MARC Record from marc_columbia

LEADER: 07169cam a22003254a 4500
001 7084437
005 20221130205041.0
008 080722t20092009njua b 001 0 eng
010 $a 2008032521
020 $a9780691129730 (hardcover : alk. paper)
020 $a0691129738 (hardcover : alk. paper)
024 $a40016440230
035 $a(OCoLC)236082858
035 $a(OCoLC)ocn236082858
035 $a(NNC)7084437
035 $a7084437
040 $aDLC$cDLC$dUKM$dBTCTA$dC#P$dBWX$dYDXCP$dOrLoB-B
050 00 $aQA24$b.V36 2009
082 00 $a516.2409$222
100 1 $aVan Brummelen, Glen.$0http://id.loc.gov/authorities/names/no2006001021
245 14 $aThe mathematics of the heavens and the earth :$bthe early history of trigonometry /$cGlen van Brummelen.
260 $aPrinceton :$bPrinceton University Press,$c[2009], ©2009.
300 $axvii, 329 pages :$billustrations ;$c24 cm
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
504 $aIncludes bibliographical references (p. 287-322) and index.
505 00 $tThe Ancient Heavens -- $gCh. 1.$tPrecursors -- $tWhat Is Trigonometry? -- $tThe Seqed in Ancient Egypt -- $tText 1.1 Finding the Slope of a Pyramid -- $tBabylonian Astronomy, Arc Measurement, and the 360 degree Circle -- $tThe Geometric Heavens: Spherics in Ancient Greece -- $tA Trigonometry of Small Angles? Aristarchus and Archimedes on Astronomical Dimensions -- $tText 1.2 Aristarchus, the Ratio of the Distances of the Sun and Moon -- $gCh. 2.$tAlexandrian Greece -- $tConvergence -- $tHipparchus -- $tA Model for the Motion of the Sun -- $tText 2.1 Deriving the Eccentricity of the Sun's Orbit -- $tHipparchus's Chord Table -- $tThe Emergence of Spherical Trigonometry -- $tTheodosius of Bithynia -- $tMenelaus of Alexandria -- $tThe Foundations of Spherical Trigonometry: Book III of Menelaus's Spherics -- $tText 2.2 Menelaus, Demonstrating Menelaus's Theorem -- $tSpherical Trigonometry before Menelaus? -- $tClaudius Ptolemy -- $tPtolemy's Chord Table -- $tPtolemy's Theorem and the Chord Subtraction/Addition Formulas -- $tThe Chord of 1 degree -- $tThe Interpolation Table -- $tChords in Geography: Gnomon Shadow Length Tables -- $tText 2.3 Ptolemy, Finding Gnomon Shadow Lengths -- $tSpherical Astronomy in the Almagest -- $tPtolemy on the Motion of the Sun -- $tText 2.4 Ptolemy, Determining the Solar Equation -- $tThe Motions of the Planets -- $tTabulating Astronomical Functions and the Science of Logistics -- $tTrigonometry in Ptolemy's Other Works -- $tText 2.5 Ptolemy, Constructing Latitude Arcs on a Map -- $tAfter Ptolemy -- $gCh. 3.$tIndia -- $tTransmission from Babylon and Greece -- $tThe First Sine Tables -- $tAryabhata's Difference Method of Calculating Sines -- $tText 3.1 Aryabhata, Computing Sines -- $tBhaskara I's Rational Approximation to the Sine -- $tImproving Sine Tables -- $tOther Trigonometric Identities -- $tText 3.2 Varahamihira, a Half-angle Formula -- $tText 3.3 Brahmagupta, the Law of Sines in Planetary Theory? -- $tBrahmagupta's Second-order Interpolation Scheme for Approximating Sines -- $tText 3.4 Brahmagupta, Interpolating Sines -- $tTaylor Series for Trigonometric Functions in Madhava's Kerala School -- $tApplying Sines and Cosines to Planetary Equations -- $tSpherical Astronomy -- $tText 3.5 Varahamihira, Finding the Right Ascension of a Point on the Ecliptic -- $tUsing Iterative Schemes to Solve Astronomical Problems -- $tText 3.6 Paramesvara, Using Fixed-point Iteration to Compute Sines -- $tConclusion -- $gCh. 4.$tIslam -- $tForeign Junkets: The Arrival of Astronomy from India -- $tBasic Plane Trigonometry -- $tBuilding a Better Sine Table -- $tText 4.1 Al-Samaw'al ibn Yahya al-Maghribi, Why the Circle Should Have 480 Degrees -- $tIntroducing the Tangent and Other Trigonometric Functions -- $tText 4.2 Abu'l-Rayhan al-Biruni, Finding the Cardinal Points of the Compass -- $tStreamlining Astronomical Calculation -- $tText 4.3 Kushyar ibn Labban, Finding the Solar Equation -- $tNumerical Techniques: Approximation, Iteration, Interpolation -- $tText .4 Ibn Yunus, Interpolating Sine Values -- $tEarly Spherical Astronomy: Graphical Methods and Analemmas -- $tText 4.5 Al-Khwarizmi, Determining the Ortive Amplitude Geometrically -- $tMenelaus in Islam -- $tText 4.6 Al-Kuhi, Finding Rising Times Using the Transversal Theorem -- $tMenelaus's Replacements -- $tSystematizing Spherical Trigonometry: Ibn Mucadh's Determination of the Magnitudes and Nasir al-Din al-Tusi's Transversal Figure -- $tApplications to Religious Practice: The Qibla and Other Ritual Needs -- $tText 4.7 Al-Battani, a Simple Approximation to the Qibla -- $tAstronomical Timekeeping: Approximating the Time of Day Using the Height of the Sun -- $tNew Functions from Old: Auxiliary Tables -- $tText 4.8 Al-Khalili, Using Auxiliary Tables to Find the Hour-angle -- $tTrigonometric and Astronomical Instruments -- $tText 4.9 Al-Sijzi (?), On an Application of the Sine Quadrant -- $tTrigonometry in Geography -- $tTrigonometry in al-Andalus -- $gCh. 5.$tThe West to 1550 -- $tTransmission from the Arab World -- $tAn Example of Transmission: Practical Geometry -- $tText 5.1 Hugh of St. Victor, Using an Astrolabe to Find the Height of an Object -- $tText 5.2 Finding the Time of Day from the Altitude of the Sun -- $tConsolidation and the Beginnings of Innovation: The Trigonometry of Levi ben Gerson, Richard of Wallingford, and John of Murs -- $tText 5.3 Levi ben Gerson, The Best Step Size for a Sine Table -- $tText 5.4 Richard of Wallingford, Finding Sin(1 degree) with Arbitrary Accuracy -- $tInterlude: The Marteloio in Navigation -- $tText 5.5 Michael of Rhodes, a Navigational Problem from His Manual -- $tFrom Ptolemy to Triangles: John of Gmunden, Peurbach, Regiomontanus -- $tText 5.6 Regiomontanus, Finding the Side of a Rectangle from Its Area and Another Side -- $tText 5.7 Regiomontanus, the Angle-angle-angle Case of Solving Right Triangles -- $tSuccessors to Regiomontanus: Werner and Copernicus -- $tText 5.8 Copernicus, the Angle-angle-angle Case of Solving Triangles -- $tText 5.9 Copernicus, Determining the Solar Eccentricity -- $tBreaking the Circle: Rheticus, Otho, Pitiscus and the Opus Palatinum.
520 1 $a"The Mathematics of the Heavens and the Earth is the first major history in English of the origins and early development of trigonometry. Glen Van Brummelen identifies the earliest known trigonometric precursors in ancient Egypt, Babylon, and Greece, and he examines the revolutionary discoveries of Hipparchus, the Greek astronomer believed to have been the first to make systematic use of trigonometry in the second century BC while studying the motions of the stars. The book traces trigonometry's development into a full-fledged mathematical discipline in India and Islam; explores its applications to such areas as geography and seafaring navigation in the European Middle Ages and Renaissance; and shows how trigonometry retained its ancient roots at the same time that it became an important part of the foundation of modern mathematics."--BOOK JACKET.
650 0 $aTrigonometry$xHistory.
852 00 $bglx$hQA24$i.V36 2009