De Crepusculis liber unus, nunc recens & natus et editus. Item Allacen Arabis vetustissimi, De causis Crepusculorum Libert unus, à Gerardo Cremonensi iam olim Latinitate donatus, nunc vero omnium primum in lucem editus by NUNES (or NUÑEZ), Pedro

Title within fine woodcut architectural border, many woodcuts in the text, & a full-page woodcut printer's device on verso of penultimate leaf. 74 unnumbered leaves (the final leaf a blank). Small 4to, attractive antique panelled calf (three inoffensive old stamps on title of the public library of Douai, one of which is a release stamp). [Lisbon: L. Rodriguez, 1542]. First edition of an extremely rare book which contains two notable texts on atmospheric refraction, both entitled De Crepusculis. The first is by Pedro Nuñez (or Nunes) (1502-78), who is considered to be the greatest of the Portuguese mathematicians. He served as chief royal cosmographer and professor of mathematics at the University of Coimbra. His writings reveal him to have been a first-rate geographer, physicist, cosmologist, geometer, and algebraist. He also made important contributions to navigation. Nuñez's text, on atmospheric refraction, twilight, and scientific instruments used to make observations, belongs to his most significant works and occupies the first 65 leaves. "Nuñez made important contributions in the design of instruments. In astronomical observations the impossibility of precisely measuring small portions of an arc was an impediment, and to overcome this difficulty, he conceived the idea of the nonius. In its original form this instrument, consisting of forty-four concentric auxiliary circles, was attached to an astrolabe for measuring fractions of a degree...Each circle had one division less than the one outside it and one division more than the one inside, making it possible to take a reading from the circle that gave the most accurate approximation. This instrument has not been modified during the four centuries since it was devised."-D.S.B., X, pp. 160-61. It later developed into the vernier. The balance of the book prints De Crepusculis by Abhomadi Malfegeyr (or Abu 'Abd Allah Muhammad ibn Mu'adh), translated from Arabic into Latin by Gerard of Cremona. This text was long thought to have been by Alhazen, but A.I. Sabra (see his "The Authorship of the Liber de crepusculis" in ISIS, Vol. 58, No. 1, Spring 1967, pp. 77-85) has made a convincing case that the text was actually written by the Andalusian mathematician Ibn Mu'adh (second half of the 11th century). Ibn Mu'adh's De Crepusculis contains an estimation of the angle of depression of the sun at the beginning of the morning twilight and at the end of the evening twilight. It is an attempt to calculate on the basis of this and other data the height of the atmospheric moisture responsible for the refraction of the sun's rays. Fine and crisp copy. ❧ Palau 196748. Picatoste y Rodriguez 552. Stillwell 781 & 863. Nunes: Kiely, Surveying Instruments, p. 169.