The famous Part of Fortune used by Ptolemy, and the so-called "Arabian" or Arabic Parts are fictitious points calculated with the longitudes of three planets, angles or zodiacal points, most often following the formula:
Part = ASC + Planet X - Planet Y
Here is a list of a few Arabian/Arabic Parts described in one of the numerous articles written by the French scholar Patrice Guinard. Sometimes, over 150 Parts were used.
The calculation should be different for diurnal charts (with the Sun above the horizon, i.e. the Ascendant-Descendant axis) and for nocturnal charts (with the Sun below the horizon). According to Paul of Alexandria, Parts in diurnal charts are calculated as follows (for nocturnal charts, the + and - signs are to be reversed):
- Part of Fortune for diurnal charts = ASC + Moon - Sun (the position of the Moon at sunrise). This is the basic formula.
- Part of Fortune for nocturnal charts = ASC - Moon + Sun (the position of the Moon at sunrise). This is the advanced formula: the Part of Fortune is different for nocturnal charts. Astrotheme uses the advanced method for all charts and reports.
- Part of Spirit (Daimon) = ASC + Sun - Moon (the reverse of the preceding formula: the position of the Sun when the Moon rises).
- Part of Eros = ASC + Venus - Part of Spirit = Venus + Moon - Sun (the position of Venus when the Moon and the Sun are in conjunction).
- Part of Victory = ASC + Jupiter - Part of Spirit = Jupiter + Moon - Sun
- Part of Necessity = ASC + Part of Fortune - Mercury
- Part of Courage = ASC + Part of Fortune - Mars
- Part of Nemesis (Justice, Fairness) = ASC + Part of Fortune - Saturn.
More Parts according to Paul of Alexandria and others:
- Part of the Father= ASC + Saturn - Sun (nocturnal charts: invert).
- Part of the Mother= ASC + Moon - Venus (nocturnal charts: invert).
- Part of Siblings= ASC + Jupiter - Saturn (= nocturnal charts).
- Part of Children= ASC - Jupiter + Saturn (= nocturnal charts).
- Part of Marriage (man) = ASC + Venus - Saturn (= nocturnal charts).
- Part of Marriage (woman) = ASC - Venus + Saturn (= nocturnal charts).
According to Vettius Valens and the Liber Hermetis:
- Part of Debt = ASC + Saturn - Mercury (= nocturnal charts).
- Part of Foundation = ASC + Part of Fortune - Part of Spirit (= nocturnal charts).
- Part of Thief = Saturn + Mars - Mercury (nocturnal charts, invert).
- Part of Treachery= ASC + Mars - Sun (nocturnal charts, invert).
- Part of Difficulty= ASC + Mars - Saturn (nocturnal charts, invert).
- Part of Exaltation of the Nativity= ASC + 19° Aries - Sun (nocturnal charts = ASC + 3° Taurus. 19° Aries and 3° Taurus are believed to be the exaltation points of the Sun and the Moon, respectively.).