Note 1348 — Chapter XVII

This general mode of expression might lead us to suppose, that Record was acquainted with negative, as well as positive roots, the fictæ radices of Cardan. That a quadratic equation of a certain form has two positive roots, had long been known. In a very modern book, it is said that Mohammed ben Musa, an Arabian of the reign of Almamon, whose algebra was translated by the late Dr. Rosen in 1831, observes that there are two roots in the form ax2 + b = cx, but that this cannot be in the other three cases. Libri, Hist. des Sciences Mathématiques en Italie, vol. ii. (1838). Leonard of Pisa had some notion of this, but did not state it, according to M. Libri, so generally as Ben Musa. Upon reference to Colebrook’s Indian Algebra, it will appear that the existence of two positive roots in some cases, though the conditions of the problem will often be found to exclude the application of one of them, is clearly laid down by the Hindoo algebraists. But one of them says, People do not approve a negative absolute number.]