General Uranometric Directory (Directorium Generale Uranometricum)

Of the chapters contained in this volume.

FIRST PART.

What the Arc and Chord were among Hipparchus, Ptolemy, and the Ancients; why they were used for astronomical calculations, and also how they used them. Chapter 1, page 1. The chord was the primary trigonometric function used by ancient Greeks, representing the length of a line segment connecting two points on a circle. It was later replaced by the sine function.

How later scholars reduced the astronomical art of calculating into a better and easier form than the ancient one, regarding that which pertains to the construction of tables. Chapter 2, page 5.

On the resolution of triangles of both kinds This refers to both plane and spherical trigonometry. obtained with the help of the said tables; a matter most difficult among the Ancients, yet easier among later scholars. Chapter 3, page 10.

On the wonderful invention of logarithms by John Napier, by which, among other things, modern scholars learned to solve the Rule of Three very easily. Chapter 4, page 15. Rule of Three A mathematical method to find a fourth value from three known values based on proportion.

On another, more excellent kind of logarithms than the aforementioned, which the same Napier noticed; Henry Briggs arranged these into tables of Chiliads. By the construction of this kind, calculations are rendered easier than the previous ones by the Canon of Triangles. Chapter 5, page 27. Chiliads Groups of one thousand numbers used as the standard unit for organizing logarithmic tables. The "Canon of Triangles" refers to the standard table of trigonometric functions.

On the arrangement of the two tables, of which we shall call the first the Logarithmic Trigonometric Table, and the second the Logarithmic Arithmetic Table, and on their auxiliary parts. Chapter 6, page 34.

On certain wonderful properties of the Logarithmic Trigonometric Table, some of which also apply to the tables of Napier, Ursus, and Kepler, as well as to our Logarithmic Arithmetic table. Chapter 7, page 43. Ursus refers to Benjamin Ursinus, a German mathematician and astronomer who published some of the earliest logarithmic tables.

On the Use of the aforementioned tables in general. Chapter 8, page 54.