Focus on Pallas and the Centaur and analyze the History.
The painting is usually dated to about 1482 or 1483 on stylistic grounds, soon after Botticelli's return from Rome, where he had been part of the project to paint the Sistine Chapel.  The features of the centaur are close to those of Moses in one of his frescos there.  The painting is often connected with the wedding in 1482 of Lorenzo di Pierfrancesco de' Medici to Semiramide Appiano, perhaps as a wedding gift from Lorenzo de' Medici (Lorenzo il Magnifico").Given the Medici device on Pallas' dress, it was presumably commissioned by the Medici family, as were many of Botticelli’s paintings, and has passed to the Uffizi with much of their collection.  In 1499 an inventory lists it in the same room as Botticelli's Primavera, in the town palace in Florence of Lorenzo di Pierfrancesco de' Medici and his brother Giovanni "Il Popolano".  They were the cousins of Lorenzo de' Medici, de facto ruler of Florence, and after their father's early death had been his wards.  In the later 16th century it hung in the Palazzo Vecchio.  In 1638 it was at the Medici Villa di Castello, as was the Primavera, then it is recorded in the Pitti Palace by about 1830, by which time Botticelli was unfashionable and regarded as mainly of historical interest.
The painting was then little-known until it was noticed in 1895 in one of the ante-rooms of the Palazzo Pitti by the English artist, living in Florence, William Blundell Spence.  The painting was in the Uffizi gallery from 1922.  It has perhaps been transferred from panel to canvas.In 2015, this painting among other Botticelli paintings was in an exhibition that opened in Berlin before moving to London. It showed Botticelli’s works and other artists’ versions of his paintings such as his The Birth of Venus.
Linda Proud has written an eponymous novel which centres on an account of Botticelli's creation of this painting, and its possible interpretations.
Sistine Chapel Berlin Uffizi Lorenzo de' Medici centaur Palazzo Vecchio Florence William Blundell Spence Lorenzo di Pierfrancesco de' Medici Primavera The Birth of Venus Moses Botticelli Villa di Castello transferred from panel to canvas Giovanni "Il Popolano" Linda Proud Medici Uffizi gallery Palazzo Pitti