CiNii Books - Mathematical astronomy in Copernicus's De revolutionibus

1. General Introduction.- 1. Life of Nicolaus Copernicus.- Chronology of Copernicus's Life.- 2. The Astronomy of Copernicus.- Ptolemy's Astronomy in the Almagest and the Planetary Hypotheses.- Arabic Astronomy and the Mar?gha School.- European Astronomy and Regiomontanus.- Early Period to the Writing of the Commentariolus.- The Years of Observation.- De revolutionibus.- Conclusions.- 3. Texts, Editions, and Translations.- The Text of De revolutionibus.- Note on the Dating of M.- Editions and Translations.- Editions of Copernicus's Sources.- Purpose and Limitations of This Study.- 2. Trigonometry and Spherical Astronomy.- 1. Trigonometry (1,12-14).- 2. Spherical Astronomy.- Obliquity of the Ecliptic (II,2).- Ecliptic and Equatorial Coordinates (II,3-4).- Shadow Lengths (II,6).- Length of Daylight and Ascensional Corrections (II,7-8).- Oblique Ascension and Applications of Right and Oblique Ascension (II,9,11).- Intersection of Ecliptic with Horizon and Circles of Altitude (II,10,12).- 3. Risings and Settings (II,13).- 4. The Catalogue of Stars (II,14).- 3. The Motions of the Earth.- 1. Precession and Variation of Obliquity.- Statement of the Problem (III,1).- The Observational Record (III,2).- The Model (III,3-5).- Derivation of Parameters (III,6-7,9-11).- (a) The Anomaly of the Obliquity and Precession: ? and 2? (III,6).- (b) The Mean Precession: \[\overline \pi \] (III,6).- (c) The Maximum Equation of Precession: ?Pmax (III,7).- (d) Correction of the Location of ?= 0 (III,9).- (e) Limits of the Obliquity: ?min and ?max (III, 10).- (f) Epoch Positions of the Mean Precession and Anomaly: \[\overline \pi \]0 and ?0 (III,11).- The Tables and Their Use (III,6,8,12).- Verification of Precession and Obliquity.- 2. Solar Theory.- The Inequality of the Tropical Year (III, 13).- The Model for the First Inequality (III, 15).- Derivation of Eccentricity and Direction of the Apsidal Line (III,16-17).- Mean Motion, Length of Sidereal Year, Positions at Epoch (III,18-19).- The Mean Tropical Year and Mean Rate of Precession.- The Model for the Second Inequality (III,20).- Variation of the Eccentricity and Equation of the Apsidal Line (III,21).- Mean Motion of the Apogee (III,22).- Positions at Epoch (III, 19,23).- Remarks on the Second Inequality.- The Tables and Their Use (III,14,24,25).- Verification of the Solar Theory.- 3. The Equation of Time (III,26).- Supplementary Remark: The Quantity and Location of (? - ?)max.- Appendix: Copernicus's Chronology and Geography.- Chronology.- Geography.- 4. Lunar Theory and Related Subjects.- 1. The Lunar Theory.- The Problems of Ptolemy's Lunar Model (IV, 1-2).- Copernicus's Model (IV,3).- Preliminary Mean Motions (IV,4).- Observations of the Moon.- The First Inequality (IV,5).- 1. Ptolemy's Derivation.- 2. Copernicus's Derivation.- Correction of Mean Elongation and Anomaly (IV,6).- Mean Elongation and Anomaly at Epoch (IV,7).- The Second Inequality (IV,8-9).- Effect of the Second Inequality at Syzygy.- Trigonometric Computation of a Lunar Position (IV, 10).- Correction of the Mean Argument of Latitude (IV, 13).- Mean Argument of Latitude at Epoch (IV, 14).- The Tables and Their Use (IV,4,11,12).- Verification of the Lunar Theory.- 2. The Parallax and Apparent Diameter of the Sun and Moon.- Parallax of the Moon (IV,15-16).- Comment.- Distance of the Moon (IV, 17).- Hypothetical Determination of the Apparent Diameter of the Moon and Shadow (IV,18).- Solar Distance and Related Topics (IV, 19-20)..- 1. Ptolemy's Demonstration.- 2. Al-Batt?n?'s Demonstration.- 3. Copernicus's Demonstration.- Parallax and Apparent Diameter of the Sun (IV,21).- Parallax and Apparent Diameter of the Moon (IV,22).- Variation of the Shadow (IV,23).- Table of Apparent Semidiameters.- Table of Parallax and Its Use (IV,24-25).- Resolution of the Components of Parallax in Longitude and Latitude (IV,26).- Test of the Lunar Parallax (IV,27).- Comment.- 3. The Theory of Eclipses.- Mean Conjunction and Opposition (IV,28).- True Conjunction and Opposition (IV,29).- Distinction of Ecliptic Syzygies (IV,30).- Eclipse Magnitudes (IV,31).- Phases and Duration of Eclipses (IV,32).- 5. Planetary Theory of Longitude.- 1. General Considerations.- Model for the Second Anomaly (V,3).- The Problem of the First Anomaly (V,2).- Model for the First Anomaly (V,4).- The Equation of Center.- Transformations of the Complete Model and Technical Terms.- Mean Motions (V,l).- 2. The Derivation of the Elements of the Orbits of the Superior Planets.- Observations of the Superior Planets.- 1. Apparent and Mean Motion Between Oppositions.- 2. Solution for the Double Eccentricity and the Mean Eccentric Anomaly.- 3. Test of the Derived Elements.- 4. Correction of ? to ?'.- 5. Iteration.- 6. Mean Anomaly, Mean Longitude, and Longitude of Apogee.- 7. Correction of the Mean Anomaly and Positions at Epoch.- 8. Distance of the Planet and Equation of the Anomaly.- 3. The Individual Planets.- A. Saturn.- Observations.- Review of Ptolemy's Derivation (V,5).- Copernicus's Derivation (V,6).- Correction of the Mean Anomaly and Positions at Epoch (V,7-8).- Distance and Equation of the Anomaly (V,9).- B. Jupiter.- Observations.- Review of Ptolemy's Derivation (V, 10).- Copernicus's Derivation (V, 11).- Correction of the Mean Anomaly and Positions at Epoch (V,12-13).- Distance and Equation of the Anomaly (V, 14).- C. Mars.- Observations.- Review of Ptolemy's Derivation (V,15).- Copernicus's Derivation (V, 16).- Reduction and Division of the Eccentricity.- Correction of the Mean Anomaly and Positions at Epoch (V,17-18).- Distance and Equation of the Anomaly (V, 19).- Conclusion to the Superior Planets.- 4. The Inferior Planets.- A. Venus.- Development of the Model.- Observations.- Supplementary Remark: The Date of Observation (3).- Longitude of the Apsidal Line (V,20).- Radius of Orbit and Eccentricities (V,21-22).- Reduction of the Eccentricity from "Many Observations".- Correction of the Mean Anomaly and Positions at Epoch (V, 23-24).- 2. Revised Version.- 2. Original Version.- B. Mercury.- Development of the Models (V,25,32).- Observations.- Longitude of the Apsidal Line (V,26).- Radius of Orbit and Eccentricities (V,27).- Elongations at $$ \overline {\text{K}} $$ = +- 120 (V,28).- Comparison of Equations and Elongations in the Models of Ptolemy and Copernicus.- Correction of the Mean Anomaly and Positions at Epoch (V,29-31).- 1. Ancient Observation (V,29).- 2. Modern Observations (V,30).- Comment.- 3. Corrected Mean Anomaly and Positions at Epoch (V,30-31).- Conclusions to the Planets.- 5. The Tables and Their Use.- Arrangement and Computation of the Tables (V, 1,33).- Numerical Evaluation of the Correction Tables.- Calculation of Longitudes from the Tables (V,34).- Verification of the Planetary Theory.- 1. Superior Planets.- 2. Inferior Planets.- 6. Stations and Retrogradations.- Apollonius's Theorem (V,35).- Application of Apollonius's Theorem (V,36).- Original Version of V,36.- Appendix: The Distances of the Planets and Cosmology.- 6. Planetary Theory of Latitude.- General Considerations.- 1. Superior Planets.- Development of the Model (VI, 1-2).- Derivation of Parameters (VI,3).- Computation from the Model (VI,4).- 2. Inferior Planets.- Development of the Model (VI, 1-2).- Note on Technical Terms.- Derivation of Parameters and Computation from the Model.- A. Inclination, ?1 and i1 (VI,5).- B. Slant, ?2 and i2 (VI,6-7).- C. Deflection, ?3 and i3 (VI,8).- 3. The Tables and Their Use (VI,9).- 5. Superior Planets.- 5. Inferior Planets.- Correct Computation of ?1 and ?2 from Copernicus's Model.- Concluding Remarks.

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Mathematical astronomy in Copernicus's De revolutionibus

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