Hannah Arnold
Hannah Arnold, also known as Hannah Waterman King, was the grandmother of Benedict Arnolds children.
Archambaud VIII of Bourbon
Archambaud VIII of Bourbon, nicknamed "the Great", (1189–1242) was a ruler ("sire") of Bourbonnais in the modern region of Auvergne, France.
His parents were Guy II of Dampierre and Mathilde of Bourbon.
Archambaud’s first wife was Alix de Forez.
They married in 1205.
Before she was repudiated, Alix bore:
Archambaud later married Beatrice de Montluçon, who bore him;
Hubba bint Hulail
Hubba bint Hulail was the grandmother of Hashim ibn' Abd Manaf, thus the great- great- great- grandmother of the Islamic" Nabī"( Prophet) Muhammad ibn Abdullah.
Archambaud IX of Bourbon
Archambaud IX of Bourbon (died 15 January 1249), called Le Jeune ("The Young"), was a ruler (sire) of Bourbonnais in the modern region of Auvergne, France.
He was the son of Archambaud VIII of Bourbon.
He married Yolande I, Countess of Nevers.
They had:
He died in Cyprus on 15 January 1249 during the Seventh Crusade.
Matilda II, Countess of Nevers
Matilda II, Countess of Nevers( 1234/35–1262), also known as Maud of Dampierre or Mathilda II of Bourbon, was a sovereign Countess of Nevers, Countess of Auxerre, Countess of Tonnerre and Lady of Bourbon.
She was a daughter of Archambaud IX of Bourbon and Yolande de Châtillon, Countess of Nevers.
As heiress to the counties of Nevers, Auxerre and Tonnerre, she was married off to Odo, Count of Nevers, the son and heir of Hugh IV, Duke of Burgundy.
By this marriage Odo reunited two important areas that had previously been united as the Duchy of Burgundy, but he died leaving no male heirs, and so the united territory passed to his brother Robert II, Duke of Burgundy.
After her father's death Matilda also became Lady of Bourbon.
With Odo she had three children:
Anne Denman
Anne Denman( 1587–1661) was born in Olde Hall, Retford, Nottinghamshire.
Through a fortunate second marriage with Thomas Aylesbury, she became the grandmother of Lady Anne Hyde, Duchess of York and great- grandmother of Queen Mary II and Queen Anne.
Kaoru Hatoyama
After the elections of 2009, she became more widely known as the grandmother of Prime Minister Yukio Hatoyama and his politician brother Kunio Hatoyama.
Tjuyu
Tjuyu( sometimes transliterated as Thuya or Thuyu) was an Egyptian noblewoman and the mother of queen Tiye, and the wife of Yuya.
She is the grandmother of Akhenaten, and great grandmother of Tutankhamun.
Agnes of Dampierre
Agnes of Dampierre( 1237 – 7 September 1288) was Lady of Bourbon and heiress of all Bourbon estates.
She was the daughter of Archambaud IX de Dampierre and Yolande I, Countess of Nevers.
She married John of Burgundy, the son of Hugh IV, Duke of Burgundy.
Her daughter, Beatrix of Bourbon, married Robert, Count of Clermont in 1272 and their eldest son Louis I," le Boiteux" became the first Duke of Bourbon.
John of Burgundy (1231–68)
John of Burgundy( 1231 – 29 September 1268) was a Count of Charolais and Lord of Bourbon.
He was a younger son of Duke Hugh IV of Burgundy and his wife, Yolande of Dreux.
John married in February 1248 to Agnes( d. 1288), the heiress of Lord Archambaud IX of Bourbon from the House of Dampierre.
After the death of his father- in law in 1249 John became Lord of Bourbon in right of his wife.
John and Agnes had a daughter, Beatrice( d. 1310), who inherited possessions from both of her parents.
In 1272, she married the royal Prince Robert, Count of Clermont and thereby founded the Capetian dynasty of the Bourbons.

Question: Who is the paternal grandmother of Archambaud Ix Of Bourbon?
Answer: Mathilde of Bourbon