"Pars Fortunae is a part of the astrological tool-kit that is amply explained in all elementary introductions in Astrology and everybody is aware that it is derived from the positions of the Sun, Moon and the Ascendant. But apart from that, all manuals maintain a stony silence about the logic, or the historical background behind it.
The Arabic parts (and Bonatti mentions about 100 of them) are in fact Egyptian in origin. They are numerological or arithmetical fictions and they have no physical basis, but are fictitious points on the ecliptic. 

"In astrology, Parts, also known as Lots, are numerous particular points in a figure derived in most cases from counting the distance in degrees in a forward direction through the signs of the zodiac between two celestial bodies in a specified order, and adding the result to the degree of the Ascendant. In rare cases, another house cusp is involved instead of the Ascendant.

"Most astrologers have encountered the Part (or Lot as the Greeks called it) of Fortune, but have little idea of what to do with it. The modern literature on the subject is of little help tending to make it an extremely abstract symbol, something "karmic." To complicate things further, it is now clear that for approximately 50% of all people the Part of Fortune is usually computed incorrectly, namely those persons born at night between sunset and sunrise. I'll come back to that in a moment.

"The term 'Arabian Parts' is misleading. The medieval Arab astrologers inherited their art from a long-established tradition, which they did much to refine and develop, but did not originate. References to the parts are found in all the major astrological texts that have survived from Greek and Roman times. One such account is given in the Mathesis of Firmicus Maternus, written in the 4th century.

" In astrology, the Part of Fortune, sometimes called Fortuna, is the most popular Arabic Part. Arabic Parts are sensitive points in a chart, and are calculated using specific formulas whereby two planets or points are added together, and a third planet or point is subtracted from that result."

"According to the system of Placidus, the lots may be defined as the points of the local space chart which, having the same declination as the point B, are as many degrees away from it in right ascension (RA), as the point C is away from a point A in oblique ascension (OA) and in the same direction. The points A and B may be planets, house cusps or even lots; the point C is usually the oriental horizon or horoscope (hor).

"Greek lots (also known as arabic parts) are sensitive points in a birth chart based upon the positions of the planets at birth, and the ascendant (with a few exceptions). The theory is that the planets in the heavens signify the more general circumstances that exist in the world at any given moment in time. What makes these planetary relationships unique to the individual is the way the individual exists in them, in relation to their ascending degree and sign.