the price and one-third of the sold item to its value, then the sale is valid in the amount of that ratio, which is five-sixths of it. According to the first view, the price is subtracted from the value of the sold item, and the third is related to the remainder, so the sale is valid for the amount of that ratio, which is two-thirds of it for two-thirds of the price. If the seller leaves behind another ten, then according to the first view, the sale is valid for eight-ninths of it for eight-ninths of the price. According to the second view, the buyer takes half of it and four-ninths of it for the entire price, and returns half of a ninth. If he sold a qafiz of wheat worth thirty for a qafiz worth ten, or for a qafiz worth fifteen, the view we have chosen regarding the opinion of the Qadi and those who agree with him becomes fixed; because equality here is a condition for the validity of the sale, and it is not achieved in any other way. The method of calculating it by algebra (al-jabr) when he sells it for what is worth one-third of its value is to say: The sale is valid for a 'thing' (shay') of the more expensive item for a 'thing' of the cheaper item, and its value is one-third of a 'thing', so the concession is two-thirds of a 'thing'. Subtract both from the more expensive item, and there remains one qafiz minus two-thirds of a 'thing', which equals two parts of the concession, and that is a 'thing' and one-third of a 'thing'. When you use algebra, it equals two 'things', so the 'thing' is half a qafiz.

Section: The second division, concession in marriage. If he marries a woman during his terminal illness, and the dowry (sadaq) of her equivalent is five, but he assigns her ten—while he possesses nothing else—and then he dies, if she inherits from him, the concession is void unless the rest of the heirs authorize it. If she does not inherit from him, because she differs from him in religion or otherwise, then she is entitled to her dowry and one-third of what he conceded to her. If she dies before him and he inherits from her, and she left no wealth other than what he assigned to her as a dowry, it leads to a circular dependency (dawr). The concession is valid for a 'thing', so she has five