Greek

The study of Greek was also of primary importance in the Department. The History of Ancient Mathematics and Mathematical Astronomy seems to have reached its zentih with Ptolemy's Almagest. All subsequent astronomy up till Newton was influenced by it, both in the Western and the Islamic traditions. Its importance cannot be underestimated.

Of course, there are the astounding contributions of the other Greek mathematicians, whose names hardly bear repeating. All of them either came out of or were influenced by the thought of Plato, who gave mathematics the place of importance it now occupies in (what's left of) Western Civilization.

Greek Texts Which Dr. Pingree Reccommended to / or Read with his Students (partial list - if you can contribute more, please contact me)

Mathematical Works

• The Almagest
• Scholia to the Almagest (we used photocopies of microfilm of unpublished medieval manuscripts)
• An Anonymous Prolegomenon to the Almagest (microfilm), dealing in part with sexagesimal notation
• Theon of Alexandria's Commentary on the Almagest (Rome's edition)
• The Scholia to Euclid - Heiberg
• George Pachymeres' treatment of sexagesimal fractions
  • We used a published text, whose name I will try to find.
• Gregory Chioniades Greek translation of the Arabic Zij as-Sanjari of Al-Khazini
  • We used photocopies of microfilms of three medieval manuscripts. I hope to post at least one set here in the coming months. Two of the manuscripts came from the Vatican Library, one from Florence. For more information about this work, see the the introduction to and a sample of my dissertation.(Released here under the GNU Verbatim License) The dissertation is an edition, translation and Greek to Arabic glossary of this work. Chioniades' Zij is itself a translation of an earlier Arabic work of the same title, by Al-Khazini.

Philosophical Works

• Plato's Meno
  • A famous dialogue about Plato's Theory of Recollection, and its relation to Mathematics.
• Plato's Theaetetus
  • A Platonic dialogue about the great mathematician, Theaetetus.
• Plato's Timaeus (PDF from the Million Books Project)
  • Kepler arranged his planetary orbits so that they would fit within the five regular solids when inscribed in each other, in deference to this text. Plato postulated the five regular solids were the foundation of the Universe in the Timaeus.
• Plato's Republic
  • The metaphor of the 'divided line' in this text shows the place of importance of mathematics in Plato's ontology and epistemology.
• Aristotle's De Caelo
  • Aristostole's treatment of the Universe. Among his claims are that the Earth is at the center of the Universe, motion in the sub lunar sphere is rectilinear, whereas celestial motion is circular, and that the Universe is finite. This theory is repeated almost verbatim in the opening pages of the Almagest.
• Book Lamda of the Arisotle's Metaphysics
  • Deals with the Unmoved Mover, as well as with the 5 elements. These five are earth, air, fire, water and the 'fifth essence' - of which the heavenly bodies are composed. The Greek for 'fifth essence' is pente on, which Cicero translates into Latin as quinte essens, from which English gets the term, quintessential.
• Parmenides' Way of Truth
  • Prof. Pingree hypothesized that the Greek notion that the motion of the heavenly bodies was circular could by traced back to Parmenides, who held that the One was 'circular in form'.

Books Students used for the Study of Greek

• Smyth's Greek Grammar (PDF from TextKit.com)
• Liddell and Scott's Greek Dictionary (PDF from the Million Books Project)
• Goodwin's Moods and Tenses (PDF from TextKit.com)
• Heiberg's Edition of Euclid's Elements
• Heiberg's Edition of Apollonius of Perga's Conic Sections
• Heiberg's Almagest.

Usefule Links for the Study of Greek

• TextKit
  • Contains excellent PDF copies of most of the standard Greek reference texts, including Smyth, Goodwin's Moods and Tenses, as well as a host of 'school editions' of famous texts in Greek and Latin
• Perseus
  • Contains many online texts of the standard works in Greek and Latin, as well as dictionaries, and a morphological analyzer, which will parse most common Latin and Greek words
• Logos Bible Software
  • They sell an amazing CD version of the Liddell and Scott dictionary, and will soon be selling a CD of its Latin counterpart, the Oxford Latin Dictionary
• If you have access to one of the TLG(Greek) or PHI(Latin) CDs, Diogenes is an excellent search tool