An armillary sphere is a mechanical model of the universe. The metal bands within the spheres represented the circular orbits of the planets revolving around a central Earth or the sun, depending on the particular scientific theory depicted; pre or post Copernican. When devised, they were among the most complex mechanical devices of their time. Renaissance personages frequently had themselves portrayed in paintings standing next to an armillary sphere indicating their association with wisdom and knowledge.
Italian armillary sphere
This Western astrolabe was constructed by Bernard Sabeus in 1558. Sabeus was a craftsman who is known to have worked in Padua during the years 1552 - 1559. The artisan’s skill that had been previously used to decorate objects of warfare such as swords and suits of armor was now directed at embellishing the new objects of status and power, scientific instruments. However, in creating these new instruments, high levels of precision and mechanical ability were also required. An astrolabe was an instrument used to measure plane angles associated with navigational, terrestrial and astronomical sightings. This astrolabe (click image to enlarge) exhibits a high level of workmanship.
Italian astrolabe
Oronce Fine (1494-1555) was a French mathematician and astronomer who served as the Chair of Mathematics at the Collége Royal from 1531 until the time of his death. He revised the classical works of great masters such as Ptolemy, Aristotle and Sorobosco; compiled encyclopedic texts on mathematics; and developed astronomical measuring instruments.
This image above is from Book V of Le sphere demonstrating Fine’s “heart-shaped” projection of the spherical earth onto a flat surface.
Oronce Fine's Le Sphere du Monde
In the year 1794, André Marie Legrendre (1752 - 1833) published his Eléments de géométrie. In its preface, Legrendre says he tried to produce a geometry that will testify to the l’esprit of Euclid. The book became an immediate success in Europe and eventually went through 20 additions. The first American translation appeared in 1819, a work by John Farrar (1779 – 1853), Hollis Professor of Mathematics and Natural Philosophy (Science) at Harvard. This is the title page of Farrar’s translation of Legendre's Elements, the second edition (1825). Farrar went on to translate five French mathematical classics of this time. The style and format of these books transformed American mathematics teaching, and they became models for the new mathematical textbooks employed in the U.S military academies.
The image above (click to enlarge) is of pages 106 and 107 of Legendre’s Elements of Geometry and discuss the construction and properties of planes. Note the use of the symbol for line segment. This is one of the first applications of this symbol in an American textbook.
Legendre's Elements of Geometry
