The sign of X, which we indicate in multiplication, was employed by the English mathematician Guilherme Oughtred in the book Clavis Matematicae, published in 1631. That same year, Harriot, to also indicate the product to be made, placed a point between the factors.
By 1637 Descartes was already limited to writing the juxtaposed factors, thus abbreviating any product. In Leibniz's work there is the sign to indicate multiplication. That same symbol, placed in reverse, indicated the division. The dot was introduced as a symbol for multiplication by Leibniz.
The a / b and , indicating the division of a by b, are attributed to the Arabs. The ratio between two quantities is indicated by the sign : , which appeared in 1657 in a work by Oughtred. The sign , according to Rouse Ball, resulted from a combination of two existing signals - and :