To help keep track of my working through the Almagest, below is an index of posts, grouped by book and chapter.
Book I
Chapters 1 – 9 – Preliminary Statements
Chapter 10 – Deriving the Chord Table
- Special Angle Chords
- Ptolemy’s Theorem
- Corollaries to Ptolemy’s Theorem
- Aristarchus’ Inequality and the Chords of 1º & ½º
Chapter 11 – Table of Chords
Chapter 12 – Obliquity of the Ecliptic
Chapter 13 – Lemmas for Spherical Trigonometry
- Triangular Lemmas for Spherical Trigonometry
- Circular Lemmas for Spherical Trigonometry
- Menelaus’ Theorem
- Exploring Menelaus’ Theorem
Chapter 14 – Arcs Between Celestial Equator and Ecliptic
Chapter 15 – Table of Inclinations
Chapter 16 – Rising Times at Sphaera Recta
Book II
Chapter 1 – On the General Location of Our Part of the World
Chapter 2 – Length of Longest Day → Arc of Horizon Between Equator & Ecliptic
Chapter 3 – Length of Longest Day → Elevation of Pole/Latitude
- From Length of Longest Day Finding Elevation of the Pole
- Difference Between Length of Solstice Day vs Equinox From Latitude
- Symmetries of Arcs and Day/Night Lengths
Chapter 4 – How to Compute When, Where, and How Often the Sun Reaches the Zenith
Chapter 5 – Ratios of Gnomon Equinoctial and Solstical Noon Shadows
Chapter 6 – Special Characteristics by Latitude
Chapter 7 – On Simultaneous Risings of Arcs of the Ecliptic and Equator at Sphaera Obliqua
- Arcs of the Ecliptic Equidistant from the Same Equinox
- Arcs of the Ecliptic Equidistant from the Same Solstice
- Rising Times of the Ecliptic at Sphaera Obliqua (Part 1)
- Rising Times of the Ecliptic at Sphaera Obliqua (Part 2)
- Ascensional Difference
- Rising Times of the Ecliptic at Sphaera Obliqua (Part 3)
Chapter 8 – Table of Rising times at 10º Intervals
Chapter 9 – On the Particular Features Which Follow from the Rising Time Tables
Chapter 10 – Angles Between Ecliptic and Meridian
Chapter 11 – Angles Between Ecliptic and Horizon
Chapter 12 – Angles Between Ecliptic and Altitude Circle
Chapter 13 – Table of Zenith Distances and Ecliptic Angles
Book III
Chapter 1 – On the Length of the Year
Chapter 2 – Table of the Mean Motion of the Sun
Chapter 3 – On Hypotheses for Uniform Circular Motion
- Introduction to the Eccentric and Epicyclic Models
- Similarities in Time Between Apogee and Mean Between Models
- Similarities in the Equation of the Anomaly
- Similarities in Apparent Apogee and Perigee Distances
Chapter 4 – On The Anomaly of the Sun
Chapter 5 – On the Construction of a Table of the Equation of Anomaly
- Equation from Apogee using Eccentric Hypothesis
- Equation from Apogee using Epicyclic Hypothesis
- Equation from Perigee using Eccentric Hypothesis
- Equation from Perigee using Epicyclic Hypothesis
Chapter 6 – Table of the Sun’s Anomaly
Chapter 7 – Epoch of Solar Mean Motion
Chapter 8 – On the Calculation of the Solar Position
Chapter 9 – On the inequality of the [Solar] Days
Book IV
Chapter 1 – Observations Necessary to Examine Lunar Phenomena
Chapter 2 – On Periods of the Moon
- Mean Periods of the Moon
- Solar Anomaly and Lunar Periods
- Lunar Anomaly and Eclipses
- Favorable Positions for Lunar Eclipse Pairs
Chapter 3 – On the Individual Mean Motions of the Moon
Chapter 4 – Tables of the Mean Motions of the Moon
Chapter 5 – In the Simple Hypothesis of the Moon, the Same Phenomena are Produced by Both the Eccentric and Epicyclic Hypotheses
Chapter 6 – Demonstration of the First, Simple Anomaly of the Moon
- Babylonian Eclipse Triple – Solar/Lunar Positions & Epicyclic Anomaly
- Babylonian Eclipse Triple – Radius of the Epicycle
- Babylonian Eclipse Triple – Equation of Anomaly & The Mean Moon
- Alexandrian Eclipse Triple – Solar/Lunar Positions & Epicyclic Anomaly
- Alexandrian Eclipse Triple – Radius of the Epicycle
- Alexandrian Eclipse Triple – Equation of Anomaly & The Mean Moon
Chapter 7 – Correction of Mean Motion in Longitude and Anomaly
Chapter 8 – The Epoch of the Mean Motions in Longitude and Anomaly
Chapter 9 – Correction of the Mean Position in Latitude and its Epoch
Chapter 10 – Table of the Lunar Equation of Anomaly (First Anomaly)
Chapter 11 – Hipparchus’ Two Determinations of the Lunar Anomaly
Book V
Chapter 1 – On the Construction and Use of an Astrolabe
Chapter 2 – Model for the Second Anomaly
Chapter 3 – Size of the Second Anomaly
Chapter 4 – Ratio of the Eccentricity of the Moon’s Circle
Chapter 5 – On the Direction of the Moon’s Epicycle
Chapter 6 – Geometrical Calculation of Lunar Position
Chapter 7 – Construction of a table for Complete Lunar Anomaly
Chapter 8 – Table of Complete Lunar Anomaly
Chapter 9 – On the Complete Calculation of the Moon’s Position
Chapter 10 – The Difference at Syzygies Due to the Eccentre is Negligible
Chapter 11 – On Lunar Parallax
Chapter 12 – On the Construction of a Parallactic Instrument
Chapter 13 – Demonstration of the Distances of the Moon
Chapter 14 – On the Ratio of the Apparent Diameters of Sun, Moon, and Shadow at Syzygies
Chapter 15 – On the Distance of the Sun and Other Consequences of the Demonstration of That
Chapter 16 – On the Sizes of Sun, Moon, and Earth
Chapter 17 – On the Individual Parallaxes of the Sun and Moon
- Parallaxes of Sun and Moon
- Lunar Distance Adjustments for Epicycle
- Lunar Distance Adjustments for Eccentre
Chapter 18 – Table of the Total Parallax for Sun and Moon
Chapter 19 – On the Determination of Parallaxes
- Calculating Lunar Parallax Along Great Circle Through Zenith
- Calculating Solar Parallax Along Great Circle Through Zenith
- Components of Parallax
- Corrections to Parallax Calculation
- Correction to Parallax Example
Book VI
Chapter 1 – On Conjunctions and Oppositions of the Sun and Moon
Chapter 2 – Construction of the Tables of Mean Syzygies
Chapter 3 – Tables of Conjunctions and Oppositions
Chapter 4 – How to Determine the Mean and True Syzygies
Chapter 5 – On the Ecliptic Limits of Sun and Moon
- Lunar Diameter and Earth’s Shadow at Perigee During Syzygy
- Lunar Eclipse Limits
- Solar Eclipse Limits – Latitudinal Parallax
- Solar Eclipse Limits – Longitudinal Parallax
- Solar Eclipse Limits – Solar & Lunar Anomaly
Chapter 6 – On the Interval of Months Between Eclipses
- Solar and Lunar Eclipses Separated by Six Months
- Lunar Eclipses Separated by Five Months
- Lunar Eclipses Separated by Seven Months
- Solar Eclipses Separated by Five Months
- Solar Eclipses Separated by Seven Months
- Solar Eclipses Separated by One Month
Chapter 7 – Construction of the Eclipse Tables
- Solar Eclipse Tables
- Lunar Eclipse Tables
- Table of Eclipse Correction
- Table of Magnitudes – Solar Example
- Table of Magnitudes – Lunar Example
Chapter 8 – Eclipse Tables
Chapter 9 – Determination of Lunar Eclipses
Chapter 10 – Determination of Solar Eclipses
Chapter 11 – On the Angles of Inclination at Eclipses
Chapter 12 – Display of Diagrams for the Inclinations
Chapter 13 – Determination of the Inclinations
Book VII
Chapter 1 – That the Fixed Stars Always Maintain the Same Position Relative to Each Other
Chapter 2 – That the Sphere of the Fixed Stars, Too, Performs a Rearward Motion Along the Ecliptic
Chapter 3 – That the Rearward Motion of the Sphere of Fixed Stars, too, Takes Place About the Poles of the Ecliptic
- On the Poles of Precession
- On the Rate of Precession from Hipparchus’ Time
- On the Rate of Precession from Other Greek Astronomers
Chapter 4 – On the Method Used to Record [the Positions of] the Fixed Stars
Chapter 5 – The Star Catalog
NOTE: The authorship of the star catalog is in serious question. I have a series of posts exploring this topic, an index of which can be found here. For a more condensed version, see my article in Universe Today.
Book VIII
Chapter 2 – On the Situation of the Circle of the Milky Way
Chapter 3 – On the Construction of a Solid Globe
Chapter 4 – On the Configurations Particular to the Fixed Stars
Chapter 5 – On the Simultaneous Risings, Culminations, and Settings of the Fixed Stars
Chapter 6 – On the First and Last Visibilities of the Fixed Stars
Book IX
Chapter 1 – On the Order of the Spheres of the Sun, Moon, and the Five Planets
Chapter 2 – On Our Purpose in the Hypotheses of the Planets
Chapter 3 – On the Periodic Returns of the Five Planets
Chapter 4 – Tables of Mean Motion in Longitude and Anomaly of the Five Planets
Chapter 5 – Preliminary Notions [Necessary] for the Hypotheses of the Five Planets
Chapter 6 – On the Type and Difference Between the Hypotheses
- Model for Planets Other Than Mercury
- Model for Mercury
- Symmetries for General Planetary Model
- Symmetries for Mercury’s Model
Chapter 7 – Determination of Mercury’s Apogee from Greatest Elongations
Chapter 8 – That the Planet Mercury, Too, Comes Closest to Earth Twice in One Revolution
Chapter 9 – On the Ratio and Amount of the Anomalies of Mercury
Chapter 10 – On the Correction of the Periodic Motions of Mercury
- Position of Mercury About the Epicycle on May 17/18, 139 CE
- Position of Mercury About the Epicycle on Nov 14/15, 264 BCE
Chapter 11 – On Epoch of [Mercury’s] Periodic Motions
Book X
Chapter 1 – Demonstration of [the Position of] the Apogee of the Planet Venus
Chapter 2 – On the Size of [Venus’] Epicycle
Chapter 3 – On the ratios of the eccentricities of the planet [Venus]
Chapter 4 – On the Correction of the Periodic Motions of the Planet [Venus]
- Position of Venus about the Epicycle on Dec 15/16 138 CE
- Position of Venus about the Epicycle on Oct 10/11 271 BCE and the Motion in Anomaly
Chapter 5 – On the Epoch of [Venus’] Periodic Motions
Chapter 6 – Preliminaries for the Demonstrations Concerning the Other [Three Outer] Planets
Chapter 7 – Demonstration of the Eccentricity and Apogee [Position] of Mars
- Observations and Introduction to Iterative Calculations
- First Iteration
- Second Iteration
- Third Iteration
- Check Against Observation Intervals
Chapter 8 – Demonstration of the Size of the Epicycle of Mars
Chapter 9 – On the Correction of the Periodic Motions of Mars
Chapter 10 – On the Epoch of [Mars’] Periodic Motions
Book XI
Chapter 1 – Demonstration of the Eccentricity of Jupiter
- Jupiter’s Eccentricity
- Correction for the First Opposition
- Correction for the Second Opposition
- Correction for the Third Opposition
- Second Iteration
- Checking the Eccentricity and Apogee
Chapter 2 – Demonstration of the Size of Jupiter’s Epicycle
Chapter 3 – On the Correction of the Periodic Motions of Jupiter
Chapter 4 – On the Epoch of Jupiter’s Periodic Motions
Chapter 5 – Demonstration of Saturn’s Eccentricity and [the Position of] its Apogee
- Saturn’s Eccentricity
- Corrections for the Equant
- Second Iteration for Saturn
- Checking the Eccentricity and Apogee
Chapter 6 – Demonstration of the Size of Saturn’s Epicycle
Chapter 7 – On the Correction of Saturn’s Periodic Motions
Chapter 8 – On the Epoch of Saturn’s Periodic Motions
Chapter 9 – How the True Positions can be found Geometrically from the Periodic Motions
Chapter 10 – Method of Constructing Tables for the Anomalies
Chapter 11 – Planetary Equation Tables
Chapter 12 – On the Computation of the Longitude of the Five Planets
Reference Posts