General Uranometric Directory (Directorium Generale Uranometricum)

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(I teach the method on page 83.) I did this so that I could satisfy their needs more quickly. It was faster than if I had taken up the labor of building a similar table from the basic rules of the laws from scratch, as I had first intended.

When, however, I was shown shortly after the Arithmetica Logarithmica of the most learned Henry Briggs Henry Briggs was an English mathematician who worked with Napier to develop common logarithms, which use base 10. in the second edition printed by Adrian Vlacq Adrian Vlacq was a Dutch bookseller and mathematician who calculated and published expanded logarithmic tables that became standard for centuries., I found in it a similar table. Vlacq had derived it from the Chiliads Chiliads Groups of 1,000 numbers, the standard unit Briggs used to organize his logarithmic calculations. of Briggs. I realized then that my own work regarding the Canon of Napier was unnecessary.

Because Vlacq explained nothing there regarding Spherical Trigonometry Spherical Trigonometry The study of triangles on the surface of a sphere, which is vital for calculating planetary positions and navigation., and although it is easy for experienced men to convert trigonometric rules into logarithmic ones, they still needed tables for them. They also needed rules adapted to such tables. I believed these rules should be explained from the true foundations of all trigonometry, both the simple kind and the kind adapted to logarithms. I wanted to explain them using the easiest method possible.

Therefore, I wanted to comply with their wishes. I also believed that I could add some innovations of significant utility to the tables of Adrian Vlacq. Finally, I felt that my own pen, though modest, might produce something welcome on this occasion. For example, I have included the measure of a Spherical Triangle Cavalieri refers here to his discovery of the formula for the area of a spherical triangle based on its spherical excess.. To my knowledge, no one has taught this until now. Many other things will become clear as the work progresses. For these reasons, I took up these labors. I began both types of trigonometry from their foundations. Whether I have satisfied those who follow me is for others to judge.

The reader will find many new demonstrations here. If they are not new, they are at least clarified where they seemed obscure. I wanted to remove any obstacles for students as much as I could. I chose to provide rules applied mostly to Astronomical examples. I did this so that students would not hesitate. I also wanted those studying this doctrine to see the very rich use of logarithmic trigonometry in Astronomy.

Finally, almost everything said by Napier is confirmed here by my own reasons. I am also working on those things regarding tables that I explained in Chapter 6 of the first part. I have tried to reduce all Astronomical calculations to simple common addition. I have only lightly touched on the method for building tables of Sines, Tangents, or Secants, since almost every writer on trigonometry already teaches this. I also dealt lightly with the discovery of the first kind of logarithms, since Napier and Ursinus Benjamin Ursinus was a German mathematician and student of Johannes Kepler who published early logarithmic tables in Frankfurt. wrote of them most abundantly...