skip to content
The mathematics of the heavens and the earth : the early history of trigonometry Preview this item
ClosePreview this item
Checking...

The mathematics of the heavens and the earth : the early history of trigonometry

Author: Glen Van Brummelen
Publisher: Princeton : Princeton University Press, 2009.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Presents the history in English of the origins and early development of trigonometry. This book identifies the earliest known trigonometric precursors in ancient Egypt, Babylon, and Greece, and  Read more...

Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Istoric
Document Type: Book
All Authors / Contributors: Glen Van Brummelen
ISBN: 9780691129730 0691129738
OCLC Number: 895379100
Notes: Cu portretul autorului.
CST2013.
Description: XVII, 329 p. : fig., graf., tab. ; 24 cm
Contents: Preface xi The Ancient Heavens 1 Chapter 1: Precursors 9 What Is Trigonometry? 9 The Seqed in Ancient Egypt 10 * Text 1.1 Finding the Slope of a Pyramid 11 Babylonian Astronomy, Arc Measurement, and the 360 Circle 12 The Geometric Heavens: Spherics in Ancient Greece 18 A Trigonometry of Small Angles? Aristarchus and Archimedes on Astronomical Dimensions 20 * Text 1.2 Aristarchus, the Ratio of the Distances of the Sun and Moon 24 Chapter 2: Alexandrian Greece 33 Convergence 33 Hipparchus 34 A Model for the Motion of the Sun 37 * Text 2.1 Deriving the Eccentricity of the Sun's Orbit 39 Hipparchus's Chord Table 41 The Emergence of Spherical Trigonometry 46 Theodosius of Bithynia 49 Menelaus of Alexandria 53 The Foundations of Spherical Trigonometry: Book III of Menelaus's Spherics 56 * Text 2.2 Menelaus, Demonstrating Menelaus's Theorem 57 Spherical Trigonometry before Menelaus? 63 Claudius Ptolemy 68 Ptolemy's Chord Table 70 Ptolemy's Theorem and the Chord Subtraction/Addition Formulas 74 The Chord of 1 76 The Interpolation Table 77 Chords in Geography: Gnomon Shadow Length Tables 77 * Text 2.3 Ptolemy, Finding Gnomon Shadow Lengths 78 Spherical Astronomy in the Almagest 80 Ptolemy on the Motion of the Sun 82 * Text 2.4 Ptolemy, Determining the Solar Equation 84 The Motions of the Planets 86 Tabulating Astronomical Functions and the Science of Logistics 88 Trigonometry in Ptolemy's Other Works 90 * Text 2.5 Ptolemy, Constructing Latitude Arcs on a Map 91 After Ptolemy 93 Chapter 3: India 94 Transmission from Babylon and Greece 94 The First Sine Tables 95 Aryabhata's Difference Method of Calculating Sines 99 * Text 3.1 Aryabhata, Computing Sines 100 Bhaskara I's Rational Approximation to the Sine 102 Improving Sine Tables 105 Other Trigonometric Identities 107 * Text 3.2 Varahamihira, a Half-angle Formula 108 * Text 3.3 Brahmagupta, the Law of Sines in Planetary Theory? 109 Brahmagupta's Second-order Interpolation Scheme for Approximating Sines 111 * Text 3.4 Brahmagupta, Interpolating Sines 111 Taylor Series for Trigonometric Functions in Madhava's Kerala School 113 Applying Sines and Cosines to Planetary Equations 121 Spherical Astronomy 124 * Text 3.5 Varahamihira, Finding the Right Ascension of a Point on the Ecliptic 125 Using Iterative Schemes to Solve Astronomical Problems 129 * Text 3.6 Paramesvara, Using Fixed-point Iteration to Compute Sines 131 Conclusion 133 Chapter 4: Islam 135 Foreign Junkets: The Arrival of Astronomy from India 135 Basic Plane Trigonometry 137 Building a Better Sine Table 140 * Text 4.1 Al-Samaw'al ibn Yahya al-Maghribi, Why the Circle Should Have 480 Degrees 146 Introducing the Tangent and Other Trigonometric Functions 149 * Text 4.2 Abu'l-Rayhan al-Biruni, Finding the Cardinal Points of the Compass 152 Streamlining Astronomical Calculation 156 * Text 4.3 Kushyar ibn Labban, Finding the Solar Equation 156 Numerical Techniques: Approximation, Iteration, Interpolation 158 * Text .4 Ibn Yunus, Interpolating Sine Values 164 Early Spherical Astronomy: Graphical Methods and Analemmas 166 * Text 4.5 Al-Khwarizmi, Determining the Ortive Amplitude Geometrically 168 Menelaus in Islam 173 * Text 4.6 Al-Kuhi, Finding Rising Times Using the Transversal Theorem 175 Menelaus's Replacements 179 Systematizing Spherical Trigonometry: Ibn Mucadh's Determination of the Magnitudes and Nasir al-Din al-Tusi's Transversal Figure 186 Applications to Religious Practice: The Qibla and Other Ritual Needs 192 * Text 4.7 Al-Battani, a Simple Approximation to the Qibla 195 Astronomical Timekeeping: Approximating the Time of Day Using the Height of the Sun 201 New Functions from Old: Auxiliary Tables 205 * Text 4.8 Al-Khalili, Using Auxiliary Tables to Find the Hour-angle 207 Trigonometric and Astronomical Instruments 209 * Text 4.9 Al-Sijzi (?), On an Application of the Sine Quadrant 213 Trigonometry in Geography 215 Trigonometry in al-Andalus 217 Chapter 5: The West to 1550 223 Transmission from the Arab World 223 An Example of Transmission: Practical Geometry 224 * Text 5.1 Hugh of St. Victor, Using an Astrolabe to Find the Height of an Object 225 * Text 5.2 Finding the Time of Day from the Altitude of the Sun 227 Consolidation and the Beginnings of Innovation: The Trigonometry of Levi ben Gerson, Richard of Wallingford, and John of Murs 230 * Text 5.3 Levi ben Gerson, The Best Step Size for a Sine Table 233 * Text 5.4 Richard of Wallingford, Finding Sin(1 ) with Arbitrary Accuracy 237 Interlude: The Marteloio in Navigation 242 * Text 5.5 Michael of Rhodes, a Navigational Problem from His Manual 244 From Ptolemy to Triangles: John of Gmunden, Peurbach, Regiomontanus 247 * Text 5.6 Regiomontanus, Finding the Side of a Rectangle from Its Area and Another Side 254 * Text 5.7 Regiomontanus, the Angle-angle-angle Case of Solving Right Triangles 255 Successors to Regiomontanus: Werner and Copernicus 264 * Text 5.8 Copernicus, the Angle-angle-angle Case of Solving Triangles 267 * Text 5.9 Copernicus, Determining the Solar Eccentricity 270 Breaking the Circle: Rheticus, Otho, Pitiscus and the Opus Palatinum 273 Concluding Remarks 284 Bibliography 287 Index 323
Responsibility: Glen van Brummelen.

Reviews

Editorial reviews

Publisher Synopsis

"Fans of the history of mathematics will be richly rewarded by this exhaustively researched book, which focuses on the early development of trigonometry... Finally, the generous and lucid Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/895379100> # The mathematics of the heavens and the earth : the early history of trigonometry
    a schema:CreativeWork, schema:Book ;
   library:oclcnum "895379100" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nju> ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/891613970#Place/princeton> ; # Princeton
   schema:about <http://experiment.worldcat.org/entity/work/data/891613970#Topic/istoria_matematicii> ; # Istoria matematicii
   schema:about <http://experiment.worldcat.org/entity/work/data/891613970#Topic/trigonometrie> ; # Trigonometrie
   schema:about <http://experiment.worldcat.org/entity/work/data/891613970#Topic/astronomie_sferica> ; # Astronomie sferică
   schema:bookFormat bgn:PrintBook ;
   schema:creator <http://experiment.worldcat.org/entity/work/data/891613970#Person/van_brummelen_glen> ; # Glen Van Brummelen
   schema:datePublished "2009" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/891613970> ;
   schema:inLanguage "en" ;
   schema:name "The mathematics of the heavens and the earth : the early history of trigonometry" ;
   schema:numberOfPages "329" ;
   schema:productID "895379100" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/895379100#PublicationEvent/princeton_princeton_university_press_2009> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/891613970#Agent/princeton_university_press> ; # Princeton University Press
   schema:workExample <http://worldcat.org/isbn/9780691129730> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/895379100> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/891613970#Agent/princeton_university_press> # Princeton University Press
    a bgn:Agent ;
   schema:name "Princeton University Press" ;
    .

<http://experiment.worldcat.org/entity/work/data/891613970#Person/van_brummelen_glen> # Glen Van Brummelen
    a schema:Person ;
   schema:familyName "Van Brummelen" ;
   schema:givenName "Glen" ;
   schema:name "Glen Van Brummelen" ;
    .

<http://experiment.worldcat.org/entity/work/data/891613970#Topic/astronomie_sferica> # Astronomie sferică
    a schema:Intangible ;
   schema:name "Astronomie sferică" ;
    .

<http://experiment.worldcat.org/entity/work/data/891613970#Topic/istoria_matematicii> # Istoria matematicii
    a schema:Intangible ;
   schema:name "Istoria matematicii" ;
    .

<http://worldcat.org/isbn/9780691129730>
    a schema:ProductModel ;
   schema:isbn "0691129738" ;
   schema:isbn "9780691129730" ;
    .

<http://www.worldcat.org/title/-/oclc/895379100>
    a genont:InformationResource, genont:ContentTypeGenericResource ;
   schema:about <http://www.worldcat.org/oclc/895379100> ; # The mathematics of the heavens and the earth : the early history of trigonometry
   schema:dateModified "2017-01-18" ;
   void:inDataset <http://purl.oclc.org/dataset/WorldCat> ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.