List of Rasa'il in The Encyclopedia of The Brethren of Purity - Mathematical Sciences

Mathematical Sciences

1. Numbers, arithmetic, and numerology, especially Pythagorean; a discussion of the importance of the number four
2. Geometry (jumatriya). Euclid's definitions and how to calculate the area of a triangle
3. Ptolemaic astronomy (asturunumiya)
4. Geography (al-jughrafiya), especially geography that uses mathematics. The Brethren explain racial characteristics as resulting from varying climates' long-term influence. Interestingly, the Brethren seem to know of Japan: "The most eastern country of this climate is the island of Niphon ; then comes southern China, then the south of Ceylon, then central India, then subcentral and Sindh, then beyond the Persian Gulf the south of Oman then comes the centre of the country of Shir, then central Yaman, then across the Red Sea, central Messynia ; then across the Nile is Nubia....."
5. Music (al-musiqa) Deals with the subject in unusually many aspects. It first lays out the power of music and its uses; it uses the practical purposes of music as a defense against various Koranic proscription; another defense is that the restrictions are applicable only to entertainment and pleasure motivated music, analogous to contemporary defenses of poetry). Theologically motivated, it moves on to the abstracted essence of music, which is present in all arts.
6. Deals with ratios and proportions, which are useful in mathematics and also especially in musical scales; indeed, Thomas Davidson describes there assertion thus: "The faculty of aesthetic judgement investigates these properties, and so discovers the rules of Art." Eric van Reijn classifies this epistle as dealing with "Mathematics and Geometry".
7. The seventh and eighth epistles are the "Classification of the Sciences", or "On the scientific arts":

• The nine professional sciences are "the educational sciences, intended to help men to a maintenance, and to direct them in their intercourse with others." They are: reading and writing; grammar and language; arithmetic; sorcery and alchemy and shorthand; "Versification and poetry" or "poetry and music"; business and agriculture; "trades and professions"; selling, buying, and other things of commerce like breeding cattle; and finally, biographies and histories.
• The 6 religious sciences "help the soul in its struggle towards the other world." They consist of: learning the Koran (revelation); learning the Koran's commentaries (explanation); of the hadith and other traditions (tradition); "the knowledge of law and ordinances of God and of legal division" (law); religious obligations and asceticism; and oneiromancy ("illumination").
• The given hierarchy of philosophical sciences is complex. It appears to be as follows:
  • Mathematical sciences
    • Arithmetic
    • Geometry
    • Astronomy
    • Music
  • Logic
    • Poetry
    • Rhetoric
    • Topica
    • Analytica
    • Sophistica
  • Natural philosophy
    • "Sciences of the first principles of a body"
      • Matter
      • Shape
      • Time
      • Place
      • Motion
    • "Science of the heavens and of the universe"
      • What the heavens are made of
      • How many bodies there are in the heavens
      • Why those bodies move
      • Whether those bodies can be destroyed like mundane matter
    • "de generatione et corruptione"
      • The nature of the four elements
      • The influence of stars on the sublunary world
    • Meteorology
    • Mineralogy
    • Zoology
  • Metaphysical sciences
    • Theology
    • Knowledge of angels
    • Knowledge of dead souls
    • Knowledge of governments
    • "Science of things connected with a future state"
• "On creeds and professions"- a classification of the sciences into three categories of professional, religious, and philosophical sciences. The Brethren write:

"Know, my brother, that there are three kinds of sciences with which people are busy, namely: the propaedeutic sciences, the religious and conventional sciences, the philosophical and real sciences." This chapter deals especially with the practical arts.

9. "Where one accounts for characters, the causes of their difference and the species of the evils which them; anecdotes drawn from the educational rules of the Prophets and cream of the morals of the sages." (from Sprenger). "No. 9 examines the differences of Temperament and Character, with the view of enabling the soul to attain the proper mood and develop a perfect character. Here we have a system of Ethics." (from Thomas Davidson).

10. A summary of Porphyry's Isagoge (the Latin name for his Introduction to Categories, sometimes simply Introduction).

11. A summary of Aristotle's Categories, a portion of his Organon; it tries to encompass all things under the ten categories of Aristotle.

12. A summary of De Interpretatione, another subsection of his Organon; an essay defending the usefulness of logic in general is included after its discussion of Aristotle's propositions.

13. A summary of Prior Analytics, another work included in Aristotle's Organon

14. A summary of 'Posterior Analytics, another work included in Aristotle's Organon