Author(s):
Frank J. Swetz (The Pennsylvania State University)
Vincenzo Viviani (1622–1703) was an Italian mathematician who studied under Galileo—with whom he remained a close associate. One of his main interests was speculative geometry, particularly, the properties of the cycloid. In 1692 he published Formazione e misvra di tutti i cieli : con la struttura, e quadratura esatta dell' intero, e delle parti di un nuovo cielo ammirabile, e di uno degli antichi delle volte regolari degli architetti ; curiosa esercitazione matematica di VV (Formation and measurement of all the skies: with the exact structure and squaring of the whole and of the parts of a new admirable sky and of one of the ancient regular vaults of the architects / curious mathematical exercise of VV [Vincenzo Vivani] last pupil of Galileo).
![Title page of Viviani's 1692 Formazione, e misura di tutti i cieli.](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/Gallica/ImageProvider%20%2822%29.jpeg)
A sample page from this text:
![Dedication page for Viviani's 1692 Formazione, e misura di tutti i cieli.](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/Gallica/ImageProvider%20%2823%29.jpeg)
Vivani also kept handwritten notes of Galileo’s theories and discussions. They were later bound into a series that he named after his preferred role: Discipoli di Galileo. Here we see images of book 98 on “Pure Mathematics.”
![Cover page from one of Viviani's notes on Galileo's theories.](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/Museo-Galileo/ImageProvider%20%284%29.jpeg)
A glimpse of the notes within:
![Page from one of Viviani's volumes of notes on Galileo's theories.](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/Museo-Galileo/ImageProvider%20%285%29.jpeg)
![Diagram page from one of Viviani's volumes of notes on Galileo's theories.](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/Museo-Galileo/ImageProvider%20%286%29.jpeg)
![Page from one of Viviani's volumes of notes on Galileo's theories.](/sites/default/files/images/upload_library/46/Swetz_2012_Math_Treasures/Museo-Galileo/ImageProvider%20%287%29.jpeg)
The Bibliothèque nationale de France (BnF) offers a complete digitization of Formazione, e misura di tutti i cieli via Gallica. Viviani’s manuscript notes are held by Museo Galileo.
Index to Mathematical Treasures
Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Vincenzo Viviani’s Formazione, e misura di tutti i cieli and Manuscript Notes," Convergence (February 2023)