Archimedes of Syracuse: Leonardo da Vinci's Mentor

In the 1499 Leonardo di Vinci is hired by Cesare Borgia as a military engineer. He begins to work on a steam canon that had originally been an idea of Archimedes 1500 years earlier. Leonardo tells Cesare the story of Archimedes and how he made many discoveries in mathematics and science. Archimedes visits Alexandria and falls in love with Princess Helena, and in spite of their age difference, they marry and return to Syracuse.
Soon Helena gives birth to their only child, a daughter they name Arsinoe. For nearly fifty years of peace, Syracuse is drawn into the war between Rome and Carthage. Archimedes must use all his vast knowledge to defend Syracuse and his very family. Cesare offers to purchase the chest of ideas from Leonardo but he declines the offer. Who knows which of Leonardo de Vinci's inventions were really the brainchild of Archimedes of Syracuse?