.co.nz/rnza/hist/gun/smooth3.htm

The Gun Smoothbore Era 1550-1860: Ballistics and Gunnery previous index next At the beginning of the smooth-bore era Gunners knew little of the motion of projectiles, with which the science of ballistics is concerned. For example, they believed a shot fired from a gun travelled in a straight line to some point in space, then fell vertically to earth! Important as a pioneer attempt to establish laws of moving bodies was the publication of Nova Scientia by an Italian mathematician, Niccolo Fontana (1499 - 1559). During the sack of Brescia by the French in 1512 he suffered a sabre cut to the head which left him with an impediment in his speech - plus the nickname 'Tartaglia' (stutterer) which he later adopted as his surname and by which he is generally known. th Most other authors on the subject during the 16 th and 17 th centuries based their writings on Tartaglia, although some did dispute certain of his theories. In 1742 Benjamin Robins (1707-51) invented his ballistic pendulum, an instrument designed to measure the velocity of a projectile directed at it.Knowing the weight of the pendulum,H, with target, K, the weight of the shot fired, and the distance the pendulum moved when struck (measured by strap L), it was possible to calculate the velocity of the shot. By performing experiments at various distances Robins was able to determine the loss of velocity as range increased, and therefore the effects of air density and gravity. The instrument had its faults, but at least its design was based upon logical thought, not on rules of thumb or guesswork. Robins published his findings in

63. Old Comrades History - The Gun By WL Ruffell publication of Nova Scientia by an Italian mathematician, niccolo fontana (1499 1559 impediment in his speech - plus the nickname tartaglia (stutterer) which http://riv.co.nz/rnza/hist/art90b.htm

The Gun sights and laying - ballistics At the beginning of the smooth-bore era Gunners knew little of the motion of projectiles, with which the science of ballistics is concerned. For example, they believed a shot fired from a gun travelled in a straight line to some point in space, then fell vertically to earth! Important as a pioneer attempt to establish laws of moving bodies was the publication of Nova Scientia by an Italian mathematician, Niccolo Fontana (1499 - 1559). During the sack of Brescia by the French in 1512 he suffered a sabre cut to the head which left him with an impediment in his speech - plus the nickname Tartaglia (stutterer) which he later adopted as his surname and by which he is generally known. th Most other authors on the subject during the 16 th and 17 th centuries based their writings on Tartaglia, although some did dispute certain of his theories. In 1742 Benjamin Robins (1707-51) invented his ballistic pendulum , an instrument designed to measure the velocity of a projectile directed at it.Knowing the weight of the pendulum,H, with target, K, the weight of the shot fired, and the distance the pendulum moved when struck (measured by strap L), it was possible to calculate the velocity of the shot. By performing experiments at various distances Robins was able to determine the loss of velocity as range increased, and therefore the effects of air density and gravity. The instrument had its faults, but at least its design was based upon logical thought, not on rules of thumb or guesswork. Robins published his findings in

64. Õãʦ´óÖصãѧ¿Æµ¼º½ Simpson, Thomas (17101761) - ? Stirling, James (1692-1770) - ? tartaglia- niccolo fontana known as tartaglia (1499-1557) - Taylor http://lib.zjnu.net.cn/xueke/jcsx/zjxz.htm

EBSCOÆÚ¿¯Êý¾Ý¿â Abel - Niels Henrik Abel (1802-1829) Archimedes - Encyclopedia.com - Results for Archimedes (c. 287 B.C.-212 B.C.) Argand - Jean Robert Argand (1768-1822) Banach - The Life of Stefan Banach (1892-1945) ... Klein, Felix (1849-1925) - F.¿ËÀ³Òò Kronecker - Leopold Kronecker (1823-1891) Laplace - Pierre-Simon Laplace (1749-1827) Lebesgue - Henri Léon Lebesgue (1875-1941) Legendre - Adrien-Marie Legendre (1752-1833) ... Lie - Sophus Lie (1842-1899) - Sophus.Àî Liouville - Joseph Liouville (1809?882) Lipschitz - Rudolf Otto Sigismund Lipschitz (1832-1903) Mobius - August Ferdinand Mobius (1790-1868) Moivre - Abraham de Moivre (1667-1754) ... Noether, Max (1844-1921) - Max.ŵÌØ Peano, Giuseppe (1858-1932)

65. Grundoperationen Translate this page niccolo fontana tartaglia 1499 -1557. http://www-hm.ma.tum.de/ws0304/in1/links/Historie/Tartaglia.html

Niccolo Fontana Tartaglia 1499 -1557

66. Tartaglia Frente A Cardano Translate this page no era el autor, sino niccolo tartaglia (1500-1557 tartaglia era conocido medianteese apodo (“tartamudo”) en vez de su apellido original fontana, al haber http://ific.uv.es/rei/Historia/anecdotas3.htm

Tartaglia frente a Cardano. Se suele hacer coincidir el comienzo del álgebra moderna con la resolución de la ecuación cúbica (y cuártica también) en el Ars Magna escrita por Jerónimo Cardano (1501-1576). Sin embargo, hay que advertir inmediatamente que el descubridor original de dicha solución no era el autor, sino Niccolo Tartaglia (1500-1557), pese a que Cardano le había jurado solemnemente no desvelar el secreto pues Tartaglia esperaba publicar el resultado como culminación de su propio tratado de álgebra que estaba elaborando. Para evitar sentir una compasión excesiva por Tartaglia, hagamos notar que éste ya había publicado una traducción de Arquímedes, dejando la impresión de que el contenido era suyo propio, y más tarde, en su obra Quesiti et inventioni diverse proporciona la ley del plano inclinado obtenida a partir del trabajo anterior de Jordano Nemorario, pero sin atribuirla adecuadamente a su verdadero descubridor. De hecho, es posible que el mismo Tartaglia hallase la pista de la resolución de la ecuación cúbica de alguna fuente anterior, probablemente de un profesor de matemáticas de la universidad de Bolonia casi totalmente olvidado, Scipione del Ferro. La solución de las ecuaciones cúbica y cuártica fue probablemente la mayor aportación al álgebra desde que los babilonios habían aprendido, casi cuatro milenios antes, a completar un cuadrado para resolver ecuaciones cuadráticas. Las soluciones no tenían en realidad aplicación práctica alguna, pero las fórmulas de Tartaglia-Cardano tuvieron la virtud de estimular el desarrollo del álgebra, con un papel ciertamente relevante en el desarrollo posterior de los números complejos. En efecto, fue

67. List Of People By Name: T 1983), Pole; tartaglia, niccolo fontana, (15001557), Italian mathematician;tartaglia, Nicolo, (1499-1557), mathematician; Tartikoff http://www.fastload.org/li/List_of_people_by_name:_T.html

List of people by name: T Home Up About 'List of people by name: T' Advertisement List of people A B C ... S T U V W X ... T, Mr. , (born 1952), actor Tabor, June[?] , musician Tabori, George[?] , dramatist, author Tacer, Ales[?] , poet Tacitus, Publius (or Gaius) Cornelius , (AD 56-120), . Roman historian, ethnologist Tacitus, M. Claudius , (200 AD-276 AD), Roman Emperor Tacuma, Jamaaladeen , (born 1957), jazz musician Taft, Robert[?] , (died 1953), Senator from Ohio , former candidate for President of the United States , son of [[William Taft, Robert Alphonso[?] Senator from Ohio Taft, William Howard President of the United States Chief Justice of the United States ... Taggard, Geneviere[?] , (Calling Western Union) Tagle, Francisco Ruiz[?] , president Taglioni, Fabio Italian motorcycle engineer Tagore, Rabindranath , (1861-1941), poet Tailleferre, Germaine , (1892-1983), French composer Taimanov, Mark[?] , chess player Taimur Bin Faisal[?] , (1913-1932), Oman sultan Taira no Kiyomori , (1118-1181), samurai warlord Taisho, emperor of Japan Taisuke, Itagaki[?] , Japanese liberal activist Tait, Archibald Campbell

68. Italian Models - Online Italy Source Giuseppe Piazzi, (17461826), astronomer Gian-Carlo Rota, (1932-1999), Italian-bornAmerican mathematician and philosopher niccolo fontana tartaglia, (1500-1557 http://www.claudioxt.com/italy/italian models

ONLINE ITALY ENGINE Home Tool Links italian art italy rentals italian christmas recipes hotels in venice italy ... venice italy pictures of venice italy italian government italian models italian models Manufacturers ... catered for. Microfigs - Canadian manufacturer of resin kits and miniatures with product lines including 6mm structures, and HO scale model railroad locomotives. Pewter Craft - Producers of a range of historical, fantasy, and science fiction miniatures, which also includes ... Room - Manufacturer of historical miniature figures, buildings, terrain, naval guns, ships and boats. Also a distributor for many other model companies. Historical Miniatures - Designers of a range of historical miniatures, terrain, and buildings, as well as carrying the ... selection of historical miniatures, from such periods as WWII, the Crimean War, Vietnam and even the Dark Ages. Panzerschiffe Model Ships - Manufacturers of 1/2400 epoxy cast, scale naval miniature ships with a downloadable catalogue. Fortress Figures Inc ... Redoubt Enterprises - Provides a vast range of historical figures and an online shop. Naval Solutions - Wooden, hand built, historical model naval ships based on the original design plans. The Foundry - Producers of a large range of miniatures, including ... well as stocking a specialised paint range and modelling accessories. Leva Productions Online - Manufacturer of resin miniature wargaming and

69. Milestones: Section 2. Pre-1600 (tartaglia is better known for discovering a method to solve cubicequations) niccolo fontana tartaglia (1499-1557), Italy 212. http://www.math.yorku.ca/SCS/Gallery/milestone/sec2.html

Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization Pre-1600 Ptolemy 1842 map Mercator portrait Catalan Atlas Up: Index Introduction References Related Pre-1600 Pre-1600: Early maps and diagrams History of Cartography Project Map History Gateway The earliest seeds of visualization arose in geometric diagrams, in tables of the positions of stars and other celestial bodies, and in the making of maps to aid in navigation and exploration. We list only a few of these here to provide some early context against which later developments can be viewed. In the 16th century, techniques and instruments for precise observation and measurement of physical quantities were well-developed. As well, we see initial ideas for capturing images directly, and recording mathematical functions in tables. These early steps comprise the beginnings of the husbandry of visualization. c. 6200 BC The oldest known map? (There are several claimants for this honor.)- unknown, Museum at Konya, Turkey. IMG Konya town map (280 x 160; 7K)

70. EVENTS IN SCIENCE AND MATHEMATICS circumnavigating expedition; 1535 niccolo fontana tartaglia has amethod for solving certain types of cubic equations; 1540 Michael 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

71. Kolmannen Asteen Yhtälöä Ratkaisemassa (Solmu 1/2000-2001) Noin vuonna 1535 matemaatikko niccolo fontana alias tartaglia löysi ilmeisestikinitsenäisesti ratkaisun yhtälölle, joka on muotoa x 3 +rx 2 +q=0. Fior http://solmu.math.helsinki.fi/2000/2/saksman/

PDF Kolmannen asteen yhtälöä ratkaisemassa Taustana tarinallemme on tämän kevään lyhyen matematiikan yo-tehtävä, jossa käskettiin osoittamaan, että yhtälöllä f x x x -2=0 on juuri välillä (2,3) ja pyydettiin haarukoimaan kyseiselle juurelle kaksidesimaalinen likiarvo. Moni kokelas yritti vahingossa soveltaa probleemaan toisen asteen yhtälön ratkaisukaavaa, toki huonolla seurauksella. Tietystikään tehtävän ratkaisussa ei tarvita juuren tarkan arvon määräämistä - juuren olemassaolo annetulla välillä seuraa polynomifunktion f jatkuvuudesta ja havainnosta f f Johdamme seuraavassa yleisen ratkaisukaavan kolmannen asteen yhtälölle sekä kerromme lyhyesti asiaan liittyvästä historiasta. Esitiedoiksi riittää lukion pitkän matematiikan kurssi, liitteessä kertaamme lyhyesti kompleksilukujen juurtamista. Myöhemmässä kirjoituksessa tarkoitukseni on käsittelellä hieman yleisemmin likiarvomatematiikkaa, eli kuinka esimerkiksi yllä mainittu juuri voidaan laskea tehokkaasti niin tarkasti kuin halutaan. 1. Reaalijuurten lukumäärä.

72. Math.space In Der PRESSE Translate this page provozierte die Herausgabe des Algebra-Lehrbuches von Geronimo Cardano die Todfeindschaftdes Autors mit niccolo fontana, genannt tartaglia Dieser hatte http://math.space.or.at/presse/presse20030310.html

Das Delta der Gleichungen: Hinab in das unendlich Kleine! (RUDOLF TASCHNER) DIE PRESSE, 10.03.2003

73. Resolución De La Ecuación Algebraica Cúbica Translate this page niccolo tartaglia Geómetra italiano(1499-1557), cuyo verdadero nombre era niccoloFontana, en tanto que tartaglia era un apodo que significa el tartamudo. http://html.rincondelvago.com/resolucion-de-la-ecuacion-algebraica-cubica.html

Inicio Apuntes Amor Viajes ... Servicios document.write (' Ficha del Documento'); Ayuda document.write (' Categoría: '); Matemáticas document.write (' (ficha del documento)'); document.write (' (versión en PDF)'); document.write (' (versión para descargar en ZIP)'); Resolución de la ecuación algebraíca cúbica Introducción Los protagonistas Cardano, Girolamo(Hieronymus Cardanus. Jerome Cardan) (1501_1576): Físico, astrólogo y algebrista italiano, autor de Ars Magna (Nuremberg 1547), primer texto latino dedicado exclusivamente al álgebra. Esta obra contiene una solución para las ecuaciones cúbicas (ecuaciones con incógnitas elevadas a la tercera potencia). Procedimiento que se dice obtuvo Cardano de su descubridor Niccolo Tartaglia, con una promesa de secreto que Cardano dejó de cumplir. En mecánica inventó la suspensión Cardan, hoy ampliamente difundida, en su aplicación a los automotores, como articulación que sirve para transmitir el movimiento de un árbol a otro cuando ambos forman un cierto ángulo. Niccolo Tartaglia : Geómetra italiano(1499-1557), cuyo verdadero nombre era

74. Tartaglia Nicolo tartaglia. Born 1499 in Brescia Nicolo tartaglia was born in Bresciain 1499, the son of a humble mail rider. He was nearly killed http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Tartaglia.html

Nicolo Tartaglia Born: 1499 in Brescia, Republic of Venice (now Italy) Died: 13 Dec 1557 in Venice, Republic of Venice (now Italy) Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Nicolo Tartaglia was born in Brescia in 1499, the son of a humble mail rider. He was nearly killed as a teenager, when in 1512 the French captured his home town and put it to the sword. Amidst the general slaughter, the twelve year old boy was dealt horrific facial sabre wounds that cut his jaw and palate and he was left for dead. His mother's tender care ensured that the youngster did survive, but in later life Nicolo always wore a beard to camouflage his disfiguring scars and he could only speak with difficulty, hence his nickname Tartaglia, or stammerer. Tartaglia was self taught in mathematics but, having an extraordinary ability, was able to earn his living teaching at Verona and Venice. As a lowly mathematics teacher in Venice, Tartaglia gradually acquired a reputation as a promising mathematician by participating successfully in a large number of debates. The first person known to have solved cubic equations algebraically was del Ferro but he told nobody of his achievement. On his deathbed, however

75. A Quotation By Tartaglia A quotation by Nicolo tartaglia. The poem in which he revealed http//wwwhistory.mcs.st-andrews.ac.uk/Quotations/tartaglia.html. http://www-gap.dcs.st-and.ac.uk/~history/Quotations/Tartaglia.html

A quotation by Nicolo Tartaglia [The poem in which he revealed the secret of solving the cubic to Cardan] When the cube and the things together Are equal to some discrete number, Find two other numbers differing in this one. Then you will keep this as a habit That their product shall always be equal Exactly to the cube of a third of the things. The remainder then as a general rule Of their cube roots subtracted Will be equal to your principal thing. [Solve x cx d [Find u, v such that u - v = d and uv c [Then x u v Main index Quotations index Biographies Index History Topics ... Anniversaries for the year JOC/EFR February 2003 The URL of this page is: School of Mathematics and Statistics University of St Andrews, Scotland http://www-history.mcs.st-andrews.ac.uk/Quotations/Tartaglia.html

76. Niccolo Dell' Abbate - Encyclopedia Article About Niccolo Dell' Abbate. Free Acc niccolo dell Abbate. Word Word. Abati , or niccolo Dell Abbato (1512 Centuries15th century 16th century - 17th century http://encyclopedia.thefreedictionary.com/Niccolo dell' Abbate

Dictionaries: General Computing Medical Legal Encyclopedia Niccolo dell' Abbate Word: Word Starts with Ends with Definition Abati , or Niccolo Dell' Abbato Centuries: 15th century - 16th century - 17th century Decades: 1460s 1470s 1480s 1490s 1500s - Years: 1507 1508 1509 1510 1511 - Events April 11 - Battle of Ravenna. French forces under Gaston de Foix, Duc de Nemours defeat the Spanish under Raymond of Cardona, but Gaston is killed in the pursuit. Click the link for more information. Centuries: 15th century - 16th century - 17th century Decades: 1520s 1530s 1540s 1550s 1560s - Years: 1566 1567 1568 1569 1570 - Events January 11 - Austrian nobility is granted Freedom of religion. January 23 - The Royal Exchange opens in London. Crimean Tartars from the Ottoman Empire seize and burn Moscow, capitol of Russia October 7 Battle of Lepanto - Spanish, Venetian, and Papal naval forces under Don John of Austria defeat the Turkish fleet of Ali Monizindade Pasha. Click the link for more information. ), was a celebrated fresco In painting, the term

77. Tartaglia Translate this page Son costume est noir ou vert. tartaglia est aussi le surnom de NiccoloFontana, un célèbre mathématicien de la Renaissance. Les http://www.cssh.qc.ca/projets/carnetsma/renaissance/tarta_comm.html

Tartaglia Nom Nom italien Tartaglia Occupation Valet, homme de loi, gardien de l'ordre. Couleur du masque Ville d'origine du masque Naples Bavard, bredouilleur, vantard, poltron. Tartaglia est aussi le surnom de Niccolo Fontana Les personnages de la commedia dell'arte

78. Tartaglia Et Cardan http://math93.free.fr/Tartaglia-Cardan.htm

Tartaglia (Brescia, 1500?-Venise, 1557) et Cardan (Pavie, 1501-Rome, 1576) Home Les mathématiciens MATHÉ MATICIENS ITALIENS DU 16e SIÈCLE Les savants italiens du 16° siècle se distinguèrent surtout en algèbre élémentaire. Tartaglia. Nicolo Fontana était surnommé Tartaglia (le bègue) parce que, gravement blessé par l'épée d'un cavalier français, entré dans la grande église de Brescia le 19 février 1512 dans laquelle il se réfugiait avec sa mère, il lui en restait des difficultés d'élocution. (Les troupes françaises étaient menées par le terrible Gaston de Foix, surnommé "foudre d'Italie".) Niccolo qui avait alors 12 ans fut retrouvé la mâchoire fracassée. Aidé seulement par sa mère, veuve depuis 6 ans et trop pauvre pour faire appel à un médecin, il mit très longtemps avant de retrouver la parole. On raconte que le père de Niccolo (Fontana) avait engagé un professeur pour instruire son fils de 6 ans et que celui-ci arrêta les cours (-après la mort de Monsieur Fontana-) alors qu'il ne lui avait enseigné qu'un tiers de l'alphabet (de A à I). Il poursuivit seul son apprentissage. "Tout ce que je sais, je l'ai appris en travaillant sur les œuvres d'hommes défunts"

79. Tartaglia toujours connu par son surnom. Lorsque les Français mirent http://www.bib.ulb.ac.be/coursmath/bio/tartagli.htm

Nicolo Fontana Tartaglia né à Brescia en 1500, décédé à Venise le 13 décembre 1557. Tartaglia est célèbre pour avoir donné la démonstration de la résolution des équations du troisième degré publiée par Cardan dans Ars Magna Le véritable nom de Tartaglia était Niccolo Fontana bien qu'il fut toujours connu par son surnom. Lorsque les Français mirent Brescia à sac en 1512, les soldats tuèrent son père et le laissèrent pour mort, blessé par un sabre qui lui entailla la joue et le palais. On comprend dès lors le surnom "Tartaglia" qui signifie le "Bègue". Tartaglia fut un autodidacte en mathématique mais grâce à ses dons extraordinaires il vivait en enseignant à Vérone et Venise. Le premier à avoir résolu algébrique une équation du troisième degré est del Ferro. Sur son lit de mort, il confia son "secret" à Fior, un de ses étudiants. Un concours pour résoudre les équations du troisième degré fut organisé entre Fior et Tartaglia. Ce dernier, en la remportant en 1535, fut reconnu comme l'inventeur de la formule de résolution des équations cubiques. Comme les nombres négatifs n'étaient pas utilisés, il y avait plusieurs "types" d'équations, mais Tartaglia était à même de tous les résoudre alors que Fior ne savait résoudre qu'un seul type d'équation. Tartaglia confia sa solution à Cardan sous la condition qu'il ne la publie pas. La méthode fut toutefois publiée par

80. Karl's Calculus Tutor - Box 5.3a The Cubic Formula Generations of mathematicians searched for a cubic solution before niccolo FontanaTartaglia and Girolamo Cardano hit on it in the 16th century (Cardano http://www.karlscalculus.org/cubic.html

Box 5.3a: The Cubic Formula Solving a Cubic Note that this material is not at all likely to be on the exam. The formula is not even all that useful. It's given here merely to satisfy your curiosity. So you may skip this box if you like. If you are given a cubic equation in the form of x + px + qx + r = eq. 5.3a-1 and need to solve for x , then the first thing you do is substitute variables. Everywhere you see an x in the cubic, replace it with p x = u - eq. 5.3a-2 3 When you get done squaring and cubing this expression, then substituting stuff back in and gathering like terms, you will get u + au + b = eq. 5.3a-3a where p a = q - eq. 5.3a-3b 3 and pq 2p b = r - eq. 5.3a-3c 3 27 Now compute A and B by A = eq. 5.3a-4a

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