Final answer:
The architect from the 14th century who wrote architectural books and had Leonardo Da Vinci as a student is Vitruvius. He influenced Renaissance architecture, and his teachings were adopted by notable architects such as Filippo Brunelleschi and Leon Battista Alberti.
Step-by-step explanation:
The very influential architect during the 14th century who was a Roman engineer and wrote many architectural books, and whose student was Leonardo Da Vinci, is Vitruvius.
Vitruvius was known for his treatise on architecture, De Architectura, which influenced the Renaissance architects like Filippo Brunelleschi and Leonardo da Vinci.
Filippo Brunelleschi, born in France, was known for designing the dome of the Cattedrale di Santa Maria del Fiore in Florence, a work that marked the beginning of the Renaissance in architecture. This innovation epitomized the Renaissance's revival of classicism and moved architecture away from the traditional Gothic style.
Furthermore, Leon Battista Alberti was an important Humanist theoretician and designer, whose works included several notable buildings in Florence.
Although Francesco di Giorgio Martini was another Renaissance figure involved in architecture, engineering, and military theory, Vitruvius is more closely associated with influencing Leonardo da Vinci through his classical texts on architecture.