What is the calculated estate value when applying the third ruling concerning proportional bequests involving circular dependency (dawr)?
General Chapter
Al-Mughni
Book of Bequests
Primary text
When the third ruling is applied, the total estate value must be determined through complex calculations to resolve the circular dependency. One method involves taking the denominator of the fraction bequeathed from the remainder, subtracting one share to find the basis for the heir's portion, and then using the number of sons plus one to determine the multiplier for the denominator, resulting in the total estate size. Another method involves adding half a share to the sons' shares and multiplying by the denominator. A third method, called the inverted method (al-mankus), calculates the whole by determining what the remaining portion represents relative to the part taken.
Supporting text
A fourth method involves algebraic determination (al-jabr) where an assumed total estate is reduced by the first bequest, half of the remainder is given to the second legatee, and the resulting remainder (which equals three shares) is adjusted by adding back half of the initial bequest share to determine the total estate size, which settles at seven parts.