General Uranometric Directory (Directorium Generale Uranometricum)

Truly, if these studies are rightly judged to be the most beautiful, the most excellent, and the most useful because of the high knowledge of the object and the certainty of the method, one thing must be established for certain: Astronomy cannot be grasped by anyone who is void and ignorant of the science of Trigonometry. Without this science, one knocks on the doors of astronomy in vain. As we will show below, the whole field is composed of triangles, whether plane or spherical. Without trigonometry, to presume we can know anything certain about heavenly things is like wanting to cross the vast ocean without sails, oars, or even a ship.

Since all writers of astronomy have noticed this necessity, there has never been anyone who did not first instruct the reader in trigonometry, or at least assume the reader was already well-educated in it. This "Logic of Astronomy," so to speak, was always held in such high regard among excellent practitioners that they seem never to be able to praise its excellence and necessity enough. Among these, it is pleasing to hear the author of the Opus Palatinum The Opus Palatinum de Triangulis (1596) was a massive work on trigonometry begun by Georg Joachim Rheticus and completed by Valentinus Otho. It contained the most precise trigonometric tables of the era. speaking thus in his preface about trigonometry:

It should not seem at all strange that famous mathematicians, both ancient and modern, were so occupied in investigating and spreading the doctrine of triangles. They learned by use and experience that this alone opens the way to the noblest part of philosophy: the doctrine of the motions of heavenly bodies. Nor can anyone, unless imbued with knowledge of the doctrine of triangles, penetrate the inner secrets and mysteries of this divine art. But he who is ignorant of this doctrine, since he cannot perceive those geometric arrangements of angles, often gets stuck and cannot free himself, etc.

Since astronomy consists of two parts—the part dealing with the theories of the planets, and the part dealing with the Primum Mobile Literally "The First Mover." In the geocentric system, this is the outermost sphere of the heavens that rotates daily, carrying the stars and planets with it.—it is truly a wonder in how many ways trigonometry insinuates itself into these two branches. Like blood diffused through the whole body of a living creature, it seems to impart spirit and life to the science.

Through trigonometry, we discern the locations of the highest apsides The points in an orbit where a planet is farthest from or closest to the center of its motion. in all the Errants original: "Errantibus." This refers to the "wandering stars" or planets.. We find eccentricities and investigate the differences between equal and apparent motions, which are called Prostaphæreses Technical corrections added to or subtracted from the mean motion of a planet to find its true position. The word comes from Greek roots meaning "addition and subtraction.". We measure the distances of the planets from each other and from the Earth. We also determine the exact proportions of the three bodies: the Earth, the Sun, and the Moon.