War of the Quadruple Alliance the Triple Alliance, which became the Quadruple Alliance for which the war is named. Meanwhile, in July 1718 the Spanish, this time with 30,000 men again led by the Marquess of Lede, had also invaded Sicily, which had been awarded to the Duke of Savoy. They took Palermo on 7 July and then divided their army in two. De Lede followed the coast to besiege Messina between 18 July and 30 September, while the Duke of Montemar conquered the rest of the island. The French, Austrians, and British now demanded Spanish withdrawal from Sicily and Sardinia. The attitude of Victor
Quadruple product Quadruple product In mathematics, the quadruple product is a product of four vectors in three-dimensional Euclidean space. The name "quadruple product" is used for two different products, the scalar-valued scalar quadruple product and the vector-valued vector quadruple product or vector product of four vectors . The scalar quadruple product is defined as the dot product of two cross products: where a, b, c, d are vectors in three-dimensional Euclidean space. It can be evaluated using the identity: or using the determinant: The vector quadruple product is defined as the cross product of two cross products: where a, b, c, d