General Uranometric Directory (Directorium Generale Uranometricum)

...it exerts its strength, examines celestial things, and rises up with the Prince of Philosophers Referring to Aristotle, whom medieval and Renaissance scholars called the "Prince of Philosophers." to demonstrate the existence, infinity, immensity, and eternity of the First Motor and Governor of all things. If I were to unfold its praises here, by Hercules, there would never be an end to my speaking.

From this it happened that, since I perceived Trigonometry to be so necessary for grasping astronomy and the other fields mentioned, although my mind was burning to cultivate other mathematical branches, and I greatly desired to reveal their most excellent use in Natural Philosophy to some extent according to my meager strength (to execute which, the most loving of these studies and most learned man in every kind of discipline, the Illustrious and Reverend Lord Giovanni Ciampoli, Secretary to our Holy Lord Giovanni Ciampoli was a close friend of Galileo and a high-ranking official under Pope Urban VIII., spurred me on more than once through letters). It happened, I say, that having found the opportunity to serve this Nourishing and Renowned University of Bologna in my role, I set my mind to elaborating, adorning, and, as much as was in my power, making this part easier.

Why I have attempted to roll this stone again myself, which has been rolled so many times after so many distinguished writers on Trigonometry, though this is partly revealed in Chapter 6 of the First Part, I will nevertheless explain briefly here as well. When I was occupied with other studies and fulfilling my public office of explaining Mathematics, I was thinking of nothing less than constructing this work. However, when I applied my mind to extending the astronomical studies of the past, so that I might follow in the footsteps of my predecessors who had cultivated Astronomy for that reason: namely, among others, the most excellent men Domenico Maria Novara of Ferrara, the teacher of Copernicus; Father Master Ignazio Danti of the Order of Preachers; and also Magini Giovanni Antonio Magini, a famous astronomer who competed with Galileo for the chair of mathematics at Bologna..

When I noticed that Napier’s logarithmos Logarithms were a very recent invention at this time, published by John Napier in 1614 to simplify complex astronomical calculations. invention was quite rightly highly valued here by students of this divine faculty; yet it seemed to me that they complained most about these things. Specifically, they complained either because of the extreme and unexplained brevity of Napier’s rule for logarithms, which forced many to go back over the demonstration of his statements, or because of the calculations performed through those same logarithms, due to the addition and subtraction of them frequently performed afterward, which caused a great deal of confusion. Therefore, while I was considering how I might help with these matters, a most efficient method occurred to me: namely, of connecting Napier's logarithms into logarithms that have the unit with zeros for the logarithm of the Total Sine The "Total Sine" refers to the radius of the circle used in trigonometric tables, often set to a large power of 10 to avoid working with decimals.. For with a Table constructed in this way, those previously mentioned additions and subtractions could be more easily
avoided