which I have found it in the manuscripts. Should the favour of time bring to light one day a complete copy, I shall be happy if circumstances will allow me at once to edit the hitherto missing parts in text and translation.
The basis of my edition consists of two manuscripts of the seventeenth and one of the nineteenth century, all full of faults, and—what is worse!—agreeing with each other almost in every particular. In fact, all three copies represent one and the same original. Fortunately a chronological work offers this advantage, that in many cases mathematical examination enables the editor to correct the blunders of the tradition, e.g. in the numerous tables.
My notes are in the first place intended to give the calculations on which the tables rest. Besides, they contain contributions to the explications of certain difficult passages, short information on points of literary history, and, lastly, a few remarks on the text and corrections.
For all other introductory questions I refer the reader to the German preface to my edition of the text.
In offering my translation to the English reader, I desire to thank my friend, the Rev. Robert Gwynne, Vicar of St. Mary's, Soho, London, who not only corrected the whole manuscript, but also read the proof-sheets of the entire book.
EDWARD SACHAU.
Berlin, 24th May, 1879.
