Otherwise he resorts to power series. Hence one solution is The other is determined similarly. Newton discovered a method for finding roots of equations which is still used today. Among the curves worked on by Newton were the Cartesian ovals, the Cissoid, the Conchoid, the Cycloid, the Epicycloid, the Epitrochoid, the Hypocycloid, the Hypotrochoid, the Kappa curve and the Serpentine. Newton gave a classification of cubic curves.
Newton gives methods of finding extrema problems normals, tangents and areas.
He goes to some effort to assuage the great bulk of mathematicians still wedded to Greek geometry and thought. By studying the finest work of the time Newton was led to important new syntheses. To develop them fully he acquired a mastery of analytical techniques unsurpassed in his time. Thus he was able to derive simple and general methods compared with the laborious work of his contemporaries. Newton thought analytically in the modern sense .