John Quincy Adam's line of descent

Some may wonder how John Quincy Adams descends from Edward I - Eleanore of Castille
who had a son Edward III married to Isabella of France - and they had a son, Edward III (1312-1377) m. Philippa of Hainault (1311-1369)

2. John of Gaunt Duke of Lancaster (1340-1398)
m(3) Catherine Swynford ROET (1350-1403)
3. Henry Beaufort, Cardinal (1375-1447) m. Alice FitzAlan
4. Joan BEAUFORT (1391-) m. Edward STRADLING (1380-1453)
5. Henry STRADLING (1423-) m. Elizabeth HERBERT
6. Thomas STRADLING (1454-1480) m. Janet MATHEW (-1485)
7. Jane STRADLING (1477-1520) m. William GRIFFITH
8. Dorothy GRIFFITH m. William WILLIAMS
9. Jane WILLIAMS m. William COYTMORE
10. Rowland COYTMORE (-1626) m. Katherine MILES (-1659)
11. Elizabeth COYTMORE (1617-) m. William TYNG (1605-1653)
12. Anna TYNG (1640-1709) m. Thomas SHEPARD (1635-1677)
13. Anna (Hannah) SHEPARD (1663-1708) m. Daniel QUINCY (1651-1690)
14. John QUINCY (1689-1767) m. Elizabeth NORTON (1696-)
15. Elizabeth QUINCY (1722-1775) m. William SMITH (1707-1783)
16. Abigail SMITH (1744-1818) m. John ADAMS President (1735-1826)
17. John Quincy ADAMS President (1767-1848)

John Quincy Adams is also a descendant, of course, of Henry II and Eleanor of Aquitaine.