Take first the Addition-Formula of the Tangent :

Assume that 1 – tanx tanO is not zero for all value of x II.

The problem of describing a circle to touch three circles, including the nine special cases when one or more of the radii of the given circles are zero or infinite, was solved by Apollonius of Perga in a work which was lost, but of which Pappus has given some account in his Mathematical Collections. Towards the end of the l6th century the problem was again taken up and solved by F. Vieta, and since that time it has formed the subject of investigations by many mathematicians, from many different points of view.

The gigantic task which Mr Cantor has undertaken in writing a history of mathematics down to the year 1759 is approaching its accomplishment, the first two of the three parts forming the third and concluding volume being now published. How great is the debt of gratitude that the mathematical public owe to him for the erudition and thoroughness he has brought to bear on the work, only those can guess who have attempted to follow out some line of historical investigation. His history is totally different from a catalogue of authors and their works; it enables us to trace clearly the lines of development of mathematical knowledge and shows with wonderful skill not only the contributions made by the creators of the science but the conditions and materials that made these possible. The fact that the greatest mathematicians recognise that they obtained their position because “they stood on the shoulders of great men” does not in the least detract from their merits but is an abiding augury for future developments.