TO GUIDOBALDO II,

FOURTH DUKE OF URBINO,

PREFECT OF THE BOUNTIFUL CITY Referring to Rome..

An ornate woodcut initial 'E' features a seated scholar within a classical architectural frame.

Among all parts of philosophy, just as none is more certain and better suited to the reason of truth than that which the Greeks call mathematice mathematics, so none can be more obscure and difficult to understand at this time. The blame for this fact lies both in the very nature and subtlety of the subject, and especially in the industry of our men, who are occupied in explaining other arts, and, to speak truly, in their excessive negligence regarding matters removed from the use of common life. If there is any other part of this that is unknown to our philosophers and demands the light of interpretation, it is certainly that which is called conics the study of conic sections. For although it was diligently treated by the ancients, their monuments have either not reached us, or have reached us in such a state that they are scarcely understood, on account of the many injuries of time and the greatest difficulties. And the first, as can be gathered, who treated this discussion of conics in four published books was Euclid. When Apollonius of Perga, a man endowed with exceptional talent and exquisite learning, had subsequently carried this forward to eight books, it is incredible how much he added to the dignity and progress of this science. The first four of these are still read, written in Greek, while the remaining ones are lost due to the calamity of former times. But because he had brought forward demonstrations in these that were for the most part brief and obscure, and had used many unknown lemmata preliminary propositions as if they were known, it came about that many, for the sake of removing such great difficulty, applied themselves to their exposition. Among these, Pappus of Alexandria and Eutocius of Ascalon easily surpassed the rest in the praise of erudition and the excellence of their talent. Nor is there any doubt that they could bring the greatest help to this study at this time, if their writings were either accessible to many or were in the hands of men sufficiently corrected. And this is the cause that primarily impelled me to translate them from the Greek for the sake of supporting this discipline, and to explain them with my own commentaries. For when I was interpreting several books of Archimedes and Ptolemy, which cannot be understood by any means without the doctrine of conics, I had to employ many of Apollonius's demonstrations, which are little understood without the Greek book, because the Latin one is most corrupt. I did this not unwillingly, and that by the will of mul-