Preface

List of Abbreviations

I. Dashagitika or the Ten Giti Stanzas

**A. Invocation**

**B. System of Expressing Numbers by Letters of Alphabet**

1. Revolutions of Sun, Moon, Earth, and Planets in a Yuga

2. Revolutions of Apsis of Moon, Conjunctions of Planets, and Node of Moon in a yuga; Time and Place from Which Revolutions Are to Be Calculated

3. Number of Manus in a Kalpa; Number of Yugas in Period of a Manu; Part of Kalpa Elapsed up to Bharata Battle

4. Divisions of Circle; Circumference of Sky and Orbits of Planets in Yojanas; Earth Moves One Kala in a Prana; Orbit of Sun One-sixtieth that of Asterisms

5. Length of Yojana; Diameters of Earth, Sun, Moon, Meru, and Planets; Number of Years in a Yuga

6. Greatest Declination of Ecliptic; Greatest Deviation of Moon and Planets from Ecliptic; Measure of a nri

7. Positions of Ascending Nodes of Planets, and of Apsides of Sun and Planets

8-9. Dimensions of Epicycles of Apsides and Conjunctions of Planets; Circumference of Earth-Wind

10. Table of Sine-Differences

**C. Colophon**

**II. Ganitapada or Mathematics**

1. Invocation

2. Names and Values of Classes of Numbers Increasing by Powers of Ten

3. Definitions of Square (Varga) and Cube (Ghana)

4. Square Root

5. Cube Root

6. Area of Triangle; Volume of Pyramid

7. Area of Circle; Volume of Sphere

8. Area of Trapezium; Length of Perpendiculars from Intersection of Diagonals to Parallel Sides

9. Area of Any Plane Figure; Chord of One-sixth Circumference Equal to Radius

10. Relation of Circumference of Circle to Diameter

11. Method of Constructing Sines by Forming Triangles and Quadrilaterals in Quadrant of Circle

12. Calculation of Table of Sine-Differences from First One

13. Construction of Circles, Triangles, and Quadrilaterals; Determination of Horizontal and Perpendicular

14. Radius of Khavritta (or Svavritta); Hypotenuse of Right-Angle Triangle Formed by Gnomon and Shadow

15-16. Shadow Problems

17. Hypotenuse of Right-Angle Triangle; Relation of Half-Chord to Segments of Diameter Which Bisects Chord

18. Calculation of Sampatasharas When Two Circles Intersect

19-20. Arithmetical Progression

21. Sum of Series Formed by Taking Sums of Terms of an Arithmetical Progression

22. Sums of Series Formed by Taking Squares and Cubes of Terms of an Arithmetical Progression

23. Product of Two Factors Half the Difference between Square of Their Sum and Sum of Their Squares

24. To Find Two Factors When Product and Difference Are Known

25. Interest

26. Rule of Three (Proportion)

27. Fractions

28. Inverse Method

29. To Find Sum of Several Numbers When Results Obtained by Subtracting Each Number from Their Sum Are Known

30. To Find Value of Unknown When Two Equal Quantities Consist of Knowns and Similar Unknowns

31. To Calculate Their Past and Future Conjunctions from Distance between Two Planets

32-33. Indeterminate Equations of First Degree (kuttaka)

**III. Kalakriya or the Reckoning of Time**

1-2. Divisions of Time; Divisions of Circle Correspond

3. Conjunctions and Vyatipatas of Two Planets in a Yuga

4. Number of Revolutions of Epicycles of Planets; Years of Jupiter

5. Definition of Solar Year, Lunar Month, Civil Day, and Sidereal Day

6. Intercalary Months and Omitted Lunar Days

7-8. Year of Men, Fathers, and Gods; Yuga of All the Planets; Day of Brahman

9. Utsarpini; Avasarpini, Sushama, and Dushshama as Divisions of Yuga

10. Date of Writing of Aryabhatiya; Age of Author at Time

11. Yuga, Year, Month, and Day Began at First of Caitra; Endless Time Measured by Movements of Planets and Asterisms

12. Planets Move with Equal Speed; Time in Which They Traverse Distances Equal to Orbit of Asterisms and Circumference of Sky

13. Periods of Revolution Differ because Orbits Differ in Size

14. For Same Reason Signs, Degrees, and Minutes Differ in Length

15. Order in Which Orbits of Planets Are Arranged (beneath the Asterisms) around Earth as Center

16. Planets as “Lords of Days” (of Week)

17. Planets Move with Their Mean Motion on Orbits and Eccentric Circles Eastward from Apsis and Westward from Conjunction

18-19. Eccentric Circle Equal in Size to Orbit; Its Center Distant from Center of Earth by Radius of Epicycle

20. Movement of Planet on Epicycle; When ahead of and When behind Its Mean Position

21. Movement of Epicycles; Mean Planet (on Its Orbit) at Center of Epicycle

22-24. Calculation of True Places of Planets from Mean Places

25. Calculation of True Distance between Planet and Earth

**IV. Gola or the Sphere**

1. Zodiacal Signs in Northern and Southern Halves of Ecliptic; Even Deviation of Ecliptic from Equator

2. Sun, Nodes of Moon and Planets, and Earth’s Shadow Move along Ecliptic

3. Moon, Jupiter, Mars, and Saturn Cross Ecliptic at Their Nodes; Venus and Mercury at Their Conjunctions

4. Distance from Sun at Which Moon and Planets Become Visible

5. Sun Illumines One Half of Earth, Planets, and Asterisms; Other Half Dark

6-7. Spherical Earth, Surrounded by Orbits of Planets and by Asterisms, Situated in Center of Space; Consists of Earth, Water, Fire, and Air

8. Radius of Earth Increases and Decreases by a Yojana during Day and Night of Brahman

9. At Equator Stationary Asterisms Seem To Move Straight Westward; Simile of Moving Boat and Objects on Shore

10. Asterisms and Planets, Driven by Provector Wind, Move Straight Westward at Equator — Hence Rising and Setting

11-12. Mount Meru and VaçavÀmukha (North and South Poles); Gods and Demons Think the Others beneath Them

13. Four Cities on Equator a Quadrant Apart; Sunrise at First Is Midday, Sunset — Midnight at Others

14. Lanka (on Equator) 90A from Poles; Ujjain 22½A North of Lanka

15. From Level Place Half of Stellar Sphere minus Radius of Earth Is Visible; Other Half plus Radius of Earth Is Cut Off by Earth

16. At Meru and Vadavamukha Northern and Southern Halves of Stellar Sphere Visible Moving from Left to Right or Vice Versa

17. At Poles the Sun, after It Rises, Visible for Half-Year; on Moon the Sun Visible for Half a Lunar Month

18. Definition of Prime Vertical, Meridian, and Horizon

19. East and West Hour-Circle Passing through Poles (Unmandala)

20. Prime Vertical, Meridian, and Perpendicular from Zenith to Nadir Intersect at Place Where Observer Is

21. Vertical Circle Passing through Planet and Place Where Observer Is (Drinmandala); Vertical Circle Passing through Nonagesimal Point (Drikkshpamandala)

22. Construction of Wooden Globe Caused to Revolve so as to Keep Pace with Revolutions of Heavenly Bodies

23. Heavenly Bodies Depicted on This; Equinoctial Sine (Sine of Latitude) Is Base; Sine of Colatitude (Shanku at Midday of Equinoctial Day) Is Koti (Perpendicular to Base)

24. Radius of Day-Circle

25. Right Ascension of Signs of Zodiac

26. Earth-Sine Which Measures Increase and Decrease of Day and Night

27. Oblique Ascension of Signs of Zodiac

28. Shanku of Sun (Sine of Altitude on Vertical Circle Passing through Sun) at Any Given Time

29. Base of shanku (Distance from Rising and Setting Line)

30. Amplitude of Sun (agra)

31. Sine of Altitude of Sun When Crossing Prime Vertical

32. Midday Shanku and Shadow

33. Sine of Ecliptic Zenith-Distance (Drikkshepajya)

34. Sine of Ecliptic Altitude (Driggatijya); Parallax

35-36. Drikkarman (Aksha and Ayana)

37. Moon Causes Eclipse of Sun; Shadow of Earth Causes Eclipse of Moon

38. Time at Which Eclipses Occur

39. Length of Shadow of Earth

40. Diameter of Earth’s Shadow in Orbit of Moon

41. Sthityardha (Half of Time from First to Last Contact)

42. Vimardardha (Half of Time of Total Obscuration)

43. Part of Moon Which is Not Eclipsed

44. Amount of Obscuration at any Given Time

45. Valana

46. Color of Moon at Different Parts of Total Eclipse

47. Eclipse of Sun Not Perceptible if Less than One-eighth Obscured

48. Sun Calculated from Conjunction (Yoga) of Earth and Sun, Moon from Conjunction of Sun and Moon, and Other Planets from Conjunction of Planet and Moon

49-50. Colophon

General Index

Sanskrit Index