In the second half of the XVI th century and the first years of the XVII th century, the Diophantus Arithmetica was studied with great interest. The manuscripts of Arithmetica were discovered by A. M. Pazzi and were translated by R. Bombelli (1567, 1572), by G. Xylander (1575) and by S. Stevin (1585). Francois Viete, taking the Xylander text into account, wrote Zeteticorum Libri quinque in 1593 using his algebraic techniques. Viete's aim was only partially to translate by means of his logistica speciosa the Diophantus's quaestiones. As a matter of fact he proposes other interesting problems. Our goal is an analysis of some aspects of Viete's Zeteticorum libri quinque. In particular, we will examine some zetetici of the IV th book, which concern the indeterminate second degree problems, the relationships with some propositions which we find in the part Genesis Triangulorum of Notae Priores and the pre-eminent role of the zeteticum IV, 2. Furthermore, it is interesting to consider the geometrical interpretation of some zetetici by scholars of Viete (see i.e. J. L. Vaulezard (1630)). Moreover, we will analyze the indeterminate third degree problems by comparing them with some of Fermat's remarks. In this context we will propose an interesting mathematical philological result regarding the solution of the indeterminate equation x 3 +y 3 =a 3 + b 3 .