Page:The Algebra of Mohammed Ben Musa (1831).djvu/110

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comes to the advantage of the heirs collectively; and the legatee of the two-fifths receives eight-thirteenths, and the legatee of the one-fourth receives five-thirteenths from it. Constitute the shares as I have shown above, by taking twelve parts; the husband receives one-fourth of them, the mother one-sixth, and the son that which remains.^[1] Computation: You know that at all events the husband must give up one-third of his share, which consists of three parts. The mother must likewise give up one-third, of which each legatee partakes according to the proportion of his legacy. Besides, she must pay to the legatee to whom one-fourth is bequeathed, and whose legacy has been imposed on her, as much as the difference between the one-fourth and his

↑

{\tfrac {2}{5}}+{\tfrac {1}{4}}={\tfrac {8+5}{20}}={\tfrac {13}{20}}

The Husband, who would be entitled to

{\tfrac {1}{4}}

of the residue, is not charged by the Testator with any bequest.
The Mother who would be entitled to

{\tfrac {1}{6}}

of the residue, is charged with the payment of to the Legatee A.
The Son, who would be entitled to

{\tfrac {7}{12}}

of the residue, is charged with payment of

{\tfrac {2}{5}}

to the Legatee B.

The Husband contributes

{\tfrac {1}{4}}\times {\tfrac {1}{3}}=780\times {\tfrac {1}{9360}}

; retains

{\tfrac {1}{4}}\times {\tfrac {2}{3}}={\tfrac {1560}{9360}}

The Mother contributes

{\tfrac {1}{6}}[{\tfrac {1}{4}}+{\tfrac {8}{13}}\times {\tfrac {1}{3}}]=710\times {\tfrac {1}{9360}}

; retains ......

{\tfrac {850}{9360}}

The Son contributes

{\tfrac {7}{12}}[{\tfrac {2}{5}}+{\tfrac {5}{13}}\times {\tfrac {1}{3}}]=2884\times {\tfrac {1}{9360}}

; retains ......

{\tfrac {2576}{9360}}

Total contributed =

{\tfrac {4374}{9360}}

; Total retained =

{\tfrac {4986}{9360}}

$\left.{\begin{aligned}{\text{The Legatee A, to whom}}{\tfrac {1}{4}}\;{\text{is}}\\{\text{bequeathed, receives}}\end{aligned}}\right\}\;{\tfrac {5}{13}}\times {\tfrac {4374}{9360}}={\tfrac {5\times 4374}{964080}}$

$\left.{\begin{aligned}{\text{The Legatee B, to whom}}{\tfrac {2}{5}}\;{\text{is}}\\{\text{bequeathed, receives}}\end{aligned}}\right\}\;{\tfrac {8}{13}}\times {\tfrac {4374}{9360}}={\tfrac {8\times 4374}{964080}}$

[1] ${\tfrac {2}{5}}+{\tfrac {1}{4}}={\tfrac {8+5}{20}}={\tfrac {13}{20}}$
The Husband, who would be entitled to ${\tfrac {1}{4}}$ of the residue, is not charged by the Testator with any bequest.
The Mother who would be entitled to ${\tfrac {1}{6}}$ of the residue, is charged with the payment of to the Legatee A.
The Son, who would be entitled to ${\tfrac {7}{12}}$ of the residue, is charged with payment of ${\tfrac {2}{5}}$ to the Legatee B.

The Husband contributes ${\tfrac {1}{4}}\times {\tfrac {1}{3}}=780\times {\tfrac {1}{9360}}$ ; retains ${\tfrac {1}{4}}\times {\tfrac {2}{3}}={\tfrac {1560}{9360}}$

The Mother contributes ${\tfrac {1}{6}}[{\tfrac {1}{4}}+{\tfrac {8}{13}}\times {\tfrac {1}{3}}]=710\times {\tfrac {1}{9360}}$ ; retains ...... ${\tfrac {850}{9360}}$

The Son contributes ${\tfrac {7}{12}}[{\tfrac {2}{5}}+{\tfrac {5}{13}}\times {\tfrac {1}{3}}]=2884\times {\tfrac {1}{9360}}$ ; retains ...... ${\tfrac {2576}{9360}}$

Total contributed = ${\tfrac {4374}{9360}}$ ; Total retained = ${\tfrac {4986}{9360}}$

$\left.{\begin{aligned}{\text{The Legatee A, to whom}}{\tfrac {1}{4}}\;{\text{is}}\\{\text{bequeathed, receives}}\end{aligned}}\right\}\;{\tfrac {5}{13}}\times {\tfrac {4374}{9360}}={\tfrac {5\times 4374}{964080}}$
$\left.{\begin{aligned}{\text{The Legatee B, to whom}}{\tfrac {2}{5}}\;{\text{is}}\\{\text{bequeathed, receives}}\end{aligned}}\right\}\;{\tfrac {8}{13}}\times {\tfrac {4374}{9360}}={\tfrac {8\times 4374}{964080}}$

[1]

Page:The Algebra of Mohammed Ben Musa (1831).djvu/110

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