General Uranometric Directory (Directorium Generale Uranometricum)

...should be explained. Therefore, the reader should not be at all surprised if on page 24, seeking brevity, I did not distinctly show how the fundamental table is constructed and how logarithms are extracted from it after the terms between which they are enclosed have been found, according to proposition 30. Instead, to make the matter easier to grasp, I simply stated that they are found through a proportional part. This is also repeated on page 52 for obtaining logarithms of the second kind Cavalieri distinguishes between "first kind" (Napierian) and "second kind" (Briggsian or common) logarithms., whose discovery I have clarified somewhat.

However, I did not expand much on this point either, since their discovery is explained most extensively in Henry Briggs's Logarithmic Arithmetic. Nevertheless, regarding the derivation of our table from the same Briggs's Chiliads Chiliads Groups of 1,000 numbers used as the standard unit for organizing logarithmic calculations., I have declared everything as was necessary. I have attempted to provide the reasoning for almost everything I have stated in both forms of Trigonometry This refers to plane and spherical trigonometry.. I did this to satisfy those who requested it. I also did it because I remember learning this way from my greatest teachers: the most excellent Galileo and the Very Reverend Father Benedetto Castelli. Castelli is a public professor of mathematics at the Roman Gymnasium The Roman Gymnasium refers to the Archiginnasio della Sapienza, the historic University of Rome. and a distinguished mathematician to Our Lord original: "S.D.N." (Sanctissimus Dominus Noster), a title for the Pope, referring here to Urban VIII..

I hope that both the learned and the unlearned will be satisfied in some measure. If it happens otherwise, I ask that you, kind reader, look favorably upon these efforts of mine. I also ask, again and again, that you excuse the many errors with which this work swarms. These mistakes did not arise from the negligence of the printer, who is skilled in the Latin language. Instead, they come from a most troublesome joint disease articulari morbo Cavalieri suffered severely from gout, which often left him bedridden or unable to write.. Because I was troubled by this, I was unable to devote the necessary care to the work.