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lish them together with supplementary documents (especially the instructions and letters sent to the nuncios). Heretofore more has been done, in the way of publication, for the German nunciatures than for the others. H. Lammer published a series of nuncia- ture reports from Germany as early as 1860 in his "Monumenta Vaticana historiam ecclesiasticam sse- culi XVI illustrantia"; upon the opening of the Vati- can archives, the assistant archivist. Father Balan, brought out further material pertaining to the same subject in his work " Monumenta reformationis Luth- eranae" (Ratisbon, 1883-4). Father Dittrich treats the reports sent by the nuncio Giovanni Morone from the Diet of Ratisbon (1541) in the "Historisches Jahr- buch der Gorresgescllschaft", IV (1883), 395-472, 618-73, and, as a complement to this, edited the " Nuntiaturberichte Morones vom deutschen Konigs- hofe" for the years 1539-40 in "Quellen und Forsch- ungen aus dem Gebiete der Geschichte", I (Pa- derborn, 1892). In the mean time three historical in.stitutes at Rome (the Prussian, the Austrian, and that of the Gorresgescllschaft) divided among them the publication of all the nunciature reports sent from the German Empire for the period of the sixteenth and the first half of the seventeenth centuries. These societies have already published a large number of volumes: the first division, extending to 1559, is being published by the Prussian Institute; there have ap- peared so far vols. I-IV, VIII-X, and XII, comprising the nunciatures of Vergerio, Morone, Migganelli, Varallo, Poggio, Bertano, and Camiani, the legations of Farnese, Cervini, Campegio, Aleander, andSfon- drato (Gotha-Berlin, 1892 — ). The second division covering the period 1560-72, was undertaken by the Austrian Institute; up to the present vols. I and III, containing the reports of the nuncios Hosius and Bel- fino, have appeared (Vienna, 1897-1903). A third division, covering the years 1572-85, was also assigned to the Prussian institute which has already issued this series (Berlin, 1892 — ): vol. I, containing the struggle over Cologne; vol. II, containing the Diets of Ratisbon (1576) and of Augsburg (1582); vols. III-V, contain- ing the nunciature of Bartoloma?us of Portia. At this point begin the publications of the Institute of the Gorresgescllschaft, which has so far edited in four volumes the reports of the nuncios Bonomi (Bonho- mini), Santonio, Frangipani, Malaspina, and Sega, and the nunciature correspondence of Caspar Gropper (Paderborn, 1895 — ). The period a.ssigned to this institute covers 1585-1605. With 1606 begins an- other period (the fourth division), assigned to the Prussian Institute and covering the seventeenth cen- tury. Of this division two volumes have been pub- lished containing the reports of the nuncio Paletto (Berlin, 1895 — ). In this way the material concern- ing the German nunciatures for the period from the beginning of the sixteenth to the middle of the seven- teenth century, that is for the age of the Reformation, will be available at a not far distant date.

Professors Reinhard and Steffens of Fribourg under- took the editing of the nunciature reports for Switzer- land and began with Nuncio Bonomi (Bonhomini), of whose reports one volume has been issued (Solothurn, 1907); the introductory volume completed by Stef- fens after Reinhard's death has since appeared (Solo- thurn, 1910). As regard other countries the reports of the nuncio Andrea da Burgo, who was in Hungary during the years 1524-6, have been issued in the "Monumenta Vaticana Hungarian", second series, vol. I: "Relationes oratorura pontificiorum " (Buda- pest, 1884). For France the publication of the nunci- ature reports has been begun in the "Archives de I'his- toire religieuse de France"; of this Fraikin undertook the nunciatures during the pontificate of Clement VII and has issued so far vol. I (Paris, 1906), covering the 3'ears 1525-7, and including the nunciatures of Capino da Capo and Roberto Acciainolo, and the legation of

Cardinal Salviati. Ancel, meanwhile, began the nunci- atures during the reign of Paul IV, and edited (vol. I, pt. i) the dispatches of Sebastiano Gualterio and Ce- sare Brancato (1554-7). The general reports of Otta- vio Mirto Frangipani and Fabio della Lionessa, the nuncios in Flanders (1605 and 1634), have been pub- lished by Cauchie in the " Analectes pour servir k I'his- toire ecclfeiastique de la Belgique" (Louvain). The publication of the dispatches of the papal nunciature in Spain has been commenced by Hinojosa, "Los Despachos de la Diplomacia Pontificia en Espana", I (Madrid, 1896). So far no comprehensive publica- tion of this kind has been undertaken for Italy, al- though individual reports have been published. Tolo- mei has treated the Venetian nunciature during the pontificate of Clement VII, "La nunziatura di Vene- zia nel pontificato di Clemente VII" (Turin, 1892), and Curasi has edited the dispatches that have been preserved of the legation of Giacomo Gherardi, " Dis- pacci e letere di Giac. Gherardi, nunzio pontificio a Firenze e Milano, 11 settembre, 1487-10 ottobre, 1490", in "Studi e Testi", fasc. xxi (Rome, 1909). Besides these comprehensive publications various historians in treating the sixteenth and seventeenth centuries in their works have made use of and pub- lished individual dispatches of this kind.

See the introductiona to the different publications of the nun- ciature reporta and the bibliography of the article Nuncio.

J. P. KiRSCH.

Nunez (Nonios), Pedro, mathematician and as- tronomer, b. at Alcacer-do-Sol, 1492; d. at Coimbra, 1577. He studied ancient languages, philosophy, and medicine at Lisbon and mathematics at Salamanca. In 1519 he went as inspector-general of customs to Goa, India, returning to become in 1.529 royal cosmog- rapher. After lecturing for three years at Lisbon, a professorship of higher mathematics was established for him at the University of Coimbra, which he held from 1544 to 1562. His utterances on science plunged him into discussions with foreign savants, particularly the French mathematician, Oronce Fine. Having been tutor in the reigning family, he was enabled to spend his last years in ease.

To mathematics, astronomy, and navigation, Nunez made important contributions. He devised a method for obtaining the highest common divisor of two algebraic expressions. In his " De crepusculis " he announced a new and accurate solution of the astro- nomical problem of minimum twilight and suggested an instrument for the measurement of angles. The nonius, never in common use, consisted essentially of forty-six concentric circles divided into quadrants by two diameters at right angles to each other, each quad- rantal arc being divided into equal parts, the number of parts diminishing from ninety for the outermost arc to forty-five for the innermost. If one side of any angle is made to coincide with one of the radii, the vertex of the angle falling at the centre of the circles, the other side of the angle will fall on or near some point of division of one of the arcs. If then a is the number of parts intercepted and n is the whole num- ber of parts in the relevant arc, the magnitude of the angle will be 90X -ifdegrees. In "De arte navigandi" he announced his discovery and analysis of the curve of double curvature called the rumhus, better known as loxodrome, which is the line traced by a ship cutting the meridians at a constant angle. His collected works were published under the title "Petri Nonii Opera" (Basle, 1592). Among them are: "Tratado da sphera com a theorica do sol e da lua e o primeiro livro da gcographia de Claudio Ptolomeo Alexan- drino" (Lisbon, 1537); " De crepusculis liber unus" (Lisbon, 1542); "De arte atque ratione na\ngandi" (Coimbra, 1546); "De erratis Orontii Finei" (Coim- bra, 1546); "Annotatio in extrema verba capitis do chmatibis (Cologne, 1566); "Livro de algebra em