General Uranometric Directory (Directorium Generale Uranometricum)

circumference of a circle original: "circuli circumferentia" into as many parts as they wished, and likewise the diameter into as many as they wished. By taking a portion of that circumference and joining its endpoints with a straight line, they wanted to know how many parts of the diameter would correspond to that joining line. They called this line the chord A straight line segment whose endpoints both lie on a circular arc. of that chosen circumference, and called the circumference itself the arc of that same chord. Conversely, if a chord consisted of a certain number of parts of the diameter, they wanted to know how many parts of the entire circumference that arc would be. In this way, if a chord or the side of a triangle was known, the arc beneath it original: "subtensus arcus" could be known, and subsequently the opposite angle. On the other hand, if the angle was known, the arc became manifest, and consequently its chord, which is the side of the proposed plane triangle. In this manner, they gathered angles from sides and sides from angles. They proceeded similarly in the study of spheres.

The Ancients divided the circumference of a circle into 360 parts, which they called degrees original: "gradus". They divided a degree into 60 minutes, a minute into 60 seconds, and so on. They chose this number 360 especially because of the many aliquot parts Numbers that divide into a larger number exactly, without leaving a remainder. For example, 360 can be divided by 2, 3, 4, 5, 6, 8, 9, 10, 12, and many others. it possesses. They divided the diameter into 120 units, which they called parts, and likewise divided a part into 60 minutes, a minute into 60 seconds, and so forth. They constructed a table, as can be seen in the first book of the Almagest The most influential mathematical and astronomical treatise of antiquity, written by Claudius Ptolemy in the 2nd century. by Ptolemy. In this table, it is shown for any known arc how many parts of the diameter the chord corresponds to, and for any known chord, how many degrees the arc corresponds to. They completed problems so that, with the help of these tables, the remaining unknown parts could be gathered from certain known ones, whether angles or sides, in both plane and spherical triangles.

Thus, Hipparchus A Greek astronomer often considered the founder of trigonometry. wrote twelve books on this subject. Later, Menelaus Cavalieri uses the name "Mileus." Menelaus of Alexandria was a Greek mathematician known for his work on spherical geometry. did the same, and finally Ptolemy illustrated this matter with wondrous skill and brevity beyond the others. However, anyone who attempts to solve even one problem by their rules will easily understand how difficult their practical methods are. This difficulty is clearer than light to those who are accustomed to spend time in the study of Ptolemy’s Great Composition original: "Magnae Ptolemaei Compositionis," another name for the Almagest.. Concerning the efforts they held toward these things, it will be enough to have tasted them briefly for now.

A horizontal ornamental divider consisting of a row of repeating decorative fleurons with floral and scroll-like motifs.