a wife, a paternal half-sister, and a paternal uncle—four cases with a denominator of four.

An eighth and the remainder applies to a wife and a son. An eighth, a half, and the remainder applies to a wife, a daughter, and a paternal uncle. All of these have a denominator of eight. Instead of this, we may say: the denominator of an inheritance case is the least common multiple of its prescribed shares, without fractions. This is easy for anyone versed in calculation: whenever one obtains a whole number, without a fraction—one-half is based on two, one-third on three, one-quarter on four, one-sixth on six, and so on.

His statement, “These four are not subject to proportional reduction,” means that their prescribed shares never exceed the denominator of the case. They either equal its denominator, in which case the case is called equitable, or fall short of it, in which case it is called deficient; but they can never be subject to proportional reduction. Thus, two full sisters and two uterine sisters constitute an equitable case, while two full sisters and a paternal uncle constitute a deficient case, because the prescribed share is only two-thirds.

These four—the denominator of two, the denominator of three, the denominator of four, and the denominator of eight—can never be subject to proportional reduction.

His statement, “And a half with two-thirds”: the smallest number from which the shares of one-half and two-thirds can be allocated is six. An example is a woman who dies leaving a husband and two full sisters: the husband receives one-half, namely three, and the two sisters receive two-thirds, namely four. Three plus four is seven, whereas the denominator of the case is six; it is therefore subject to proportional reduction. The husband’s share then becomes three-sevenths, and the two sisters’ share becomes four-sevenths; thus, each share is reduced.

His statement, “Or a third”: one-half together with one-third is based on six, because the smallest number divisible by both a half and a third is six. An example is a deceased person leaving a full sister and a mother. The case is based on six: the full sister receives one-half, and the mother