REGIOMONTANUS (Johann Müller).
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Tabulae directionum et profectionum. Tabella sinus recti. [Bound with:] ANGELUS, Johannes. Astrolabium planum in Tabulis ascendens. First editions of both works, each printed by Erhard Ratdolt, bound together in a contemporary vellum wrapper. Ratdolt was the greatest scientific printer of the incunable period, producing elegant and accurate texts of the most important astronomers and mathematicians of his time. The first text here is by Regiomontanus, an early practitioner of modern observational astronomy and an influence on Copernicus, who owned a copy of this book. It is a series of tables for calculating the positions of celestial bodies, a major advance in accuracy over earlier attempts such as the Alfonsine Tables. The development of European tables during the Late Middle Ages was the result of the assimilation of Arabic materials which circulated in al-Andalus. Among Regiomontanus's major sources for astronomy and mathematics were the zījes (astronomical handbooks) of al-Khwārizmī and al-Battānī, written around the ninth century. One of the most important sections of the present work is a set of trigonometric tables that includes the first modern tangent table, "tabula fecunda" (fruitful table). The origin of the tangent function is found in "shadow tables" that first appeared in early Arabic zījes. Regiomontanus's works played an important role in making Arabic scientific observations accessible in Europe; his commentary on al-Battānī's De motu stellarum was published
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