Abú Rayḥán Bírúní says in the first chapter of his “Explanation of the Science of Astrology” (Kitábu't-Tafhím fí ṣaná'ati 't-tanjím*):

“A man does not deserve the title of Astrologer until he attains proficiency in four sciences: first, Mathematics; secondly, Arithmetic; thirdly, Cosmo­graphy; and fourthly, Judicial Astrology.”

Now Mathematical Science is that whereby are known the natures and qualities of lines and geometrical figures, plain and solid, and the general relations of quantities, and what partakes of the quantitative nature, to what has position and form. It includes the principles of the Book of Euclid the geometrician*

in the recension of Thábit ibn Qurra.*

Arithmetic is that science whereby are known the natures of all sorts of numbers;*

the nature of their relation to one another; their generation from each other; and the applications thereof, such as halving, doubling, multiplication, division, addition, subtraction, and Algebra. The principles thereof are contained in the book of the , and the applications in the “Supplement” (Takmila) of Abú Manṣúr of Baghdad,*

and the “Hundred Chapters” (Ṣad Báb) of as-Sajzí.*

Cosmography is that science whereby are known the natures of the Celestial and Terrestrial Bodies,*

their shapes and positions, their relations to one another, and the measure­ments and distances which are between them, together with the nature of the movements of each one of the stars and heavens, and the co-ordination of the spheres, axes, and circles whereby these movements are fulfilled. It includes a knowledge of the Al-Magest and the best of its com­mentaries and elucidations, which are the Commentary of Tabrízí*

and the Al-Magest of Shifá. And amongst the applications of this science is the science of the Calendar and of Almanacs.

Judicial Astrology is a branch of Natural Science, and its special use is prognostication, by which is meant the deducing by analogy from configurations, and from an estimation of the degrees and zodiacal signs and their influences, those events which are brought about by their movements, in respect to the condition of the cycles of the world, politics, cities, nativities, changes, transitions, decisions, and other questions; and it is contained in these five [books] which we have enumerated, to wit, the writings of Abú Ma'shar of Balkh,*

Aḥmad 'Abdu'l-Jalíl-i-Sajzí, Abú Rayḥán Bírúní, and Gúshyár-i-Jílí.*

So the Astrologer must be a man of acute mind, approved character, and great natural intelligence. And one of the essentials of this art is that the astrologer who would pronounce prognostications should possess in his own horoscope the Share of the Unseen, and that the Lord of the House of this Share of the Unseen should be lucky, and in a favourable position, in order that such pronounce­ments as he gives may be near the truth. And one of the conditions of being a good astrologer is that he should have in mind the whole of the “Principia” (Uṣúl) of Gúshyár, and should continually study the “Opus Majus,”*

and should look frequently into the Qánún-i-Mas'údí*

and the Jámi'-i-Sháhí, so that his knowledge and concepts may be refreshed.