(With reference to the “triangles” in the above quotation from Sachau,
it should be observed that the word in the original is
“Modus inveniendi dominum decani.”
“Et ex hoc adorogen, hoc est ut dividas ascendens in tres partes; et sit omnis divisio 10 graduum; dabisque divisionem primam domino ascendentis; et secundam domino quinti signi ab eo; et tertium domino noni; nam ascendens, 5, et 9 una semper sunt triplicitas. Verbi gratiâ, ab initio Arietis usque in decimum gradum ejus est dorogen i. (i.e.) decanus est Martis. Et si fuerit ex 10 gradu usque 20 gradum erit ejus dorongen sol, dominus Leonis. Et si fuerit 20 usque in finem ejus erit dorongen Jupiter, dominus Sagittarii.”
The same volume contains a commentary on Alchabitius by John of Saxony and at M.M. 3, we have these words, “Et ex hoc adoringen. Hic docet invenire decanum.” This commentary, it seems, was written in 1331, though apparently not printed till 1485.
The book is in the British Museum, and there is another copy of Alchabitius
and of John of Saxony's Commentary which was printed at Venice in 1521.
In this, too, we have the expression, “Et ex hoc adorogen” and “et ex hoc
adorogen.” This is the passage according to the Venetian editions of 1485
and 1521. In another edition, printed at Bologna in 1473 (B.M. press-mark
8610 d. 10.) we have the form abdorungen, but otherwise the wording is the
same. It begins, “Et ex hoc abdorungen” and lower down has the important
expression “ejus abdorungen, id est, decanus, est Mars.” The occurrence of
the letter b certainly seems to favour the supposition that the first syllable
is merely the Arabic article, the b being a misprint for l. As for the expression
et ex hoc, the explanation is that the Differentia Quarta is a glossary of astrological
terms and that et ex hoc seems a literal rendering of the Arabic
This is due, I think, to the fact that each House of a horoscope consists of about 30° i.e., of three decanates or darījāns. Hence, in mentioning the dignities or properties of a House, instead of saying darījān and darījān or using the word wajh (face) three times over, he varies the expression for the sake of euphony. What the exact etymology of the word ādarjān or darījān is, I am unable to say. The varieties of spelling lead one to suppose it a foreign word. It is clear from Alchabitius, that ādarjān or ādarajān is the proper spelling, and that the form aradjān of the Bādshāhnāma and the Dictionaries is incorrect.
Most probably the word comes from the Greek
If anything were necessary to prove that the word ādarjān is identical in meaning with wajh, facies, I think it is furnished by the fact that Haly, (i.e., Abu-l-ḥasan ‘Alī ibn Abī-'l Rajāl al-Shaibānī) in his elaborate work on astrology, says nothing about darījān or ādarjān, though he has a chapter De Faciebus or, (as the Arabic has it) Fi-l-wujūh.
Moreover Guido Bonatus has this passage (ed. Basle 1550 825) De dorungez non dico hic (the passage occurs in a chapter on the triplicities) aliquid quoniam videtur spectare ad considerationem facierum, de quibus latius ac sufficienter dictum est superius in Tractatu primo in cap. ed Faciebus.
Scaliger has yet another spelling of darījān; he calls it dorogen and says the Arabs apply the term to the dodecatemoria. (Notes on Manilius 179 1.38.) This seems to be a mistake.