Page:A History of Mathematics (1893).djvu/161

 and, later on, another with the radius = 1,000,000,000,000,000, and proceeding from 10" to 10". He began also the construction of tables of tangents and secants, to be carried to the same degree of accuracy; but he died before finishing them. For twelve years he had had in continual employment several calculators. The work was completed by his pupil, Valentine Otho; in 1596. This was indeed a gigantic work,—a monument of German diligence and indefatigable perseverance. The tables were republished in 1613 by Pitiscus, who spared no pains to free them of errors. Astronomical tables of so great a degree of accuracy had never been dreamed of by the Greeks, Hindoos, or Arabs. That Rhæticus was not a ready calculator only, is indicated by his views on trignometricaltrigonometrical [sic] lines. Up to his time, the trigonometric functions had been considered always with relation to the arc; he was the first to construct the right triangle and to make them depend directly upon its angles. It was from the right triangle that Rhæticus this idea of calculating the hypotenuse; i.e. he was the first to plan a table of secants. Good work in trigonometry was done also by Vieta and Romanus.

We shall now leave the subject of trigonometry to witness the progress in the solution of algebraical equations. To do so, we must quit Germany for Italy. The first comprehensive algebra printed was that of Lucas Pacioli. He closes his book by saying that the solution of the equations $$\scriptstyle{x^3+mx=n,~x^3+n=mx}$$ is as impossible at the present state of science as the quadrature of the circle. This remark doubtless stimulated thought. The first step in the algebraic solution of cubics was taken by Scipio Ferro (died 1526), a professor of mathematics at Bologna, who solved the equation $$\scriptstyle{x^3+mx=n}$$. Nothing more is known of his discovery than that he imparted it to his pupil, Floridas, in 1505. It was the practice in those days and for two centuries afterwards to keep discoveries