KoG • 15–2011 M. Triplat Horvat, M. Lapaine, D. Tuti´ c: Application of Boˇ skovi´ c’s Geometric Adjustment Method.... Professional paper Accepted 30. 11. 2011. MARTINA TRIPLAT HORVAT MILJENKO LAPAINE DRA ˇ ZEN TUTI ´ C Application of Boˇ skovi´ c’s Geometric Adjustment Method on Five Meridian Degrees On the Occasion of 300th Anniversary of the Birth of Rud - er Josip Boˇ skovi ´ c Application of Boˇ skovi´ c’s Geometric Adjustment Method on Five Meridian Degrees ABSTRACT In this paper, the first method of adjustment, proposed by Josip Rud - er Boˇ skovi´ c, is described in detail, on the exam- ple on five meridian degrees. Boˇ skovi´ c sets three condi- tions on the data of the lengths of the meridian degrees to calculate corrections that would fix all degrees in order to get a better estimate of true values. The conditions that have to be satisfied are explained by geometric method which Boˇ skovi´ c described in all his studies. For the pur- pose of this paper, in the process of computing these five meridian degrees, data from Boˇ skovi´ c original book have been used. Geometric solution, described by Boˇ skovi´ c himself, is not easy to understand at first, as this is noted by other au- thors who have studied Boˇ skovi´ c’s method as well. Hence, geometric description of the Boˇ skovi´ c’s method is shown in analytical form as well. Key words: Josip Rud - er Boˇ skovi´ c, geometric adjustment method MSC 2010: 01A50, 86A30, 62-03, 51-03, 62A01, 62P99, 62J05, 41A10 Primjena Boˇ skovi´ ceve geometrijske metode izjednaˇ cenja na pet meridijanskih stupnjeva SA ˇ ZETAK U ovom radu detaljno je prikazana prva metoda izjedna- ˇ cenja, koju je osmislio Josip Rud - er Boˇ skovi´ c, na primjeru pet stupnjeva meridijana. Boˇ skovi´ c je izraˇ cunao popravke kojima bi popravio duljine meridijanskih stupnjeva i na taj naˇ cin dobio ˇ sto bolje procjene njihovih pravih vrije- dnosti. Postavljaju´ ci tri uvjeta tom prilikom formirao je svoju metodu izjednaˇ cenja koju je primijenio na podatke o duljinama meridijanskih stupnjeva. Uvjeti koji moraju biti zadovoljeni objaˇ snjeni su geometrijskom metodom kakvu Boˇ skovi´ c opisuje u svim svojim djelima. U postupku raˇ cunanja, koja su provedena u ovom radu na pet me- ridijanskih stupnjeva, koriˇ steni su podaci iz Boˇ skovi´ cevih originalnih djela. Geometrijsko rjeˇ senje kako ga je Boˇ skovi´ c opisao nije odmah lako razumljivo, ˇ sto su uoˇ cili i drugi autori koji su prouˇ cavali Boˇ skovi´ cevu metodu. Stoga ´ ce geometrij- ski opisana Boˇ skovi´ ceva metoda biti takod - er prikazana i u analitiˇ ckom obliku. Kljuˇ cne rijeˇ ci: Josip Rud - er Boˇ skovi´ c, geometrijska metoda izjednaˇ cenja 1 Introduction Rud - er Josip Boˇ skovi´ c (Dubrovnik, 18th May 1711 - Milan, 13th February 1787) began to publish theses on Earth’s shape and size as a young scientist. These issues were a major scientific problem of the 18th century. In 1739, when he was only 28, he published two dissertations: De veterum argumentis pro telluris sphaericitate (On the ar- guments of the ancients for the sphericity of the Earth) and Dissertatio de telluris figura (A dissertation on the shape of the Earth). During the 18th century scientists were having a great dis- cussion about the question whether the Earth was oblate or oblong (prolate) at the poles. In the late 17th century, New- ton proved that the Earth should be flattened at the poles because of its rotation. Domenico Cassini assumed the op- posite, that Earth had the shape of an egg so, at the end of 67